Wiley: Statistics in Medicine: Table of ContentsTable of Contents for Statistics in Medicine. List of articles from both the latest and EarlyView issues.
https://onlinelibrary.wiley.com/journal/10970258?af=R
Wiley: Statistics in Medicine: Table of ContentsWileyen-USStatistics in MedicineStatistics in Medicinehttps://onlinelibrary.wiley.com/pb-assets/journal-banners/10970258.jpg
https://onlinelibrary.wiley.com/journal/10970258?af=R
Dynamic prediction of disease processes based on recurrent history and functional principal component analysis of longitudinal biomarkers: Application for ovarian epithelial cancerOvarian epithelial cancer is a gynecological tumor with a high risk of recurrence and death. In the clinical diagnosis of ovarian epithelial cancer, CA125 has become an important indicator of disease burden. To account for patient recurrence and death, a proper method is needed to integrate information from biomarkers and recurrence simultaneously. In the past 10 years, many methods have been proposed for joint modeling of longitudinal biomarkers and survival data, but few of them are applicable to longitudinal data and disease processes, including recurrence and death. In this article, we proposed a new joint frailty model based on functional principal component analysis for dynamic prediction of survival probabilities on the total time scale, which took recurrent history and longitudinal data into account simultaneously. The estimation of the joint frailty model is achieved by maximizing the penalized log‐likelihood function. The simulation results demonstrated the advantages of our method in both discrimination and accuracy under different scenarios. To indicate the method's practicality, it is applied to an actual dataset of patients with ovarian epithelial cancer to predict survival dynamically using longitudinal data of biomarker CA125 and recurrent history data.
Yizhou Hong,
Liwen Su,
Siyi Song,
Fangrong Yan
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8885?af=R
<p>Ovarian epithelial cancer is a gynecological tumor with a high risk of recurrence and death. In the clinical diagnosis of ovarian epithelial cancer, CA125 has become an important indicator of disease burden. To account for patient recurrence and death, a proper method is needed to integrate information from biomarkers and recurrence simultaneously. In the past 10 years, many methods have been proposed for joint modeling of longitudinal biomarkers and survival data, but few of them are applicable to longitudinal data and disease processes, including recurrence and death. In this article, we proposed a new joint frailty model based on functional principal component analysis for dynamic prediction of survival probabilities on the total time scale, which took recurrent history and longitudinal data into account simultaneously. The estimation of the joint frailty model is achieved by maximizing the penalized log‐likelihood function. The simulation results demonstrated the advantages of our method in both discrimination and accuracy under different scenarios. To indicate the method's practicality, it is applied to an actual dataset of patients with ovarian epithelial cancer to predict survival dynamically using longitudinal data of biomarker CA125 and recurrent history data.</p>
Statistics in Medicine, EarlyView. Dynamic prediction of disease processes based on recurrent history and functional principal component analysis of longitudinal biomarkers: Application for ovarian epithelial cancerdoi:10.1002/sim.8885Statistics in Medicine2021-01-22T05:14:40-08:00Statistics in Medicine10.1002/sim.8885https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8885?af=RRESEARCH ARTICLELink predictions for incomplete network data with outcome misclassification
Abstract
Link prediction is a fundamental problem in network analysis. In a complex network, links can be unreported and/or under detection limits due to heterogeneous sources of noise and technical challenges during data collection. The incomplete network data can lead to an inaccurate inference of network based data analysis. We propose a parametric link prediction model and consider latent links as misclassified binary outcomes. We develop new algorithms to optimize model parameters and yield robust predictions of unobserved links. Theoretical properties of the predictive model are also discussed. We apply the new method to a partially observed social network data and incomplete brain network data. The results demonstrate that our method outperforms the existing latent‐link prediction methods.
Qiong Wu,
Zhen Zhang,
Tianzhou Ma,
James Waltz,
Donald Milton,
Shuo Chen
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8856?af=R
<h2>Abstract</h2>
<p>Link prediction is a fundamental problem in network analysis. In a complex network, links can be unreported and/or under detection limits due to heterogeneous sources of noise and technical challenges during data collection. The incomplete network data can lead to an inaccurate inference of network based data analysis. We propose a parametric link prediction model and consider latent links as misclassified binary outcomes. We develop new algorithms to optimize model parameters and yield robust predictions of unobserved links. Theoretical properties of the predictive model are also discussed. We apply the new method to a partially observed social network data and incomplete brain network data. The results demonstrate that our method outperforms the existing latent‐link prediction methods.</p>
Statistics in Medicine, EarlyView. Link predictions for incomplete network data with outcome misclassificationdoi:10.1002/sim.8856Statistics in Medicine2021-01-22T04:40:21-08:00Statistics in Medicine10.1002/sim.8856https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8856?af=RRESEARCH ARTICLEConditional adaptive Bayesian spectral analysis of replicated multivariate time seriesThis article introduces a flexible nonparametric approach for analyzing the association between covariates and power spectra of multivariate time series observed across multiple subjects, which we refer to as multivariate conditional adaptive Bayesian power spectrum analysis (MultiCABS). The proposed procedure adaptively collects time series with similar covariate values into an unknown number of groups and nonparametrically estimates group‐specific power spectra through penalized splines. A fully Bayesian framework is developed in which the number of groups and the covariate partition defining the groups are random and fit using Markov chain Monte Carlo techniques. MultiCABS offers accurate estimation and inference on power spectra of multivariate time series with both smooth and abrupt dynamics across covariate by averaging over the distribution of covariate partitions. Performance of the proposed method compared with existing methods is evaluated in simulation studies. The proposed methodology is used to analyze the association between fear of falling and power spectra of center‐of‐pressure trajectories of postural control while standing in people with Parkinson's disease.
Zeda Li,
Scott A. Bruce,
Clinton J. Wutzke,
Yang Long
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8884?af=R
<p>This article introduces a flexible nonparametric approach for analyzing the association between covariates and power spectra of multivariate time series observed across multiple subjects, which we refer to as multivariate conditional adaptive Bayesian power spectrum analysis (MultiCABS). The proposed procedure adaptively collects time series with similar covariate values into an unknown number of groups and nonparametrically estimates group‐specific power spectra through penalized splines. A fully Bayesian framework is developed in which the number of groups and the covariate partition defining the groups are random and fit using Markov chain Monte Carlo techniques. MultiCABS offers accurate estimation and inference on power spectra of multivariate time series with both smooth and abrupt dynamics across covariate by averaging over the distribution of covariate partitions. Performance of the proposed method compared with existing methods is evaluated in simulation studies. The proposed methodology is used to analyze the association between fear of falling and power spectra of center‐of‐pressure trajectories of postural control while standing in people with Parkinson's disease.</p>
Statistics in Medicine, EarlyView. Conditional adaptive Bayesian spectral analysis of replicated multivariate time seriesdoi:10.1002/sim.8884Statistics in Medicine2021-01-20T08:31:15-08:00Statistics in Medicine10.1002/sim.8884https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8884?af=RRESEARCH ARTICLESpatial modeling of individual‐level infectious disease transmission: Tuberculosis data in Manitoba, Canada
Geographically dependent individual level models (GD‐ILMs) are a class of statistical models that can be used to study the spread of infectious disease through a population in discrete‐time in which covariates can be measured both at individual and area levels. The typical ILMs to illustrate spatial data are based on the distance between susceptible and infectious individuals. A key feature of GD‐ILMs is that they take into account the spatial location of the individuals in addition to the distance between susceptible and infectious individuals. As a motivation of this article, we consider tuberculosis (TB) data which is an infectious disease which can be transmitted through individuals. It is also known that certain areas/demographics/communities have higher prevalent of TB (see Section 4 for more details). It is also of interest of policy makers to identify those areas with higher infectivity rate of TB for possible preventions. Therefore, we need to analyze this data properly to address those concerns. In this article, the expectation conditional maximization algorithm is proposed for estimating the parameters of GD‐ILMs to be able to predict the areas with the highest average infectivity rates of TB. We also evaluate the performance of our proposed approach through some simulations. Our simulation results indicate that the proposed method provides reliable estimates of parameters which confirms accuracy of the infectivity rates.
Leila Amiri,
Mahmoud Torabi,
Rob Deardon,
Michael Pickles
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8863?af=R
<p>Geographically dependent individual level models (GD‐ILMs) are a class of statistical models that can be used to study the spread of infectious disease through a population in discrete‐time in which covariates can be measured both at individual and area levels. The typical ILMs to illustrate spatial data are based on the distance between susceptible and infectious individuals. A key feature of GD‐ILMs is that they take into account the spatial location of the individuals in addition to the distance between susceptible and infectious individuals. As a motivation of this article, we consider tuberculosis (TB) data which is an infectious disease which can be transmitted through individuals. It is also known that certain areas/demographics/communities have higher prevalent of TB (see Section 4 for more details). It is also of interest of policy makers to identify those areas with higher infectivity rate of TB for possible preventions. Therefore, we need to analyze this data properly to address those concerns. In this article, the expectation conditional maximization algorithm is proposed for estimating the parameters of GD‐ILMs to be able to predict the areas with the highest average infectivity rates of TB. We also evaluate the performance of our proposed approach through some simulations. Our simulation results indicate that the proposed method provides reliable estimates of parameters which confirms accuracy of the infectivity rates.</p>
Statistics in Medicine, EarlyView. Spatial modeling of individual‐level infectious disease transmission: Tuberculosis data in Manitoba, Canadadoi:10.1002/sim.8863Statistics in Medicine2021-01-20T01:58:53-08:00Statistics in Medicine10.1002/sim.8863https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8863?af=RRESEARCH ARTICLEMultiple imputation strategies for a bounded outcome variable in a competing risks
analysis
In patient follow‐up studies, events of interest may take place between periodic clinical assessments and so the exact time of onset is not observed. Such events are known as “bounded” or “interval‐censored.” Methods for handling such events can be categorized as either (i) applying multiple imputation (MI) strategies or (ii) taking a full likelihood‐based (LB) approach. We focused on MI strategies, rather than LB methods, because of their flexibility. We evaluated MI strategies for bounded event times in a competing risks analysis, examining the extent to which interval boundaries, features of the data distribution and substantive analysis model are accounted for in the imputation model. Candidate imputation models were predictive mean matching (PMM); log‐normal regression with postimputation back‐transformation; normal regression with and without restrictions on the imputed values and Delord and Genin's method based on sampling from the cumulative incidence function. We used a simulation study to compare MI methods and one LB method when data were missing at random and missing not at random, also varying the proportion of missing data, and then applied the methods to a hematopoietic stem cell transplantation dataset. We found that cumulative incidence and median event time estimation were sensitive to model misspecification. In a competing risks analysis, we found that it is more important to account for features of the data distribution than to restrict imputed values based on interval boundaries or to ensure compatibility with the substantive analysis by sampling from the cumulative incidence function. We recommend MI by type 1 PMM.
Elinor Curnow,
Rachael A. Hughes,
Kate Birnie,
Michael J. Crowther,
Margaret T. May,
Kate Tilling
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8879?af=R
<p>In patient follow‐up studies, events of interest may take place between periodic clinical assessments and so the exact time of onset is not observed. Such events are known as “bounded” or “interval‐censored.” Methods for handling such events can be categorized as either (i) applying multiple imputation (MI) strategies or (ii) taking a full likelihood‐based (LB) approach. We focused on MI strategies, rather than LB methods, because of their flexibility. We evaluated MI strategies for bounded event times in a competing risks analysis, examining the extent to which interval boundaries, features of the data distribution and substantive analysis model are accounted for in the imputation model. Candidate imputation models were predictive mean matching (PMM); log‐normal regression with postimputation back‐transformation; normal regression with and without restrictions on the imputed values and Delord and Genin's method based on sampling from the cumulative incidence function. We used a simulation study to compare MI methods and one LB method when data were missing at random and missing not at random, also varying the proportion of missing data, and then applied the methods to a hematopoietic stem cell transplantation dataset. We found that cumulative incidence and median event time estimation were sensitive to model misspecification. In a competing risks analysis, we found that it is more important to account for features of the data distribution than to restrict imputed values based on interval boundaries or to ensure compatibility with the substantive analysis by sampling from the cumulative incidence function. We recommend MI by type 1 PMM.</p>
Statistics in Medicine, EarlyView. Multiple imputation strategies for a bounded outcome variable in a competing risks
analysisdoi:10.1002/sim.8879Statistics in Medicine2021-01-19T07:03:58-08:00Statistics in Medicine10.1002/sim.8879https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8879?af=RRESEARCH ARTICLEA powerful test for the maximum treatment effect in thorough QT/QTc studiesParallel‐group thorough QT/QTc studies focus on the change of QT/QTc values at several time‐matched points from a pretreatment day (baseline) to a posttreatment day for different groups of treatment. The International Council for Harmonisation E14 stresses that QTc prolongation beyond a threshold represents high cardiac risk and calls for a test on the largest time‐matched treatment effect (QTc prolongation). QT/QTc analysis usually assumes a jointly multivariate normal (MVN) distribution of pretreatment and posttreatment QT/QTc values, with a blocked compound symmetry covariance matrix. Existing methods use an analysis of covariance (ANCOVA) model including day‐averaged baseline as a covariate to deal with the MVN model. However, the ANCOVA model tends to underestimate the variation of the estimator for treatment effects, resulting in the inflation of empirical type I error rate when testing whether the largest QTc prolongation is beyond a threshold. In this article, we propose two new methods to estimate the time‐matched treatment effects under the MVN model, including maximum likelihood estimation and ordinary‐least‐square‐based two‐stage estimation. These two methods take advantage of the covariance structure and are asymptotically efficient. Based on these estimators, powerful tests for QT/QTc prolongation are constructed. Simulation shows that the proposed estimators have smaller mean square error, and the tests can control the type I error rate with high power. The proposed methods are applied on testing the carryover effect of diltiazem to inhibit dofetilide in a randomized phase 1 trial.
Yuhao Deng,
Fangyi Chen,
Yang Li,
Kaihuan Qian,
Rui Wang,
Xiao‐Hua Zhou
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8881?af=R
<p>Parallel‐group thorough QT/QTc studies focus on the change of QT/QTc values at several time‐matched points from a pretreatment day (baseline) to a posttreatment day for different groups of treatment. The International Council for Harmonisation E14 stresses that QTc prolongation beyond a threshold represents high cardiac risk and calls for a test on the largest time‐matched treatment effect (QTc prolongation). QT/QTc analysis usually assumes a jointly multivariate normal (MVN) distribution of pretreatment and posttreatment QT/QTc values, with a blocked compound symmetry covariance matrix. Existing methods use an analysis of covariance (ANCOVA) model including day‐averaged baseline as a covariate to deal with the MVN model. However, the ANCOVA model tends to underestimate the variation of the estimator for treatment effects, resulting in the inflation of empirical type I error rate when testing whether the largest QTc prolongation is beyond a threshold. In this article, we propose two new methods to estimate the time‐matched treatment effects under the MVN model, including maximum likelihood estimation and ordinary‐least‐square‐based two‐stage estimation. These two methods take advantage of the covariance structure and are asymptotically efficient. Based on these estimators, powerful tests for QT/QTc prolongation are constructed. Simulation shows that the proposed estimators have smaller mean square error, and the tests can control the type I error rate with high power. The proposed methods are applied on testing the carryover effect of diltiazem to inhibit dofetilide in a randomized phase 1 trial.</p>
Statistics in Medicine, EarlyView. A powerful test for the maximum treatment effect in thorough QT/QTc studiesdoi:10.1002/sim.8881Statistics in Medicine2021-01-19T03:49:32-08:00Statistics in Medicine10.1002/sim.8881https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8881?af=RRESEARCH ARTICLEA comparison of parametric propensity score‐based methods for causal inference with multiple treatments and a binary outcome
We consider comparative effectiveness research (CER) from observational data with two or more treatments. In observational studies, the estimation of causal effects is prone to bias due to confounders related to both treatment and outcome. Methods based on propensity scores are routinely used to correct for such confounding biases. A large fraction of propensity score methods in the current literature consider the case of either two treatments or continuous outcome. There has been extensive literature with multiple treatment and binary outcome, but interest often lies in the intersection, for which the literature is still evolving. The contribution of this article is to focus on this intersection and compare across methods, some of which are fairly recent. We describe propensity‐based methods when more than two treatments are being compared, and the outcome is binary. We assess the relative performance of these methods through a set of simulation studies. The methods are applied to assess the effect of four common therapies for castration‐resistant advanced‐stage prostate cancer. The data consist of medical and pharmacy claims from a large national private health insurance network, with the adverse outcome being admission to the emergency room within a short time window of treatment initiation.
Youfei Yu,
Min Zhang,
Xu Shi,
Megan E. V. Caram,
Roderick J. A. Little,
Bhramar Mukherjee
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8862?af=R
<p>We consider comparative effectiveness research (CER) from observational data with two or more treatments. In observational studies, the estimation of causal effects is prone to bias due to confounders related to both treatment and outcome. Methods based on propensity scores are routinely used to correct for such confounding biases. A large fraction of propensity score methods in the current literature consider the case of either two treatments or continuous outcome. There has been extensive literature with multiple treatment and binary outcome, but interest often lies in the intersection, for which the literature is still evolving. The contribution of this article is to focus on this intersection and compare across methods, some of which are fairly recent. We describe propensity‐based methods when more than two treatments are being compared, and the outcome is binary. We assess the relative performance of these methods through a set of simulation studies. The methods are applied to assess the effect of four common therapies for castration‐resistant advanced‐stage prostate cancer. The data consist of medical and pharmacy claims from a large national private health insurance network, with the adverse outcome being admission to the emergency room within a short time window of treatment initiation.</p>
Statistics in Medicine, EarlyView. A comparison of parametric propensity score‐based methods for causal inference with multiple treatments and a binary outcomedoi:10.1002/sim.8862Statistics in Medicine2021-01-18T10:41:12-08:00Statistics in Medicine10.1002/sim.8862https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8862?af=RRESEARCH ARTICLEA Bayesian‐bandit adaptive design for N‐of‐1 clinical trialsN‐of‐1 trials, which are randomized, double‐blinded, controlled, multiperiod, crossover trials on a single subject, have been applied to determine the heterogeneity of the individual's treatment effect in precision medicine settings. An aggregated N‐of‐1 design, which can estimate the population effect from these individual trials, is a pragmatic alternative when a randomized controlled trial (RCT) is infeasible. We propose a Bayesian adaptive design for both the individual and aggregated N‐of‐1 trials using a multiarmed bandit framework that is estimated via efficient Markov chain Monte Carlo. A Bayesian hierarchical structure is used to jointly model the individual and population treatment effects. Our proposed adaptive trial design is based on Thompson sampling, which randomly allocates individuals to treatments based on the Bayesian posterior probability of each treatment being optimal. While we use a subject‐specific treatment effect and Bayesian posterior probability estimates to determine an individual's treatment allocation, our hierarchical model facilitates these individual estimates to borrow strength from the population estimates via shrinkage to the population mean. We present the design's operating characteristics and performance via a simulation study motivated by a recently completed N‐of‐1 clinical trial. We demonstrate that from a patient‐centered perspective, subjects are likely to benefit from our adaptive design, in particular, for those individuals that deviate from the overall population effect.
Sama Shrestha,
Sonia Jain
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8873?af=R
<p>N‐of‐1 trials, which are randomized, double‐blinded, controlled, multiperiod, crossover trials on a single subject, have been applied to determine the heterogeneity of the individual's treatment effect in precision medicine settings. An aggregated N‐of‐1 design, which can estimate the population effect from these individual trials, is a pragmatic alternative when a randomized controlled trial (RCT) is infeasible. We propose a Bayesian adaptive design for both the individual and aggregated N‐of‐1 trials using a multiarmed bandit framework that is estimated via efficient Markov chain Monte Carlo. A Bayesian hierarchical structure is used to jointly model the individual and population treatment effects. Our proposed adaptive trial design is based on Thompson sampling, which randomly allocates individuals to treatments based on the Bayesian posterior probability of each treatment being optimal. While we use a subject‐specific treatment effect and Bayesian posterior probability estimates to determine an individual's treatment allocation, our hierarchical model facilitates these individual estimates to borrow strength from the population estimates via shrinkage to the population mean. We present the design's operating characteristics and performance via a simulation study motivated by a recently completed N‐of‐1 clinical trial. We demonstrate that from a patient‐centered perspective, subjects are likely to benefit from our adaptive design, in particular, for those individuals that deviate from the overall population effect.</p>
Statistics in Medicine, EarlyView. A Bayesian‐bandit adaptive design for N‐of‐1 clinical trialsdoi:10.1002/sim.8873Statistics in Medicine2021-01-18T10:35:43-08:00Statistics in Medicine10.1002/sim.8873https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8873?af=RRESEARCH ARTICLETwo‐wave two‐phase outcome‐dependent sampling designs, with applications to longitudinal binary dataTwo‐phase outcome‐dependent sampling (ODS) designs are useful when resource constraints prohibit expensive exposure ascertainment on all study subjects. One class of ODS designs for longitudinal binary data stratifies subjects into three strata according to those who experience the event at none, some, or all follow‐up times. For time‐varying covariate effects, exclusively selecting subjects with response variation can yield highly efficient estimates. However, if interest lies in the association of a time‐invariant covariate, or the joint associations of time‐varying and time‐invariant covariates with the outcome, then the optimal design is unknown. Therefore, we propose a class of two‐wave two‐phase ODS designs for longitudinal binary data. We split the second‐phase sample selection into two waves, between which an interim design evaluation analysis is conducted. The interim design evaluation analysis uses first‐wave data to conduct a simulation‐based search for the optimal second‐wave design that will improve the likelihood of study success. Although we focus on longitudinal binary response data, the proposed design is general and can be applied to other response distributions. We believe that the proposed designs can be useful in settings where (1) the expected second‐phase sample size is fixed and one must tailor stratum‐specific sampling probabilities to maximize estimation efficiency, or (2) relative sampling probabilities are fixed across sampling strata and one must tailor sample size to achieve a desired precision. We describe the class of designs, examine finite sampling operating characteristics, and apply the designs to an exemplar longitudinal cohort study, the Lung Health Study.
Ran Tao,
Nathaniel D. Mercaldo,
Sebastien Haneuse,
Jacob M. Maronge,
Paul J. Rathouz,
Patrick J. Heagerty,
Jonathan S. Schildcrout
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8876?af=R
<p>Two‐phase outcome‐dependent sampling (ODS) designs are useful when resource constraints prohibit expensive exposure ascertainment on all study subjects. One class of ODS designs for longitudinal binary data stratifies subjects into three strata according to those who experience the event at none, some, or all follow‐up times. For time‐varying covariate effects, exclusively selecting subjects with response variation can yield highly efficient estimates. However, if interest lies in the association of a time‐invariant covariate, or the joint associations of time‐varying and time‐invariant covariates with the outcome, then the optimal design is unknown. Therefore, we propose a class of two‐wave two‐phase ODS designs for longitudinal binary data. We split the second‐phase sample selection into two waves, between which an interim design evaluation analysis is conducted. The interim design evaluation analysis uses first‐wave data to conduct a simulation‐based search for the optimal second‐wave design that will improve the likelihood of study success. Although we focus on longitudinal binary response data, the proposed design is general and can be applied to other response distributions. We believe that the proposed designs can be useful in settings where (1) the expected second‐phase sample size is fixed and one must tailor stratum‐specific sampling probabilities to maximize estimation efficiency, or (2) relative sampling probabilities are fixed across sampling strata and one must tailor sample size to achieve a desired precision. We describe the class of designs, examine finite sampling operating characteristics, and apply the designs to an exemplar longitudinal cohort study, the Lung Health Study.</p>
Statistics in Medicine, EarlyView. Two‐wave two‐phase outcome‐dependent sampling designs, with applications to longitudinal binary datadoi:10.1002/sim.8876Statistics in Medicine2021-01-13T08:00:06-08:00Statistics in Medicine10.1002/sim.8876https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8876?af=RRESEARCH ARTICLEComplexity and bias in cross‐sectional data with binary disease outcome in observational studiesA cross sectional population is defined as a population of living individuals at the sampling or observational time. Cross‐sectionally sampled data with binary disease outcome are commonly analyzed in observational studies for identifying how covariates correlate with disease occurrence. It is generally understood that cross‐sectional binary outcome is not as informative as longitudinally collected time‐to‐event data, but there is insufficient understanding as to whether bias can possibly exist in cross‐sectional data and how the bias is related to the population risk of interest. As the progression of a disease typically involves both time and disease status, we consider how the binary disease outcome from the cross‐sectional population is connected to birth‐illness‐death process in the target population. We argue that the distribution of cross‐sectional binary outcome is different from the risk distribution from the target population and that bias would typically arise when using cross‐sectional data to draw inference for population risk. In general, the cross‐sectional risk probability is determined jointly by the population risk probability and the ratio of duration of diseased state to the duration of disease‐free state. Through explicit formulas we conclude that bias can almost never be avoided from cross‐sectional data. We present age‐specific risk probability (ARP) and argue that models based on ARP offers a compromised but still biased approach to understand the population risk. An analysis based on Alzheimer's disease data is presented to illustrate the ARP model and possible critiques for the analysis results.
Mei‐Cheng Wang,
Yuchen Yang
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8812?af=R
<p>A cross sectional population is defined as a population of living individuals at the sampling or observational time. Cross‐sectionally sampled data with binary disease outcome are commonly analyzed in observational studies for identifying how covariates correlate with disease occurrence. It is generally understood that cross‐sectional binary outcome is not as informative as longitudinally collected time‐to‐event data, but there is insufficient understanding as to whether bias can possibly exist in cross‐sectional data and how the bias is related to the population risk of interest. As the progression of a disease typically involves both time and disease status, we consider how the binary disease outcome from the cross‐sectional population is connected to birth‐illness‐death process in the target population. We argue that the distribution of cross‐sectional binary outcome is different from the risk distribution from the target population and that bias would typically arise when using cross‐sectional data to draw inference for population risk. In general, the cross‐sectional risk probability is determined jointly by the population risk probability and the ratio of duration of diseased state to the duration of disease‐free state. Through explicit formulas we conclude that bias can almost never be avoided from cross‐sectional data. We present age‐specific risk probability (ARP) and argue that models based on ARP offers a compromised but still biased approach to understand the population risk. An analysis based on Alzheimer's disease data is presented to illustrate the ARP model and possible critiques for the analysis results.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 950-962, 20 February 2021. Complexity and bias in cross‐sectional data with binary disease outcome in observational studiesdoi:10.1002/sim.8812Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8812https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8812?af=RRESEARCH ARTICLEBayesian methods to compare dose levels with placebo in a small n, sequential, multiple assignment, randomized trialClinical trials studying treatments for rare diseases are challenging to design and conduct due to the limited number of patients eligible for the trial. One design used to address this challenge is the small n, sequential, multiple assignment, randomized trial (snSMART). We propose a new snSMART design that investigates the response rates of a drug tested at a low and high dose compared with placebo. Patients are randomized to an initial treatment (stage 1). In stage 2, patients are rerandomized, depending on their initial treatment and their response to that treatment in stage 1, to either the same or a different dose of treatment. Data from both stages are used to determine the efficacy of the active treatment. We present a Bayesian approach where information is borrowed between stage 1 and stage 2. We compare our approach to standard methods using only stage 1 data and a log‐linear Poisson model that uses data from both stages where parameters are estimated using generalized estimating equations. We observe that the Bayesian method has smaller root‐mean‐square‐error and 95% credible interval widths than standard methods in the tested scenarios. We conclude that it is advantageous to utilize data from both stages for a primary efficacy analysis and that the specific snSMART design shown here can be used in the registration of a drug for the treatment of rare diseases.
Fang Fang,
Kimberly A. Hochstedler,
Roy N. Tamura,
Thomas M. Braun,
Kelley M. Kidwell
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8813?af=R
<p>Clinical trials studying treatments for rare diseases are challenging to design and conduct due to the limited number of patients eligible for the trial. One design used to address this challenge is the small n, sequential, multiple assignment, randomized trial (snSMART). We propose a new snSMART design that investigates the response rates of a drug tested at a low and high dose compared with placebo. Patients are randomized to an initial treatment (stage 1). In stage 2, patients are rerandomized, depending on their initial treatment and their response to that treatment in stage 1, to either the same or a different dose of treatment. Data from both stages are used to determine the efficacy of the active treatment. We present a Bayesian approach where information is borrowed between stage 1 and stage 2. We compare our approach to standard methods using only stage 1 data and a log‐linear Poisson model that uses data from both stages where parameters are estimated using generalized estimating equations. We observe that the Bayesian method has smaller root‐mean‐square‐error and 95% credible interval widths than standard methods in the tested scenarios. We conclude that it is advantageous to utilize data from both stages for a primary efficacy analysis and that the specific snSMART design shown here can be used in the registration of a drug for the treatment of rare diseases.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 963-977, 20 February 2021. Bayesian methods to compare dose levels with placebo in a small n, sequential, multiple assignment, randomized trialdoi:10.1002/sim.8813Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8813https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8813?af=RRESEARCH ARTICLEDetermination of correlations in multivariate longitudinal data with modified Cholesky and hypersphere decomposition using Bayesian variable selection approachIn this article, we present a Bayesian framework for multivariate longitudinal data analysis with a focus on selection of important elements in the generalized autoregressive matrix. An efficient Gibbs sampling algorithm was developed for the proposed model and its implementation in a comprehensive R package called MLModelSelection is available on the comprehensive R archive network. The performance of the proposed approach was studied via a comprehensive simulation study. The effectiveness of the methodology was illustrated using a nonalcoholic fatty liver disease dataset to study correlations in multiple responses over time to explain the joint variability of lung functions and body mass index. Supplementary materials for this article, including a standardized description of the materials needed to reproduce the work, are available as an online supplement.
Kuo‐Jung Lee,
Ray‐Bing Chen,
Min‐Sun Kwak,
Keunbaik Lee
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8815?af=R
<p>In this article, we present a Bayesian framework for multivariate longitudinal data analysis with a focus on selection of important elements in the generalized autoregressive matrix. An efficient Gibbs sampling algorithm was developed for the proposed model and its implementation in a comprehensive R package called <span style="font-family:monospace">MLModelSelection</span> is available on the comprehensive R archive network. The performance of the proposed approach was studied via a comprehensive simulation study. The effectiveness of the methodology was illustrated using a nonalcoholic fatty liver disease dataset to study correlations in multiple responses over time to explain the joint variability of lung functions and body mass index. Supplementary materials for this article, including a standardized description of the materials needed to reproduce the work, are available as an online supplement.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 978-997, 20 February 2021. Determination of correlations in multivariate longitudinal data with modified Cholesky and hypersphere decomposition using Bayesian variable selection approachdoi:10.1002/sim.8815Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8815https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8815?af=RRESEARCH ARTICLESurvival analysis under the Cox proportional hazards model with pooled covariatesFor a continuous time‐to‐event outcome and an expensive‐to‐measure exposure, we develop a pooling design and propose a likelihood‐based approach to estimate the hazard ratios (HRs) of a Cox proportional hazards (PH) model. Our proposed approach fits a PH model based on pooled exposures with individually observed time‐to‐event outcomes. The design and estimation exploits the equivalence of the conditional logistic likelihood functions arising from a matched case‐control study and the partial likelihood function of a riskset‐matched, nested case‐control (NCC) subset of a cohort study. To create the pools, we first focus on an NCC subcohort. Pools are formed at random while keeping the matching intact. Pool‐level exposure and confounders are then evaluated and used in the likelihood to estimate the HR and the standard error of the estimates. The estimators are MLEs, provide consistent estimates of the individual‐level HRs, and are asymptotically normal. Our simulation results indicate that the pooled estimates are comparable to the estimates obtained from the NCC subcohort. The units of analysis for the pooled design are the pools and not the individual participants. Hence the effective sample size is reduced. Therefore, the variance of the HR estimate increases with increasing poolsize. However, this variance inflation in small samples can be offset by including more matched controls per case within the NCC subcohort. An application is demonstrated with the Second Manifestations of ARTerial disease (SMART) study.
Paramita Saha‐Chaudhuri,
Lamin Juwara
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8816?af=R
<p>For a continuous time‐to‐event outcome and an expensive‐to‐measure exposure, we develop a pooling design and propose a likelihood‐based approach to estimate the hazard ratios (HRs) of a Cox proportional hazards (PH) model. Our proposed approach fits a PH model based on pooled exposures with individually observed time‐to‐event outcomes. The design and estimation exploits the equivalence of the conditional logistic likelihood functions arising from a matched case‐control study and the partial likelihood function of a riskset‐matched, nested case‐control (NCC) subset of a cohort study. To create the pools, we first focus on an NCC subcohort. Pools are formed at random while keeping the matching intact. Pool‐level exposure and confounders are then evaluated and used in the likelihood to estimate the HR and the standard error of the estimates. The estimators are MLEs, provide consistent estimates of the individual‐level HRs, and are asymptotically normal. Our simulation results indicate that the pooled estimates are comparable to the estimates obtained from the NCC subcohort. The units of analysis for the pooled design are the pools and not the individual participants. Hence the effective sample size is reduced. Therefore, the variance of the HR estimate increases with increasing poolsize. However, this variance inflation in small samples can be offset by including more matched controls per case within the NCC subcohort. An application is demonstrated with the Second Manifestations of ARTerial disease (SMART) study.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 998-1020, 20 February 2021. Survival analysis under the Cox proportional hazards model with pooled covariatesdoi:10.1002/sim.8816Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8816https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8816?af=RRESEARCH ARTICLEError‐corrected estimation of a diagnostic accuracy index of a biomarker against a continuous gold standardThis article concerns evaluating the effectiveness of a continuous diagnostic biomarker against a continuous gold standard that is measured with error. Extending the work of Obuchowski (2005, 2016), Wu et al (2016) suggested an accuracy index and proposed an estimator for the index with error‐prone standard when the reliability coefficient is known. Combining with additional measurements (without measurement errors) on the continuous gold standard collected from some subjects, this article proposes two adaptive estimators of the accuracy index when the reliability coefficient is unknown, and further establish the consistency and asymptotic normality of these estimators. Simulation studies are conducted to compare various estimators. Data from an intervention trial on glycemic control among children with type 1 diabetes are used to illustrate the proposed methods.
Mixia Wu,
Xiaoyu Zhang,
Wei Zhang,
Xu Zhang,
Aiyi Liu
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8818?af=R
<p>This article concerns evaluating the effectiveness of a continuous diagnostic biomarker against a continuous gold standard that is measured with error. Extending the work of Obuchowski (2005, 2016), Wu et al (2016) suggested an accuracy index and proposed an estimator for the index with error‐prone standard when the reliability coefficient is known. Combining with additional measurements (without measurement errors) on the continuous gold standard collected from some subjects, this article proposes two adaptive estimators of the accuracy index when the reliability coefficient is unknown, and further establish the consistency and asymptotic normality of these estimators. Simulation studies are conducted to compare various estimators. Data from an intervention trial on glycemic control among children with type 1 diabetes are used to illustrate the proposed methods.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 1034-1058, 20 February 2021. Error‐corrected estimation of a diagnostic accuracy index of a biomarker against a continuous gold standarddoi:10.1002/sim.8818Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8818https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8818?af=RRESEARCH ARTICLEOptimal two‐phase sampling for estimating the area under the receiver operating characteristic
curve
Statistical methods are well developed for estimating the area under the receiver operating characteristic curve (AUC) based on a random sample where the gold standard is available for every subject in the sample, or a two‐phase sample where the gold standard is ascertained only at the second phase for a subset of subjects sampled using fixed sampling probabilities. However, the methods based on a two‐phase sample do not attempt to optimize the sampling probabilities to minimize the variance of AUC estimator. In this paper, we consider the optimal two‐phase sampling design for evaluating the performance of an ordinal test in classifying disease status. We derived the analytic variance formula for the AUC estimator and used it to obtain the optimal sampling probabilities. The efficiency of the two‐phase sampling under the optimal sampling probabilities (OA) is evaluated by a simulation study, which indicates that two‐phase sampling under OA achieves a substantial amount of variance reduction with an over‐sample of subjects with low and high ordinal levels, compared with two‐phase sampling under proportional allocation (PA). Furthermore, in comparison with an one‐phase random sampling, two‐phase sampling under OA or PA have a clear advantage in reducing the variance of AUC estimator when the variance of diagnostic test results in the disease population is small relative to its counterpart in nondisease population. Finally, we applied the optimal two‐phase sampling design to a real‐world example to evaluate the performance of a questionnaire score in screening for childhood asthma.
Yougui Wu
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8819?af=R
<p>Statistical methods are well developed for estimating the area under the receiver operating characteristic curve (AUC) based on a random sample where the gold standard is available for every subject in the sample, or a two‐phase sample where the gold standard is ascertained only at the second phase for a subset of subjects sampled using fixed sampling probabilities. However, the methods based on a two‐phase sample do not attempt to optimize the sampling probabilities to minimize the variance of AUC estimator. In this paper, we consider the optimal two‐phase sampling design for evaluating the performance of an ordinal test in classifying disease status. We derived the analytic variance formula for the AUC estimator and used it to obtain the optimal sampling probabilities. The efficiency of the two‐phase sampling under the optimal sampling probabilities (OA) is evaluated by a simulation study, which indicates that two‐phase sampling under OA achieves a substantial amount of variance reduction with an over‐sample of subjects with low and high ordinal levels, compared with two‐phase sampling under proportional allocation (PA). Furthermore, in comparison with an one‐phase random sampling, two‐phase sampling under OA or PA have a clear advantage in reducing the variance of AUC estimator when the variance of diagnostic test results in the disease population is small relative to its counterpart in nondisease population. Finally, we applied the optimal two‐phase sampling design to a real‐world example to evaluate the performance of a questionnaire score in screening for childhood asthma.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 1059-1071, 20 February 2021. Optimal two‐phase sampling for estimating the area under the receiver operating characteristic
curvedoi:10.1002/sim.8819Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8819https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8819?af=RRESEARCH ARTICLEA note on estimating the Cox‐Snell R2 from a reported C statistic (AUROC) to inform sample size calculations for developing a prediction model with a binary outcome
In 2019 we published a pair of articles in Statistics in Medicine that describe how to calculate the minimum sample size for developing a multivariable prediction model with a continuous outcome, or with a binary or time‐to‐event outcome. As for any sample size calculation, the approach requires the user to specify anticipated values for key parameters. In particular, for a prediction model with a binary outcome, the outcome proportion and a conservative estimate for the overall fit of the developed model as measured by the Cox‐Snell R2 (proportion of variance explained) must be specified. This proposal raises the question of how to identify a plausible value for R2 in advance of model development. Our articles suggest researchers should identify R2 from closely related models already published in their field. In this letter, we present details on how to derive R2 using the reported C statistic (AUROC) for such existing prediction models with a binary outcome. The C statistic is commonly reported, and so our approach allows researchers to obtain R2 for subsequent sample size calculations for new models. Stata and R code is provided, and a small simulation study.
Richard D. Riley,
Ben Calster,
Gary S. Collins
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8806?af=R
<p>In 2019 we published a pair of articles in <i>Statistics in Medicine</i> that describe how to calculate the minimum sample size for developing a multivariable prediction model with a continuous outcome, or with a binary or time‐to‐event outcome. As for any sample size calculation, the approach requires the user to specify anticipated values for key parameters. In particular, for a prediction model with a binary outcome, the outcome proportion and a conservative estimate for the overall fit of the developed model as measured by the Cox‐Snell <i>R</i>
<sup>2</sup> (proportion of variance explained) must be specified. This proposal raises the question of how to identify a plausible value for <i>R</i>
<sup>2</sup> in advance of model development. Our articles suggest researchers should identify <i>R</i>
<sup>2</sup> from closely related models already published in their field. In this letter, we present details on how to derive <i>R</i>
<sup>2</sup> using the reported <i>C</i> statistic (AUROC) for such existing prediction models with a binary outcome. The <i>C</i> statistic is commonly reported, and so our approach allows researchers to obtain <i>R</i>
<sup>2</sup> for subsequent sample size calculations for new models. Stata and R code is provided, and a small simulation study.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 859-864, 20 February 2021. A note on estimating the Cox‐Snell R2 from a reported C statistic (AUROC) to inform sample size calculations for developing a prediction model with a binary outcomedoi:10.1002/sim.8806Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8806https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8806?af=RRESEARCH ARTICLEElasticity as a measure for online determination of remission points in ongoing epidemics
Abstract
The correct identification of change‐points during ongoing outbreak investigations of infectious diseases is a matter of paramount importance in epidemiology, with major implications for the management of health care resources, public health and, as the COVID‐19 pandemic has shown, social live. Onsets, peaks, and inflexion points are some of them. An onset is the moment when the epidemic starts. A "peak" indicates a moment at which the incorporated values, both before and after, are lower: a maximum. The inflexion points identify moments in which the rate of growth of the incorporation of new cases changes intensity. In this study, after interpreting the concept of elasticity of a random variable in an innovative way, we propose using it as a new simpler tool for anticipating epidemic remission change‐points. In particular, we propose that the "remission point of change" will occur just at the instant when the speed in the accumulation of new cases is lower than the average speed of accumulation of cases up to that moment. This gives stability and robustness to the estimation in the event of possible remission variations. This descriptive measure, which is very easy to calculate and interpret, is revealed as informative and adequate, has the advantage of being distribution‐free and can be estimated in real time, while the data is being collected. We use the 2014‐2016 Western Africa Ebola virus epidemic to demonstrate this new approach. A couple of examples analyzing COVID‐19 data are also included.
Ernesto J. Veres‐Ferrer,
Jose M. Pavía
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8807?af=R
<h2>Abstract</h2>
<p>The correct identification of change‐points during ongoing outbreak investigations of infectious diseases is a matter of paramount importance in epidemiology, with major implications for the management of health care resources, public health and, as the COVID‐19 pandemic has shown, social live. Onsets, peaks, and inflexion points are some of them. An onset is the moment when the epidemic starts. A "peak" indicates a moment at which the incorporated values, both before and after, are lower: a maximum. The inflexion points identify moments in which the rate of growth of the incorporation of new cases changes intensity. In this study, after interpreting the concept of elasticity of a random variable in an innovative way, we propose using it as a new simpler tool for anticipating epidemic remission change‐points. In particular, we propose that the "remission point of change" will occur just at the instant when the speed in the accumulation of new cases is lower than the average speed of accumulation of cases up to that moment. This gives stability and robustness to the estimation in the event of possible remission variations. This descriptive measure, which is very easy to calculate and interpret, is revealed as informative and adequate, has the advantage of being distribution‐free and can be estimated in real time, while the data is being collected. We use the 2014‐2016 Western Africa Ebola virus epidemic to demonstrate this new approach. A couple of examples analyzing COVID‐19 data are also included.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 865-884, 20 February 2021. Elasticity as a measure for online determination of remission points in ongoing epidemicsdoi:10.1002/sim.8807Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8807https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8807?af=RRESEARCH ARTICLEMediation effect selection in high‐dimensional and compositional microbiome dataThe microbiome plays an important role in human health by mediating the path from environmental exposures to health outcomes. The relative abundances of the high‐dimensional microbiome data have an unit‐sum restriction, rendering standard statistical methods in the Euclidean space invalid. To address this problem, we use the isometric log‐ratio transformations of the relative abundances as the mediator variables. To select significant mediators, we consider a closed testing‐based selection procedure with desirable confidence. Simulations are provided to verify the effectiveness of our method. As an illustrative example, we apply the proposed method to study the mediation effects of murine gut microbiome between subtherapeutic antibiotic treatment and body weight gain, and identify Coprobacillus and Adlercreutzia as two significant mediators.
Haixiang Zhang,
Jun Chen,
Yang Feng,
Chan Wang,
Huilin Li,
Lei Liu
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8808?af=R
<p>The microbiome plays an important role in human health by mediating the path from environmental exposures to health outcomes. The relative abundances of the high‐dimensional microbiome data have an unit‐sum restriction, rendering standard statistical methods in the Euclidean space invalid. To address this problem, we use the isometric log‐ratio transformations of the relative abundances as the mediator variables. To select significant mediators, we consider a closed testing‐based selection procedure with desirable confidence. Simulations are provided to verify the effectiveness of our method. As an illustrative example, we apply the proposed method to study the mediation effects of murine gut microbiome between subtherapeutic antibiotic treatment and body weight gain, and identify <i>Coprobacillus</i> and <i>Adlercreutzia</i> as two significant mediators.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 885-896, 20 February 2021. Mediation effect selection in high‐dimensional and compositional microbiome datadoi:10.1002/sim.8808Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8808https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8808?af=RRESEARCH ARTICLEBayesian latent factor on image regression with nonignorable missing data
Abstract
Medical imaging data have been widely used in modern health care, particularly in the prognosis, screening, diagnosis, and treatment of various diseases. In this study, we consider a latent factor‐on‐image (LoI) regression model that regresses a latent factor on ultrahigh dimensional imaging covariates. The latent factor is characterized by multiple manifest variables through a factor analysis model, while the manifest variables are subject to nonignorable missingness. We propose a two‐stage approach for statistical inference. At the first stage, an efficient functional principal component analysis method is applied to reduce the dimension and extract useful features/eigenimages. At the second stage, a factor analysis mode is proposed to characterize the latent response variable. Moreover, an LoI model is used to detect influential risk factors, and an exponential tiling model applied to accommodate nonignoreable nonresponses. A fully Bayesian method with an adjust spike‐and‐slab absolute shrinkage and selection operator (lasso) procedure is developed for the estimation and selection of influential features/eigenimages. Simulation studies show the proposed method exhibits satisfactory performance. The proposed methodology is applied to a study on the Alzheimer's Disease Neuroimaging Initiative data set.
Xiaoqing Wang,
Xinyuan Song,
Hongtu Zhu
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8810?af=R
<h2>Abstract</h2>
<p>Medical imaging data have been widely used in modern health care, particularly in the prognosis, screening, diagnosis, and treatment of various diseases. In this study, we consider a latent factor‐on‐image (LoI) regression model that regresses a latent factor on ultrahigh dimensional imaging covariates. The latent factor is characterized by multiple manifest variables through a factor analysis model, while the manifest variables are subject to nonignorable missingness. We propose a two‐stage approach for statistical inference. At the first stage, an efficient functional principal component analysis method is applied to reduce the dimension and extract useful features/eigenimages. At the second stage, a factor analysis mode is proposed to characterize the latent response variable. Moreover, an LoI model is used to detect influential risk factors, and an exponential tiling model applied to accommodate nonignoreable nonresponses. A fully Bayesian method with an adjust spike‐and‐slab absolute shrinkage and selection operator (lasso) procedure is developed for the estimation and selection of influential features/eigenimages. Simulation studies show the proposed method exhibits satisfactory performance. The proposed methodology is applied to a study on the Alzheimer's Disease Neuroimaging Initiative data set.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 920-932, 20 February 2021. Bayesian latent factor on image regression with nonignorable missing datadoi:10.1002/sim.8810Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8810https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8810?af=RRESEARCH ARTICLERobust inference in the joint modeling of multilevel zero‐inflated Poisson and Cox models
A popular method for simultaneously modeling of correlated count response with excess zeros and time to event is by means of the joint models. In these models, the likelihood‐based methods (such as expectation‐maximization algorithm and Newton‐Raphson) are used for estimating the parameters, but in the presence of contaminations, these methods are unstable. To overcome this challenge, we extend the M‐estimator methods and propose a robust estimator approach to obtain a robust estimation of the regression parameters in the joint model. Our proposed algorithm has two steps (Expectation and Solution). In the expectation step, the likelihood function is expected by conditioning on the observed data and in the solution step, the parameters are computed, with solving robust estimating equations. Therefore, this algorithm achieves robustness by applying robust estimating equations and weighted likelihood in the S‐step. Simulation studies under various situations of contaminations show that the robust algorithm gives us consistent estimates with a smaller bias than likelihood‐based methods. The application section uses data on factors affecting fertility and birth spacing.
Eghbal Zandkarimi,
Abbas Moghimbeigi,
Hossein Mahjub
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8811?af=R
<p>A popular method for simultaneously modeling of correlated count response with excess zeros and time to event is by means of the joint models. In these models, the likelihood‐based methods (such as expectation‐maximization algorithm and Newton‐Raphson) are used for estimating the parameters, but in the presence of contaminations, these methods are unstable. To overcome this challenge, we extend the M‐estimator methods and propose a robust estimator approach to obtain a robust estimation of the regression parameters in the joint model. Our proposed algorithm has two steps (Expectation and Solution). In the expectation step, the likelihood function is expected by conditioning on the observed data and in the solution step, the parameters are computed, with solving robust estimating equations. Therefore, this algorithm achieves robustness by applying robust estimating equations and weighted likelihood in the S‐step. Simulation studies under various situations of contaminations show that the robust algorithm gives us consistent estimates with a smaller bias than likelihood‐based methods. The application section uses data on factors affecting fertility and birth spacing.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 933-949, 20 February 2021. Robust inference in the joint modeling of multilevel zero‐inflated Poisson and Cox modelsdoi:10.1002/sim.8811Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8811https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8811?af=RRESEARCH ARTICLESpatio‐temporal analysis of misaligned burden of disease data using a geo‐statistical approach
Data used to estimate the burden of diseases (BOD) are usually sparse, noisy, and heterogeneous. These data are collected from surveys, registries, and systematic reviews that have different areal units, are conducted at different times, and are reported for different age groups. In this study, we developed a Bayesian geo‐statistical model to combine aggregated sparse, noisy BOD data from different sources with misaligned areal units. Our model incorporates the correlation of space, time, and age to estimate health indicators for areas with no data or a small number of observations. The model also considers the heterogeneity of data sources and the measurement errors of input data in the final estimates and uncertainty intervals. We applied the model to combine data from nine different sources of body mass index in a national and sub‐national BOD study. The cross‐validation results confirmed a high out‐of‐sample predictive ability in sparse and noisy data. The proposed model can be used by other BOD studies especially at the sub‐national level when the areal units are subject to misalignment.
Mahboubeh Parsaeian,
Majid Jafari Khaledi,
Farshad Farzadfar,
Mahdi Mahdavi,
Hojjat Zeraati,
Mahmood Mahmoudi,
Ardeshir Khosravi,
Kazem Mohammad
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8817?af=R
<p>Data used to estimate the burden of diseases (BOD) are usually sparse, noisy, and heterogeneous. These data are collected from surveys, registries, and systematic reviews that have different areal units, are conducted at different times, and are reported for different age groups. In this study, we developed a Bayesian geo‐statistical model to combine aggregated sparse, noisy BOD data from different sources with misaligned areal units. Our model incorporates the correlation of space, time, and age to estimate health indicators for areas with no data or a small number of observations. The model also considers the heterogeneity of data sources and the measurement errors of input data in the final estimates and uncertainty intervals. We applied the model to combine data from nine different sources of body mass index in a national and sub‐national BOD study. The cross‐validation results confirmed a high out‐of‐sample predictive ability in sparse and noisy data. The proposed model can be used by other BOD studies especially at the sub‐national level when the areal units are subject to misalignment.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 1021-1033, 20 February 2021. Spatio‐temporal analysis of misaligned burden of disease data using a geo‐statistical approachdoi:10.1002/sim.8817Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8817https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8817?af=RRESEARCH ARTICLEProbabilistic cause‐of‐disease assignment using case‐control diagnostic tests: A latent variable regression approach
Optimal prevention and treatment strategies for a disease of multiple causes, such as pneumonia, must be informed by the population distribution of causes among cases, or cause‐specific case fractions (CSCFs). CSCFs may further depend on additional explanatory variables. Existing methodological literature in disease etiology research does not fully address the regression problem, particularly under a case‐control design. Based on multivariate binary non‐gold‐standard diagnostic data and additional covariate information, this article proposes a novel and unified regression modeling framework for estimating covariate‐dependent CSCF functions in case‐control disease etiology studies. The model leverages critical control data for valid probabilistic cause assignment for cases. We derive an efficient Markov chain Monte Carlo algorithm for flexible posterior inference. We illustrate the inference of CSCF functions using extensive simulations and show that the proposed model produces less biased estimates and more valid inference of the overall CSCFs than analyses that omit covariates. A regression analysis of pediatric pneumonia data reveals the dependence of CSCFs upon season, age, human immunodeficiency virus status and disease severity. The article concludes with a brief discussion on model extensions that may further enhance the utility of the regression model in broader disease etiology research.
Zhenke Wu,
Irena Chen
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8804?af=R
<p>Optimal prevention and treatment strategies for a disease of multiple causes, such as pneumonia, must be informed by the population distribution of causes among cases, or cause‐specific case fractions (CSCFs). CSCFs may further depend on additional explanatory variables. Existing methodological literature in disease etiology research does not fully address the regression problem, particularly under a case‐control design. Based on multivariate binary non‐gold‐standard diagnostic data and additional covariate information, this article proposes a novel and unified regression modeling framework for estimating covariate‐dependent CSCF functions in case‐control disease etiology studies. The model leverages critical control data for valid probabilistic cause assignment for cases. We derive an efficient Markov chain Monte Carlo algorithm for flexible posterior inference. We illustrate the inference of CSCF functions using extensive simulations and show that the proposed model produces less biased estimates and more valid inference of the overall CSCFs than analyses that omit covariates. A regression analysis of pediatric pneumonia data reveals the dependence of CSCFs upon season, age, human immunodeficiency virus status and disease severity. The article concludes with a brief discussion on model extensions that may further enhance the utility of the regression model in broader disease etiology research.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 823-841, 20 February 2021. Probabilistic cause‐of‐disease assignment using case‐control diagnostic tests: A latent variable regression approachdoi:10.1002/sim.8804Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8804https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8804?af=RRESEARCH ARTICLEPropensity score weighting for covariate adjustment in randomized clinical trialsChance imbalance in baseline characteristics is common in randomized clinical trials. Regression adjustment such as the analysis of covariance (ANCOVA) is often used to account for imbalance and increase precision of the treatment effect estimate. An objective alternative is through inverse probability weighting (IPW) of the propensity scores. Although IPW and ANCOVA are asymptotically equivalent, the former may demonstrate inferior performance in finite samples. In this article, we point out that IPW is a special case of the general class of balancing weights, and advocate to use overlap weighting (OW) for covariate adjustment. The OW method has a unique advantage of completely removing chance imbalance when the propensity score is estimated by logistic regression. We show that the OW estimator attains the same semiparametric variance lower bound as the most efficient ANCOVA estimator and the IPW estimator for a continuous outcome, and derive closed‐form variance estimators for OW when estimating additive and ratio estimands. Through extensive simulations, we demonstrate OW consistently outperforms IPW in finite samples and improves the efficiency over ANCOVA and augmented IPW when the degree of treatment effect heterogeneity is moderate or when the outcome model is incorrectly specified. We apply the proposed OW estimator to the Best Apnea Interventions for Research (BestAIR) randomized trial to evaluate the effect of continuous positive airway pressure on patient health outcomes. All the discussed propensity score weighting methods are implemented in the R package PSweight.
Shuxi Zeng,
Fan Li,
Rui Wang,
Fan Li
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8805?af=R
<p>Chance imbalance in baseline characteristics is common in randomized clinical trials. Regression adjustment such as the analysis of covariance (ANCOVA) is often used to account for imbalance and increase precision of the treatment effect estimate. An objective alternative is through inverse probability weighting (IPW) of the propensity scores. Although IPW and ANCOVA are asymptotically equivalent, the former may demonstrate inferior performance in finite samples. In this article, we point out that IPW is a special case of the general class of balancing weights, and advocate to use overlap weighting (OW) for covariate adjustment. The OW method has a unique advantage of completely removing chance imbalance when the propensity score is estimated by logistic regression. We show that the OW estimator attains the same semiparametric variance lower bound as the most efficient ANCOVA estimator and the IPW estimator for a continuous outcome, and derive closed‐form variance estimators for OW when estimating additive and ratio estimands. Through extensive simulations, we demonstrate OW consistently outperforms IPW in finite samples and improves the efficiency over ANCOVA and augmented IPW when the degree of treatment effect heterogeneity is moderate or when the outcome model is incorrectly specified. We apply the proposed OW estimator to the Best Apnea Interventions for Research (BestAIR) randomized trial to evaluate the effect of continuous positive airway pressure on patient health outcomes. All the discussed propensity score weighting methods are implemented in the R package <i>PSweight</i>.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 842-858, 20 February 2021. Propensity score weighting for covariate adjustment in randomized clinical trialsdoi:10.1002/sim.8805Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8805https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8805?af=RRESEARCH ARTICLESuRF: A new method for sparse variable selection, with application in microbiome data analysis
In this article, we present a new variable selection method for regression and classification purposes, particularly for microbiome analysis. Our method, called subsampling ranking forward selection (SuRF), is based on LASSO penalized regression, subsampling and forward‐selection methods. SuRF offers major advantages over existing variable selection methods in terms of both sparsity of selected models and model inference. We provide an R package that can implement our method for generalized linear models. We apply our method to classification problems from microbiome data, using a novel agglomeration approach to deal with the special tree‐like correlation structure of the variables. Existing methods arbitrarily choose a taxonomic level a priori before performing the analysis, whereas by combining SuRF with these aggregated variables, we are able to identify the key biomarkers at the appropriate taxonomic level, as suggested by the data. We present simulations in multiple sparse settings to demonstrate that our approach performs better than several other popularly used existing approaches in recovering the true variables. We apply SuRF to two microbiome datasets: one about prediction of pouchitis and another for identifying samples from two healthy individuals. We find that SuRF can provide a better or comparable prediction with other methods while controlling the false positive rate of variable selection.
Lihui Liu,
Hong Gu,
Johan Van Limbergen,
Toby Kenney
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8809?af=R
<p>In this article, we present a new variable selection method for regression and classification purposes, particularly for microbiome analysis. Our method, called subsampling ranking forward selection (SuRF), is based on LASSO penalized regression, subsampling and forward‐selection methods. SuRF offers major advantages over existing variable selection methods in terms of both sparsity of selected models and model inference. We provide an <span style="font-family:monospace">R</span> package that can implement our method for generalized linear models. We apply our method to classification problems from microbiome data, using a novel agglomeration approach to deal with the special tree‐like correlation structure of the variables. Existing methods arbitrarily choose a taxonomic level a priori before performing the analysis, whereas by combining SuRF with these aggregated variables, we are able to identify the key biomarkers at the appropriate taxonomic level, as suggested by the data. We present simulations in multiple sparse settings to demonstrate that our approach performs better than several other popularly used existing approaches in recovering the true variables. We apply SuRF to two microbiome datasets: one about prediction of pouchitis and another for identifying samples from two healthy individuals. We find that SuRF can provide a better or comparable prediction with other methods while controlling the false positive rate of variable selection.</p>
Statistics in Medicine, Volume 40, Issue 4, Page 897-919, 20 February 2021. SuRF: A new method for sparse variable selection, with application in microbiome data analysisdoi:10.1002/sim.8809Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8809https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8809?af=RRESEARCH ARTICLEIssue Information
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8603?af=R
Statistics in Medicine, Volume 40, Issue 4, 20 February 2021. Issue Informationdoi:10.1002/sim.8603Statistics in Medicine2021-01-13T01:46:52-08:00Statistics in Medicine4042021-02-20T08:00:00Z2021-02-20T08:00:00Z10.1002/sim.8603https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8603?af=RISSUE INFORMATIONDetecting rare haplotype association with two correlated phenotypes of binary and continuous types
Abstract
Multiple correlated traits/phenotypes are often collected in genetic association studies and they may share a common genetic mechanism. Joint analysis of correlated phenotypes has well‐known advantages over one‐at‐a‐time analysis including gain in power and better understanding of genetic etiology. However, when the phenotypes are of discordant types such as binary and continuous, the joint modeling is more challenging. Another research area of current interest is discovery of rare genetic variants. Currently there is no method available for detecting association of rare (or common) haplotypes with multiple discordant phenotypes jointly. Our goal is to fill this gap specifically for two discordant phenotypes. We consider a rare haplotype association method for a binary phenotype, logistic Bayesian LASSO (univariate LBL) and its extension for two correlated binary phenotypes (bivariate LBL‐2B). Under this framework, we propose a haplotype association test with binary and continuous phenotypes jointly (bivariate LBL‐BC). Specifically, we use a latent variable to induce correlation between the two phenotypes. We carry out extensive simulations to investigate bivariate LBL‐BC and compare it with univariate LBL and bivariate LBL‐2B. In most settings, bivariate LBL‐BC performs the best. In only two situations, bivariate LBL‐BC has similar performance—when the two phenotypes are (1) weakly or not correlated and the target haplotype affects the binary phenotype only and (2) strongly positively correlated and the target haplotype affects both phenotypes in positive direction. Finally, we apply the method to a data set on lung cancer and nicotine dependence and detect several haplotypes including a rare one.
Xiaochen Yuan,
Swati Biswas
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8877?af=R
<h2>Abstract</h2>
<p>Multiple correlated traits/phenotypes are often collected in genetic association studies and they may share a common genetic mechanism. Joint analysis of correlated phenotypes has well‐known advantages over one‐at‐a‐time analysis including gain in power and better understanding of genetic etiology. However, when the phenotypes are of discordant types such as binary and continuous, the joint modeling is more challenging. Another research area of current interest is discovery of rare genetic variants. Currently there is no method available for detecting association of rare (or common) haplotypes with multiple discordant phenotypes jointly. Our goal is to fill this gap specifically for two discordant phenotypes. We consider a rare haplotype association method for a binary phenotype, logistic Bayesian LASSO (univariate LBL) and its extension for two correlated binary phenotypes (bivariate LBL‐2B). Under this framework, we propose a haplotype association test with binary and continuous phenotypes jointly (bivariate LBL‐BC). Specifically, we use a latent variable to induce correlation between the two phenotypes. We carry out extensive simulations to investigate bivariate LBL‐BC and compare it with univariate LBL and bivariate LBL‐2B. In most settings, bivariate LBL‐BC performs the best. In only two situations, bivariate LBL‐BC has similar performance—when the two phenotypes are (1) weakly or not correlated and the target haplotype affects the binary phenotype only and (2) strongly positively correlated and the target haplotype affects both phenotypes in positive direction. Finally, we apply the method to a data set on lung cancer and nicotine dependence and detect several haplotypes including a rare one.</p>
Statistics in Medicine, EarlyView. Detecting rare haplotype association with two correlated phenotypes of binary and continuous typesdoi:10.1002/sim.8877Statistics in Medicine2021-01-12T10:54:29-08:00Statistics in Medicine10.1002/sim.8877https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8877?af=RRESEARCH ARTICLEInformation content of stepped wedge designs with unequal cluster‐period sizes in linear mixed models: Informing incomplete designsIn practice, stepped wedge trials frequently include clusters of differing sizes. However, investigations into the theoretical aspects of stepped wedge designs have, until recently, typically assumed equal numbers of subjects in each cluster and in each period. The information content of the cluster‐period cells, clusters, and periods of stepped wedge designs has previously been investigated assuming equal cluster‐period sizes, and has shown that incomplete stepped wedge designs may be efficient alternatives to the full stepped wedge. How this changes when cluster‐period sizes are not equal is unknown, and we investigate this here. Working within the linear mixed model framework, we show that the information contributed by design components (clusters, sequences, and periods) does depend on the sizes of each cluster‐period. Using a particular trial that assessed the impact of an individual education intervention on log‐length of stay in rehabilitation units, we demonstrate how strongly the efficiency of incomplete designs depends on which cells are excluded: smaller incomplete designs may be more powerful than alternative incomplete designs that include a greater total number of participants. This also serves to demonstrate how the pattern of information content can be used to inform a set of incomplete designs to be considered as alternatives to the complete stepped wedge design. Our theoretical results for the information content can be extended to a broad class of longitudinal (ie, multiple period) cluster randomized trial designs.
Jessica Kasza,
Rhys Bowden,
Andrew B. Forbes
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8867?af=R
<p>In practice, stepped wedge trials frequently include clusters of differing sizes. However, investigations into the theoretical aspects of stepped wedge designs have, until recently, typically assumed equal numbers of subjects in each cluster and in each period. The information content of the cluster‐period cells, clusters, and periods of stepped wedge designs has previously been investigated assuming equal cluster‐period sizes, and has shown that incomplete stepped wedge designs may be efficient alternatives to the full stepped wedge. How this changes when cluster‐period sizes are not equal is unknown, and we investigate this here. Working within the linear mixed model framework, we show that the information contributed by design components (clusters, sequences, and periods) does depend on the sizes of each cluster‐period. Using a particular trial that assessed the impact of an individual education intervention on log‐length of stay in rehabilitation units, we demonstrate how strongly the efficiency of incomplete designs depends on which cells are excluded: smaller incomplete designs may be more powerful than alternative incomplete designs that include a greater total number of participants. This also serves to demonstrate how the pattern of information content can be used to inform a set of incomplete designs to be considered as alternatives to the complete stepped wedge design. Our theoretical results for the information content can be extended to a broad class of longitudinal (ie, multiple period) cluster randomized trial designs.</p>
Statistics in Medicine, EarlyView. Information content of stepped wedge designs with unequal cluster‐period sizes in linear mixed models: Informing incomplete designsdoi:10.1002/sim.8867Statistics in Medicine2021-01-12T10:54:11-08:00Statistics in Medicine10.1002/sim.8867https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8867?af=RRESEARCH ARTICLEScale mixture of skew‐normal linear mixed models with within‐subject serial dependenceIn longitudinal studies, repeated measures are collected over time and hence they tend to be serially correlated. These studies are commonly analyzed using linear mixed models (LMMs), and in this article we consider an extension of the skew‐normal/independent LMM, where the error term has a dependence structure, such as damped exponential correlation or autoregressive correlation of order p. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously when continuous repeated measures are serially correlated. For this robust model, we present an efficient EM‐type algorithm for parameters estimation via maximum likelihood and the observed information matrix is derived analytically to account for standard errors. The methodology is illustrated through an application to schizophrenia data and some simulation studies. The proposed algorithm and methods are implemented in the new R package skewlmm.
Fernanda L. Schumacher,
Victor H. Lachos,
Larissa A. Matos
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8870?af=R
<p>In longitudinal studies, repeated measures are collected over time and hence they tend to be serially correlated. These studies are commonly analyzed using linear mixed models (LMMs), and in this article we consider an extension of the skew‐normal/independent LMM, where the error term has a dependence structure, such as damped exponential correlation or autoregressive correlation of order <i>p</i>. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously when continuous repeated measures are serially correlated. For this robust model, we present an efficient EM‐type algorithm for parameters estimation via maximum likelihood and the observed information matrix is derived analytically to account for standard errors. The methodology is illustrated through an application to schizophrenia data and some simulation studies. The proposed algorithm and methods are implemented in the new <span style="font-family:sans-serif">R</span> package <i>skewlmm</i>.</p>
Statistics in Medicine, EarlyView. Scale mixture of skew‐normal linear mixed models with within‐subject serial dependencedoi:10.1002/sim.8870Statistics in Medicine2021-01-12T10:42:36-08:00Statistics in Medicine10.1002/sim.8870https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8870?af=RRESEARCH ARTICLEThe optimal design of clinical trials with potential biomarker effects: A novel computational approachAs a future trend of healthcare, personalized medicine tailors medical treatments to individual patients. It requires to identify a subset of patients with the best response to treatment. The subset can be defined by a biomarker (eg, expression of a gene) and its cutoff value. Topics on subset identification have received massive attention. There are over two million hits by keyword searches on Google Scholar. However, designing clinical trials that utilize the discovered uncertain subsets/biomarkers is not trivial and rarely discussed in the literature. This leads to a gap between research results and real‐world drug development. To fill in this gap, we formulate the problem of clinical trial design into an optimization problem involving high‐dimensional integration, and propose a novel computational solution based on Monte Carlo and smoothing methods. Our method utilizes the modern techniques of general purpose computing on graphics processing units for large‐scale parallel computing. Compared to a published method in three‐dimensional problems, our approach is more accurate and 133 times faster. This advantage increases when dimensionality increases. Our method is scalable to higher dimensional problems since the precision bound of our estimated study power is a finite number not affected by dimensionality. To design clinical trials incorporating the potential biomarkers, users can use our software "DesignCTPB". This software can be found on Github and will be available as an R package on CRAN. Although our research is motivated by the design of clinical trials, the method can be used widely to solve other optimization problems involving high‐dimensional integration.
Yitao Lu,
Julie Zhou,
Li Xing,
Xuekui Zhang
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8868?af=R
<p>As a future trend of healthcare, personalized medicine tailors medical treatments to individual patients. It requires to identify a subset of patients with the best response to treatment. The subset can be defined by a biomarker (eg, expression of a gene) and its cutoff value. Topics on subset identification have received massive attention. There are over two million hits by keyword searches on Google Scholar. However, designing clinical trials that utilize the discovered uncertain subsets/biomarkers is not trivial and rarely discussed in the literature. This leads to a gap between research results and real‐world drug development. To fill in this gap, we formulate the problem of clinical trial design into an optimization problem involving high‐dimensional integration, and propose a novel computational solution based on Monte Carlo and smoothing methods. Our method utilizes the modern techniques of general purpose computing on graphics processing units for large‐scale parallel computing. Compared to a published method in three‐dimensional problems, our approach is more accurate and 133 times faster. This advantage increases when dimensionality increases. Our method is scalable to higher dimensional problems since the precision bound of our estimated study power is a finite number not affected by dimensionality. To design clinical trials incorporating the potential biomarkers, users can use our software "DesignCTPB". This software can be found on Github and will be available as an R package on CRAN. Although our research is motivated by the design of clinical trials, the method can be used widely to solve other optimization problems involving high‐dimensional integration.</p>
Statistics in Medicine, EarlyView. The optimal design of clinical trials with potential biomarker effects: A novel computational approachdoi:10.1002/sim.8868Statistics in Medicine2021-01-11T12:10:30-08:00Statistics in Medicine10.1002/sim.8868https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8868?af=RRESEARCH ARTICLEFlexible multivariate joint model of longitudinal intensity and binary process for medical monitoring of frequently collected data
A frequent problem in longitudinal studies is that data may be assessed at subject‐selected, irregularly spaced time‐points, resulting in highly unbalanced outcome data, inducing bias, especially if availability of data is directly related to outcome. Our aim was to develop a multivariate joint model in a mixed outcomes framework to minimize irregular sampling bias. We demonstrate using blood glucose monitoring throughout pregnancy and risk of preterm birth among women with type 1 diabetes mellitus. Blood glucose measurements were unequally spaced and intensity of sampling varied between and within individuals over time. Multivariate linear mixed effects submodel for the longitudinal outcome (blood glucose), Poisson model for the intensity of glucose sampling, and logistic regression model for binary process (preterm birth) were specified. Association between models is captured through shared random effects. Markov chain Monte Carlo methods were used to fit the model. The multivariate joint model provided better prediction, compared with a joint model with a multivariate linear mixed effects submodel (ignoring intensity of glucose sampling) and a two‐stage model. Most association parameters were significant in the preterm birth outcome model, signifying improvement of predictive ability of the binary endpoint by sharing random effects between glucose monitoring and preterm birth. A simulation study is presented to illustrate the effectiveness of the multivariate joint modeling approach.
Resmi Gupta,
Jane C. Khoury,
Mekibib Altaye,
Roman Jandarov,
Rhonda D. Szczesniak
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8875?af=R
<p>A frequent problem in longitudinal studies is that data may be assessed at subject‐selected, irregularly spaced time‐points, resulting in highly unbalanced outcome data, inducing bias, especially if availability of data is directly related to outcome. Our aim was to develop a multivariate joint model in a mixed outcomes framework to minimize irregular sampling bias. We demonstrate using blood glucose monitoring throughout pregnancy and risk of preterm birth among women with type 1 diabetes mellitus. Blood glucose measurements were unequally spaced and intensity of sampling varied between and within individuals over time. Multivariate linear mixed effects submodel for the longitudinal outcome (blood glucose), Poisson model for the intensity of glucose sampling, and logistic regression model for binary process (preterm birth) were specified. Association between models is captured through shared random effects. Markov chain Monte Carlo methods were used to fit the model. The multivariate joint model provided better prediction, compared with a joint model with a multivariate linear mixed effects submodel (ignoring intensity of glucose sampling) and a two‐stage model. Most association parameters were significant in the preterm birth outcome model, signifying improvement of predictive ability of the binary endpoint by sharing random effects between glucose monitoring and preterm birth. A simulation study is presented to illustrate the effectiveness of the multivariate joint modeling approach.</p>
Statistics in Medicine, EarlyView. Flexible multivariate joint model of longitudinal intensity and binary process for medical monitoring of frequently collected datadoi:10.1002/sim.8875Statistics in Medicine2021-01-10T11:57:08-08:00Statistics in Medicine10.1002/sim.8875https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8875?af=RRESEARCH ARTICLEAn alternative formulation of Coxian phase‐type distributions with covariates: Application to emergency department length of
stay
In this article, we present a new methodology to model patient transitions and length of stay in the emergency department using a series of conditional Coxian phase‐type distributions, with covariates. We reformulate the Coxian models (standard Coxian, Coxian with multiple absorbing states, joint Coxian, and conditional Coxian) to take into account heterogeneity in patient characteristics such as arrival mode, time of admission, and age. The approach differs from previous research in that it reduces the computational time, and it allows the inclusion of patient covariate information directly into the model. The model is applied to emergency department data from University Hospital Limerick in Ireland, where we find broad agreement with a number of commonly used survival models (parametric Weibull and log‐normal regression models and the semiparametric Cox proportional hazards model).
Jean Rizk,
Cathal Walsh,
Kevin Burke
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8860?af=R
<p>In this article, we present a new methodology to model patient transitions and length of stay in the emergency department using a series of conditional Coxian phase‐type distributions, with covariates. We reformulate the Coxian models (standard Coxian, Coxian with multiple absorbing states, joint Coxian, and conditional Coxian) to take into account heterogeneity in patient characteristics such as arrival mode, time of admission, and age. The approach differs from previous research in that it reduces the computational time, and it allows the inclusion of patient covariate information directly into the model. The model is applied to emergency department data from University Hospital Limerick in Ireland, where we find broad agreement with a number of commonly used survival models (parametric Weibull and log‐normal regression models and the semiparametric Cox proportional hazards model).</p>
Statistics in Medicine, EarlyView. An alternative formulation of Coxian phase‐type distributions with covariates: Application to emergency department length of
staydoi:10.1002/sim.8860Statistics in Medicine2021-01-10T11:47:07-08:00Statistics in Medicine10.1002/sim.8860https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8860?af=RRESEARCH ARTICLEEstimating the marginal hazard ratio by simultaneously using a set of propensity score models: A multiply robust approach
The inverse probability weighted Cox model is frequently used to estimate the marginal hazard ratio. Its validity requires a crucial condition that the propensity score model be correctly specified. To provide protection against misspecification of the propensity score model, we propose a weighted estimation method rooted in the empirical likelihood theory. The proposed estimator is multiply robust in that it is guaranteed to be consistent when a set of postulated propensity score models contains a correctly specified model. Our simulation studies demonstrate satisfactory finite sample performance of the proposed method in terms of consistency and efficiency. We apply the proposed method to compare the risk of postoperative hospitalization between sleeve gastrectomy and Roux‐en‐Y gastric bypass using data from a large medical claims and billing database. We further extend the development to multisite studies to enable each site to postulate multiple site‐specific propensity score models.
Di Shu,
Peisong Han,
Rui Wang,
Sengwee Toh
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8837?af=R
<p>The inverse probability weighted Cox model is frequently used to estimate the marginal hazard ratio. Its validity requires a crucial condition that the propensity score model be correctly specified. To provide protection against misspecification of the propensity score model, we propose a weighted estimation method rooted in the empirical likelihood theory. The proposed estimator is multiply robust in that it is guaranteed to be consistent when a set of postulated propensity score models contains a correctly specified model. Our simulation studies demonstrate satisfactory finite sample performance of the proposed method in terms of consistency and efficiency. We apply the proposed method to compare the risk of postoperative hospitalization between sleeve gastrectomy and Roux‐en‐Y gastric bypass using data from a large medical claims and billing database. We further extend the development to multisite studies to enable each site to postulate multiple site‐specific propensity score models.</p>
Statistics in Medicine, EarlyView. Estimating the marginal hazard ratio by simultaneously using a set of propensity score models: A multiply robust approachdoi:10.1002/sim.8837Statistics in Medicine2021-01-06T08:04:14-08:00Statistics in Medicine10.1002/sim.8837https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8837?af=RRESEARCH ARTICLECause‐specific quantile regression on inactivity timeIn time‐to‐event analysis, the traditional summary measures have been based on the hazard function, survival function, quantile event time, restricted mean event time, and residual lifetime. Under competing risks, furthermore, typical summary measures have been the cause‐specific hazard function and cumulative incidence function. Recently inactivity time has recaptured attention in the literature, being interpreted as life lost. In this paper, we further interpret it as quality of life reduced and time period after transition to a drug, and propose a quantile regression model to associate the inactivity time with potential predictors under competing risks. We define the proper cumulative distribution function of the inactivity time distribution for each specific event type among those subjects who experience the same type of events during a follow‐up period. A score function‐type estimating equation is developed and asymptotic properties of the regression coefficient estimators are derived by assuming that competing events are censored at their occurrence times as in the cause‐specific hazard analysis. The proposed approach reduces to a regular quantile regression on the inactivity time without competing risks when all types of competing events are collapsed into the same type. Due to difficulty in estimating the improper probability density function of the cause‐specific inactivity distribution to evaluate the variance of the quantiles, a computationally efficient perturbation method is adopted to infer the regression coefficients. Simulation results show that our proposed method works well under the assumed finite sample settings. The proposed method is illustrated with a real dataset from a breast cancer study.
Yichen Jia,
Jong‐Hyeon Jeong
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8871?af=R
<p>In time‐to‐event analysis, the traditional summary measures have been based on the hazard function, survival function, quantile event time, restricted mean event time, and residual lifetime. Under competing risks, furthermore, typical summary measures have been the cause‐specific hazard function and cumulative incidence function. Recently inactivity time has recaptured attention in the literature, being interpreted as life lost. In this paper, we further interpret it as quality of life reduced and time period after transition to a drug, and propose a quantile regression model to associate the inactivity time with potential predictors under competing risks. We define the proper cumulative distribution function of the inactivity time distribution for each specific event type among those subjects who experience the same type of events during a follow‐up period. A score function‐type estimating equation is developed and asymptotic properties of the regression coefficient estimators are derived by assuming that competing events are censored at their occurrence times as in the cause‐specific hazard analysis. The proposed approach reduces to a regular quantile regression on the inactivity time without competing risks when all types of competing events are collapsed into the same type. Due to difficulty in estimating the improper probability density function of the cause‐specific inactivity distribution to evaluate the variance of the quantiles, a computationally efficient perturbation method is adopted to infer the regression coefficients. Simulation results show that our proposed method works well under the assumed finite sample settings. The proposed method is illustrated with a real dataset from a breast cancer study.</p>
Statistics in Medicine, EarlyView. Cause‐specific quantile regression on inactivity timedoi:10.1002/sim.8871Statistics in Medicine2021-01-06T06:37:39-08:00Statistics in Medicine10.1002/sim.8871https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8871?af=RRESEARCH ARTICLEA depth‐based global envelope test for comparing two groups of functions with applications to biomedical data
Abstract
Functional data are commonly observed in many emerging biomedical fields and their analysis is an exciting developing area in statistics. Numerous statistical methods, such as principal components, analysis of variance, and linear regression, have been extended to functional data. The statistical analysis of functions can be significantly improved using nonparametric and robust estimators. New ideas of depth for functional data have been proposed in recent years and can be extended to image data. They provide a way of ordering curves or images from center‐outward, and of defining robust order statistics in a functional context. In this paper we develop depth‐based global envelope tests for comparing two groups of functions or images. In addition to providing global P‐values, the proposed envelope test can be displayed graphically and indicates the specific portion(s) of the functional data (eg, in pixels or in time) that may have led to rejection of the null hypothesis. We show in a simulation study the performance of the envelope test in terms of empirical power and size in different scenarios. The proposed depth‐based global approach has good power even for small differences and is robust to outliers. The methodology introduced is applied to test whether children with normal and low birth weight have similar growth pattern. We also analyzed a brain image dataset consisting of positron emission tomography scans of severe depressed patients and healthy controls. The global envelope test was used to find and visualize differences between the two groups.
Sara Lopez‐Pintado,
Kun Qian
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8861?af=R
<h2>Abstract</h2>
<p>Functional data are commonly observed in many emerging biomedical fields and their analysis is an exciting developing area in statistics. Numerous statistical methods, such as principal components, analysis of variance, and linear regression, have been extended to functional data. The statistical analysis of functions can be significantly improved using nonparametric and robust estimators. New ideas of depth for functional data have been proposed in recent years and can be extended to image data. They provide a way of ordering curves or images from center‐outward, and of defining robust order statistics in a functional context. In this paper we develop depth‐based global envelope tests for comparing two groups of functions or images. In addition to providing global <i>P</i>‐values, the proposed envelope test can be displayed graphically and indicates the specific portion(s) of the functional data (eg, in pixels or in time) that may have led to rejection of the null hypothesis. We show in a simulation study the performance of the envelope test in terms of empirical power and size in different scenarios. The proposed depth‐based global approach has good power even for small differences and is robust to outliers. The methodology introduced is applied to test whether children with normal and low birth weight have similar growth pattern. We also analyzed a brain image dataset consisting of positron emission tomography scans of severe depressed patients and healthy controls. The global envelope test was used to find and visualize differences between the two groups.</p>Statistics in Medicine, EarlyView. A depth‐based global envelope test for comparing two groups of functions with applications to biomedical datadoi:10.1002/sim.8861Statistics in Medicine2021-01-06T06:22:39-08:00Statistics in Medicine10.1002/sim.8861https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8861?af=RRESEARCH ARTICLEExtending the Mann‐Whitney‐Wilcoxon rank sum test to survey data for comparing mean ranksStatistical methods for analysis of survey data have been developed to facilitate research. More recently, Lumley and Scott (2013) developed an approach to extend the Mann‐Whitney‐Wilcoxon (MWW) rank sum test to survey data. Their approach focuses on the null of equal distribution. In many studies, the MWW test is called for when two‐sample t‐tests (with or without equal variance assumed) fail to provide meaningful results, as they are highly sensitive to outliers. In such situations, the null of equal distribution is too restrictive, as interest lies in comparing centers of groups. In this article, we develop an approach to extend the MWW test to survey data to test the null of equal mean rank. Although not as popular as the mean and median, the mean rank is also a meaningful measure of the center of a distribution and is the same as the median for a symmetric distribution. We illustrate the proposed approach and show major differences with Lumley and Scott's alternative using both real and simulated data.
Tuo Lin,
Tian Chen,
Jinyuan Liu,
Xin M. Tu
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8865?af=R
<p>Statistical methods for analysis of survey data have been developed to facilitate research. More recently, Lumley and Scott (2013) developed an approach to extend the Mann‐Whitney‐Wilcoxon (MWW) rank sum test to survey data. Their approach focuses on the null of equal distribution. In many studies, the MWW test is called for when two‐sample t‐tests (with or without equal variance assumed) fail to provide meaningful results, as they are highly sensitive to outliers. In such situations, the null of equal distribution is too restrictive, as interest lies in comparing centers of groups. In this article, we develop an approach to extend the MWW test to survey data to test the null of equal mean rank. Although not as popular as the mean and median, the mean rank is also a meaningful measure of the center of a distribution and is the same as the median for a symmetric distribution. We illustrate the proposed approach and show major differences with Lumley and Scott's alternative using both real and simulated data.</p>
Statistics in Medicine, EarlyView. Extending the Mann‐Whitney‐Wilcoxon rank sum test to survey data for comparing mean ranksdoi:10.1002/sim.8865Statistics in Medicine2021-01-04T10:26:27-08:00Statistics in Medicine10.1002/sim.8865https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8865?af=RRESEARCH ARTICLEUsing propensity scores to estimate effects of treatment initiation decisions: State of the science
Abstract
Confounding can cause substantial bias in nonexperimental studies that aim to estimate causal effects. Propensity score methods allow researchers to reduce bias from measured confounding by summarizing the distributions of many measured confounders in a single score based on the probability of receiving treatment. This score can then be used to mitigate imbalances in the distributions of these measured confounders between those who received the treatment of interest and those in the comparator population, resulting in less biased treatment effect estimates. This methodology was formalized by Rosenbaum and Rubin in 1983 and, since then, has been used increasingly often across a wide variety of scientific disciplines. In this review article, we provide an overview of propensity scores in the context of real‐world evidence generation with a focus on their use in the setting of single treatment decisions, that is, choosing between two therapeutic options. We describe five aspects of propensity score analysis: alignment with the potential outcomes framework, implications for study design, estimation procedures, implementation options, and reporting. We add context to these concepts by highlighting how the types of comparator used, the implementation method, and balance assessment techniques have changed over time. Finally, we discuss evolving applications of propensity scores.
Michael Webster‐Clark,
Til Stürmer,
Tiansheng Wang,
Kenneth Man,
Danica Marinac‐Dabic,
Kenneth J. Rothman,
Alan R. Ellis,
Mugdha Gokhale,
Mark Lunt,
Cynthia Girman,
Robert J. Glynn
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8866?af=R
<h2>Abstract</h2>
<p>Confounding can cause substantial bias in nonexperimental studies that aim to estimate causal effects. Propensity score methods allow researchers to reduce bias from measured confounding by summarizing the distributions of many measured confounders in a single score based on the probability of receiving treatment. This score can then be used to mitigate imbalances in the distributions of these measured confounders between those who received the treatment of interest and those in the comparator population, resulting in less biased treatment effect estimates. This methodology was formalized by Rosenbaum and Rubin in 1983 and, since then, has been used increasingly often across a wide variety of scientific disciplines. In this review article, we provide an overview of propensity scores in the context of real‐world evidence generation with a focus on their use in the setting of single treatment decisions, that is, choosing between two therapeutic options. We describe five aspects of propensity score analysis: alignment with the potential outcomes framework, implications for study design, estimation procedures, implementation options, and reporting. We add context to these concepts by highlighting how the types of comparator used, the implementation method, and balance assessment techniques have changed over time. Finally, we discuss evolving applications of propensity scores.</p>
Statistics in Medicine, EarlyView. Using propensity scores to estimate effects of treatment initiation decisions: State of the sciencedoi:10.1002/sim.8866Statistics in Medicine2020-12-29T07:50:25-08:00Statistics in Medicine10.1002/sim.8866https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8866?af=RRESEARCH ARTICLERobust Wald‐type tests under random censoringRandomly censored survival data are frequently encountered in biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to get conclusive inference but the existing likelihood‐based tests, under a fully parametric model, are extremely nonrobust against outliers in the data. Although there exists a few robust estimators given randomly censored data, there is hardly any robust testing procedure available in the literature in this context. One of the major difficulties here is the construction of a suitable consistent estimator of the asymptotic variance of robust estimators, since the latter is a function of the unknown censoring distribution. In this article, we take the first step in this direction by proposing a consistent estimator of asymptotic variance of the M‐estimators based on randomly censored data without any assumption on the censoring scheme. We then describe and study a class of robust Wald‐type tests for parametric statistical hypothesis, both simple as well as composite, under such a set‐up. Robust tests for comparing two independent randomly censored samples and robust tests against one sided alternatives are also discussed. Their advantages and usefulness are demonstrated for the tests based on the minimum density power divergence estimators and illustrated with clinical trials and other medical data.
Abhik Ghosh,
Ayanendranath Basu,
Leandro Pardo
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8841?af=R
<p>Randomly censored survival data are frequently encountered in biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to get conclusive inference but the existing likelihood‐based tests, under a fully parametric model, are extremely nonrobust against outliers in the data. Although there exists a few robust estimators given randomly censored data, there is hardly any robust testing procedure available in the literature in this context. One of the major difficulties here is the construction of a suitable consistent estimator of the asymptotic variance of robust estimators, since the latter is a function of the unknown censoring distribution. In this article, we take the first step in this direction by proposing a consistent estimator of asymptotic variance of the M‐estimators based on randomly censored data without any assumption on the censoring scheme. We then describe and study a class of robust Wald‐type tests for parametric statistical hypothesis, both simple as well as composite, under such a set‐up. Robust tests for comparing two independent randomly censored samples and robust tests against one sided alternatives are also discussed. Their advantages and usefulness are demonstrated for the tests based on the minimum density power divergence estimators and illustrated with clinical trials and other medical data.</p>
Statistics in Medicine, EarlyView. Robust Wald‐type tests under random censoringdoi:10.1002/sim.8841Statistics in Medicine2020-12-28T10:17:40-08:00Statistics in Medicine10.1002/sim.8841https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8841?af=RRESEARCH ARTICLEBayesian meta‐analysis models for cross cancer genomic investigation of pleiotropic effects using group structure
Abstract
An increasing number of genome‐wide association studies (GWAS) summary statistics is made available to the scientific community. Exploiting these results from multiple phenotypes would permit identification of novel pleiotropic associations. In addition, incorporating prior biological information in GWAS such as group structure information (gene or pathway) has shown some success in classical GWAS approaches. However, this has not been widely explored in the context of pleiotropy. We propose a Bayesian meta‐analysis approach (termed GCPBayes) that uses summary‐level GWAS data across multiple phenotypes to detect pleiotropy at both group‐level (gene or pathway) and within group (eg, at the SNP level). We consider both continuous and Dirac spike and slab priors for group selection. We also use a Bayesian sparse group selection approach with hierarchical spike and slab priors that enables us to select important variables both at the group level and within group. GCPBayes uses a Bayesian statistical framework based on Markov chain Monte Carlo (MCMC) Gibbs sampling. It can be applied to multiple types of phenotypes for studies with overlapping or nonoverlapping subjects, and takes into account heterogeneity in the effect size and allows for the opposite direction of the genetic effects across traits. Simulations show that the proposed methods outperform benchmark approaches such as ASSET and CPBayes in the ability to retrieve pleiotropic associations at both SNP and gene‐levels. To illustrate the GCPBayes method, we investigate the shared genetic effects between thyroid cancer and breast cancer in candidate pathways.
Taban Baghfalaki,
Pierre‐Emmanuel Sugier,
Therese Truong,
Anthony N. Pettitt,
Kerrie Mengersen,
Benoit Liquet
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8855?af=R
<h2>Abstract</h2>
<p>An increasing number of genome‐wide association studies (GWAS) summary statistics is made available to the scientific community. Exploiting these results from multiple phenotypes would permit identification of novel pleiotropic associations. In addition, incorporating prior biological information in GWAS such as group structure information (gene or pathway) has shown some success in classical GWAS approaches. However, this has not been widely explored in the context of pleiotropy. We propose a Bayesian meta‐analysis approach (termed GCPBayes) that uses summary‐level GWAS data across multiple phenotypes to detect pleiotropy at both group‐level (gene or pathway) and within group (eg, at the SNP level). We consider both continuous and Dirac spike and slab priors for group selection. We also use a Bayesian sparse group selection approach with hierarchical spike and slab priors that enables us to select important variables both at the group level and within group. GCPBayes uses a Bayesian statistical framework based on Markov chain Monte Carlo (MCMC) Gibbs sampling. It can be applied to multiple types of phenotypes for studies with overlapping or nonoverlapping subjects, and takes into account heterogeneity in the effect size and allows for the opposite direction of the genetic effects across traits. Simulations show that the proposed methods outperform benchmark approaches such as ASSET and CPBayes in the ability to retrieve pleiotropic associations at both SNP and gene‐levels. To illustrate the GCPBayes method, we investigate the shared genetic effects between thyroid cancer and breast cancer in candidate pathways.</p>
Statistics in Medicine, EarlyView. Bayesian meta‐analysis models for cross cancer genomic investigation of pleiotropic effects using group structuredoi:10.1002/sim.8855Statistics in Medicine2020-12-27T03:16:35-08:00Statistics in Medicine10.1002/sim.8855https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8855?af=RRESEARCH ARTICLEComparing methods for estimating patient‐specific treatment effects in individual patient data meta‐analysis
Abstract
Meta‐analysis of individual patient data (IPD) is increasingly used to synthesize data from multiple trials. IPD meta‐analysis offers several advantages over meta‐analyzing aggregate data, including the capacity to individualize treatment recommendations. Trials usually collect information on many patient characteristics. Some of these covariates may strongly interact with treatment (and thus be associated with treatment effect modification) while others may have little effect. It is currently unclear whether a systematic approach to the selection of treatment‐covariate interactions in an IPD meta‐analysis can lead to better estimates of patient‐specific treatment effects. We aimed to answer this question by comparing in simulations the standard approach to IPD meta‐analysis (no variable selection, all treatment‐covariate interactions included in the model) with six alternative methods: stepwise regression, and five regression methods that perform shrinkage on treatment‐covariate interactions, that is, least absolute shrinkage and selection operator (LASSO), ridge, adaptive LASSO, Bayesian LASSO, and stochastic search variable selection. Exploring a range of scenarios, we found that shrinkage methods performed well for both continuous and dichotomous outcomes, for a variety of settings. In most scenarios, these methods gave lower mean squared error of the patient‐specific treatment effect as compared with the standard approach and stepwise regression. We illustrate the application of these methods in two datasets from cardiology and psychiatry. We recommend that future IPD meta‐analysis that aim to estimate patient‐specific treatment effects using multiple effect modifiers should use shrinkage methods, whereas stepwise regression should be avoided.
Michael Seo,
Ian R. White,
Toshi A. Furukawa,
Hissei Imai,
Marco Valgimigli,
Matthias Egger,
Marcel Zwahlen,
Orestis Efthimiou
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8859?af=R
<h2>Abstract</h2>
<p>Meta‐analysis of individual patient data (IPD) is increasingly used to synthesize data from multiple trials. IPD meta‐analysis offers several advantages over meta‐analyzing aggregate data, including the capacity to individualize treatment recommendations. Trials usually collect information on many patient characteristics. Some of these covariates may strongly interact with treatment (and thus be associated with treatment effect modification) while others may have little effect. It is currently unclear whether a systematic approach to the selection of treatment‐covariate interactions in an IPD meta‐analysis can lead to better estimates of patient‐specific treatment effects. We aimed to answer this question by comparing in simulations the standard approach to IPD meta‐analysis (no variable selection, all treatment‐covariate interactions included in the model) with six alternative methods: stepwise regression, and five regression methods that perform shrinkage on treatment‐covariate interactions, that is, least absolute shrinkage and selection operator (LASSO), ridge, adaptive LASSO, Bayesian LASSO, and stochastic search variable selection. Exploring a range of scenarios, we found that shrinkage methods performed well for both continuous and dichotomous outcomes, for a variety of settings. In most scenarios, these methods gave lower mean squared error of the patient‐specific treatment effect as compared with the standard approach and stepwise regression. We illustrate the application of these methods in two datasets from cardiology and psychiatry. We recommend that future IPD meta‐analysis that aim to estimate patient‐specific treatment effects using multiple effect modifiers should use shrinkage methods, whereas stepwise regression should be avoided.</p>
Statistics in Medicine, EarlyView. Comparing methods for estimating patient‐specific treatment effects in individual patient data meta‐analysisdoi:10.1002/sim.8859Statistics in Medicine2020-12-27T03:06:26-08:00Statistics in Medicine10.1002/sim.8859https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8859?af=RRESEARCH ARTICLEA longitudinal Bayesian mixed effects model with hurdle Conway‐Maxwell‐Poisson distributionDental caries (i.e., cavities) is one of the most common chronic childhood diseases and may continue to progress throughout a person's lifetime. The Iowa Fluoride Study (IFS) was designed to investigate the effects of various fluoride, dietary and nondietary factors on the progression of dental caries among a cohort of Iowa school children. We develop a mixed effects model to perform a comprehensive analysis of the longitudinal clustered data of IFS at ages 5, 9, 13, and 17. We combine a Bayesian hurdle framework with the Conway‐Maxwell‐Poisson regression model, which can account for both excessive zeros and various levels of dispersion. A hierarchical shrinkage prior distribution is used to share the temporal information for predictors in the fixed‐effects model. The dependence among teeth of each individual child is modeled through a sparse covariance structure of the random effects across time. Moreover, we obtain the parameter estimates and credible intervals from a Gibbs sampler. Simulation studies are conducted to assess the accuracy and effectiveness of our statistical methodology. The results of this article provide novel tools to statistical practitioners and offer fresh insights to dental researchers on effects of various risk and protective factors on caries progression.
Tong Kang,
Jeremy Gaskins,
Steven Levy,
Somnath Datta
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8844?af=R
<p>Dental caries (i.e., cavities) is one of the most common chronic childhood diseases and may continue to progress throughout a person's lifetime. The Iowa Fluoride Study (IFS) was designed to investigate the effects of various fluoride, dietary and nondietary factors on the progression of dental caries among a cohort of Iowa school children. We develop a mixed effects model to perform a comprehensive analysis of the longitudinal clustered data of IFS at ages 5, 9, 13, and 17. We combine a Bayesian hurdle framework with the Conway‐Maxwell‐Poisson regression model, which can account for both excessive zeros and various levels of dispersion. A hierarchical shrinkage prior distribution is used to share the temporal information for predictors in the fixed‐effects model. The dependence among teeth of each individual child is modeled through a sparse covariance structure of the random effects across time. Moreover, we obtain the parameter estimates and credible intervals from a Gibbs sampler. Simulation studies are conducted to assess the accuracy and effectiveness of our statistical methodology. The results of this article provide novel tools to statistical practitioners and offer fresh insights to dental researchers on effects of various risk and protective factors on caries progression.</p>
Statistics in Medicine, EarlyView. A longitudinal Bayesian mixed effects model with hurdle Conway‐Maxwell‐Poisson distributiondoi:10.1002/sim.8844Statistics in Medicine2020-12-23T08:25:28-08:00Statistics in Medicine10.1002/sim.8844https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8844?af=RRESEARCH ARTICLEA machine learning compatible method for ordinal propensity score stratification and matching
Although machine learning techniques that estimate propensity scores for observational studies with multivalued treatments have advanced rapidly in recent years, the development of propensity score adjustment techniques has not kept pace. While machine learning propensity models provide numerous benefits, they do not produce a single variable balancing score that can be used for propensity score stratification and matching. This issue motivates the development of a flexible ordinal propensity scoring methodology that does not require parametric assumptions for the propensity model. The proposed method fits a one‐parameter power function to the cumulative distribution function (CDF) of the generalized propensity score (GPS) vector resulting from any machine learning propensity model, and is henceforth called the GPS‐CDF method. The estimated parameter from the GPS‐CDF method, ã, is a scalar balancing score that can be used to group similar subjects in outcome analyses. Specifically, subjects who received different levels of the treatment are stratified or matched based on their ã value to produce unbiased estimates of the average treatment effect (ATE). Simulation studies presented show remediation of covariate balance, minimal bias in ATEs, and maintain coverage probability. The proposed method is applied to the Mexican‐American Tobacco use in Children (MATCh) study to determine whether an ordinal treatment of exposure to smoking imagery in movies causes cigarette experimentation in Mexican‐American adolescents.
Thomas J. Greene,
Stacia M. DeSantis,
Derek W. Brown,
Anna V. Wilkinson,
Michael D. Swartz
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8846?af=R
<p>Although machine learning techniques that estimate propensity scores for observational studies with multivalued treatments have advanced rapidly in recent years, the development of propensity score adjustment techniques has not kept pace. While machine learning propensity models provide numerous benefits, they do not produce a single variable balancing score that can be used for propensity score stratification and matching. This issue motivates the development of a flexible ordinal propensity scoring methodology that does not require parametric assumptions for the propensity model. The proposed method fits a one‐parameter power function to the cumulative distribution function (CDF) of the generalized propensity score (GPS) vector resulting from any machine learning propensity model, and is henceforth called the GPS‐CDF method. The estimated parameter from the GPS‐CDF method, ã, is a scalar balancing score that can be used to group similar subjects in outcome analyses. Specifically, subjects who received different levels of the treatment are stratified or matched based on their ã value to produce unbiased estimates of the average treatment effect (ATE). Simulation studies presented show remediation of covariate balance, minimal bias in ATEs, and maintain coverage probability. The proposed method is applied to the Mexican‐American Tobacco use in Children (MATCh) study to determine whether an ordinal treatment of exposure to smoking imagery in movies causes cigarette experimentation in Mexican‐American adolescents.</p>
Statistics in Medicine, EarlyView. A machine learning compatible method for ordinal propensity score stratification and matchingdoi:10.1002/sim.8846Statistics in Medicine2020-12-22T02:30:23-08:00Statistics in Medicine10.1002/sim.8846https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8846?af=RRESEARCH ARTICLEOn the properties of the toxicity index and its statistical efficiencyCancer clinical trials typically generate detailed patient toxicity data. The most common measure used to summarize patient toxicity is the maximum grade among all toxicities and it does not fully represent the toxicity burden experienced by patients. In this article, we study the mathematical and statistical properties of the toxicity index (TI), in an effort to address this deficiency. We introduce a total ordering, (T‐rank), that allows us to fully rank the patients according to how frequently they exhibit toxicities, and show that TI is the only measure that preserves the T‐rank among its competitors. Moreover, we propose a Poisson‐Limit model for sparse toxicity data. Under this model, we develop a general two‐sample test, which can be applied to any summary measure for detecting differences among two population of toxicity data. We derive the asymptotic power function of this class as well as the asymptotic relative efficiency (ARE) of the members of the class. We evaluate the ARE formula empirically and show that if the data are drawn from a random Poisson‐Limit model, the TI is more efficient, with high probability, than the maximum and the average summary measures. Finally, we evaluate our method on clinical trial toxicity data and show that TI has a higher power in detecting the differences in toxicity profile among treatments. The results of this article can be applied beyond toxicity modeling, to any problem where one observes a sparse array of scores on subjects and a ranking based on extreme scores is desirable.
Zahra S. Razaee,
Arash A. Amini,
Márcio A. Diniz,
Mourad Tighiouart,
Greg Yothers,
André Rogatko
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8858?af=R
<p>Cancer clinical trials typically generate detailed patient toxicity data. The most common measure used to summarize patient toxicity is the maximum grade among all toxicities and it does not fully represent the toxicity burden experienced by patients. In this article, we study the mathematical and statistical properties of the toxicity index (TI), in an effort to address this deficiency. We introduce a total ordering, (T‐rank), that allows us to fully rank the patients according to how frequently they exhibit toxicities, and show that TI is the only measure that preserves the T‐rank among its competitors. Moreover, we propose a Poisson‐Limit model for sparse toxicity data. Under this model, we develop a general two‐sample test, which can be applied to any summary measure for detecting differences among two population of toxicity data. We derive the asymptotic power function of this class as well as the asymptotic relative efficiency (ARE) of the members of the class. We evaluate the ARE formula empirically and show that if the data are drawn from a random Poisson‐Limit model, the TI is more efficient, with high probability, than the maximum and the average summary measures. Finally, we evaluate our method on clinical trial toxicity data and show that TI has a higher power in detecting the differences in toxicity profile among treatments. The results of this article can be applied beyond toxicity modeling, to any problem where one observes a sparse array of scores on subjects and a ranking based on extreme scores is desirable.</p>
Statistics in Medicine, EarlyView. On the properties of the toxicity index and its statistical efficiencydoi:10.1002/sim.8858Statistics in Medicine2020-12-20T09:20:21-08:00Statistics in Medicine10.1002/sim.8858https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8858?af=RRESEARCH ARTICLEComparisons of zero‐augmented continuous regression models from a Bayesian perspective
Summary
The two‐part model and the Tweedie model are two essential methods to analyze the positive continuous and zero‐augmented responses. Compared with other continuous zero‐augmented models, the zero‐augmented gamma model (ZAG) demonstrates its performance on the mass zeros data. In this article, we compare the Bayesian model for continuous data of excess zeros by considering the ZAG and Tweedie model. We model the mean of both models in a logarithmic scale and the probability of zero within the zero‐augmented model in a logit scale. As previous researchers employed different priors in Bayesian settings for the Tweedie model, by conducting a sensitivity analysis, we select the optimal priors for Tweedie model. Furthermore, we present a simulation study to evaluate the performance of two models in the comparison and apply them to a dataset about the daily fish intake and blood mercury levels from National Health and Nutrition Examination Survey. According to the Watanabe‐Akaike information criterion and leave‐one‐out cross‐validation criterion, the Tweedie model provides higher predictive accuracy for the positive continuous and zero‐augmented data.
Tairan Ye,
Victor H. Lachos,
Xiaojing Wang,
Dipak K. Dey
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8795?af=R
<h2>Summary</h2>
<p>The two‐part model and the Tweedie model are two essential methods to analyze the positive continuous and zero‐augmented responses. Compared with other continuous zero‐augmented models, the zero‐augmented gamma model (ZAG) demonstrates its performance on the mass zeros data. In this article, we compare the Bayesian model for continuous data of excess zeros by considering the ZAG and Tweedie model. We model the mean of both models in a logarithmic scale and the probability of zero within the zero‐augmented model in a logit scale. As previous researchers employed different priors in Bayesian settings for the Tweedie model, by conducting a sensitivity analysis, we select the optimal priors for Tweedie model. Furthermore, we present a simulation study to evaluate the performance of two models in the comparison and apply them to a dataset about the daily fish intake and blood mercury levels from National Health and Nutrition Examination Survey. According to the Watanabe‐Akaike information criterion and leave‐one‐out cross‐validation criterion, the Tweedie model provides higher predictive accuracy for the positive continuous and zero‐augmented data.</p>
Statistics in Medicine, EarlyView. Comparisons of zero‐augmented continuous regression models from a Bayesian perspectivedoi:10.1002/sim.8795Statistics in Medicine2020-12-20T03:43:20-08:00Statistics in Medicine10.1002/sim.8795https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8795?af=RRESEARCH ARTICLEBayesian penalized cumulative logit model for high‐dimensional data with an ordinal responseMany previous studies have identified associations between gene expression, measured using high‐throughput genomic platforms, and quantitative or dichotomous traits. However, we note that health outcome and disease status measurements frequently appear on an ordinal scale, that is, the outcome is categorical but has inherent ordering. Identification of important genes may be useful for developing novel diagnostic and prognostic tools to predict or classify stage of disease. Gene expression data are usually high‐dimensional, meaning that the number of genes is much larger than the sample size or number of patients. Herein we describe some existing frequentist methods for modeling an ordinal response in a high‐dimensional predictor space. Following Tibshirani (1996), who described the LASSO estimate as the Bayesian posterior mode when the regression coefficients have independent Laplace priors, we propose a new approach for high‐dimensional data with an ordinal response that is rooted in the Bayesian paradigm. We show that our proposed Bayesian approach outperforms existing frequentist methods through simulation studies. We then compare the performance of frequentist and Bayesian approaches using a study evaluating progression to hepatocellular carcinoma in hepatitis C infected patients.
Yiran Zhang,
Kellie J. Archer
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8851?af=R
<p>Many previous studies have identified associations between gene expression, measured using high‐throughput genomic platforms, and quantitative or dichotomous traits. However, we note that health outcome and disease status measurements frequently appear on an ordinal scale, that is, the outcome is categorical but has inherent ordering. Identification of important genes may be useful for developing novel diagnostic and prognostic tools to predict or classify stage of disease. Gene expression data are usually high‐dimensional, meaning that the number of genes is much larger than the sample size or number of patients. Herein we describe some existing frequentist methods for modeling an ordinal response in a high‐dimensional predictor space. Following Tibshirani (1996), who described the LASSO estimate as the Bayesian posterior mode when the regression coefficients have independent Laplace priors, we propose a new approach for high‐dimensional data with an ordinal response that is rooted in the Bayesian paradigm. We show that our proposed Bayesian approach outperforms existing frequentist methods through simulation studies. We then compare the performance of frequentist and Bayesian approaches using a study evaluating progression to hepatocellular carcinoma in hepatitis C infected patients.</p>
Statistics in Medicine, EarlyView. Bayesian penalized cumulative logit model for high‐dimensional data with an ordinal responsedoi:10.1002/sim.8851Statistics in Medicine2020-12-18T04:51:37-08:00Statistics in Medicine10.1002/sim.8851https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8851?af=RRESEARCH ARTICLESpatial process decomposition for quantitative imaging biomarkers using multiple images of varying shapesQuantitative imaging biomarkers (QIB) are extracted from medical images in radiomics for a variety of purposes including noninvasive disease detection, cancer monitoring, and precision medicine. The existing methods for QIB extraction tend to be ad hoc and not reproducible. In this article, a general and flexible statistical approach is proposed for handling up to three‐dimensional medical images and reasonably capturing features with respect to specific spatial patterns. In particular, a model‐based spatial process decomposition is developed where the random weights are unique to individual patients for component functions common across patients. Model fitting and selection are based on maximum likelihood, while feature extractions are via optimal prediction of the underlying true image. Simulation studies are conducted to investigate the properties of the proposed methodology. For illustration, a cancer image data set is analyzed and QIBs are extracted in association with a clinical endpoint.
ShengLi Tzeng,
Jun Zhu,
Amy J. Weisman,
Tyler J. Bradshaw,
Robert Jeraj
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8838?af=R
<p>Quantitative imaging biomarkers (QIB) are extracted from medical images in radiomics for a variety of purposes including noninvasive disease detection, cancer monitoring, and precision medicine. The existing methods for QIB extraction tend to be ad hoc and not reproducible. In this article, a general and flexible statistical approach is proposed for handling up to three‐dimensional medical images and reasonably capturing features with respect to specific spatial patterns. In particular, a model‐based spatial process decomposition is developed where the random weights are unique to individual patients for component functions common across patients. Model fitting and selection are based on maximum likelihood, while feature extractions are via optimal prediction of the underlying true image. Simulation studies are conducted to investigate the properties of the proposed methodology. For illustration, a cancer image data set is analyzed and QIBs are extracted in association with a clinical endpoint.</p>
Statistics in Medicine, EarlyView. Spatial process decomposition for quantitative imaging biomarkers using multiple images of varying shapesdoi:10.1002/sim.8838Statistics in Medicine2020-12-17T11:45:13-08:00Statistics in Medicine10.1002/sim.8838https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8838?af=RRESEARCH ARTICLEHeritability curves: A local measure of heritability in family modelsClassical heritability models for family data split the phenotype variance into genetic and environmental components. For instance, the ACE model in twin studies assumes the phenotype variance decomposes as a2 + c2 + e2, representing (additive) genetic effects, common (shared) environment, and residual environment, respectively. However, for some phenotypes it is biologically plausible that the genetic and environmental components may vary over the range of the phenotype. For instance, very large or small values of the phenotype may be caused by “sporadic” environmental factors, whereas the mid‐range phenotype variation may be more under the control of common genetic factors. This article introduces a “local” measure of heritability, where the genetic and environmental components are allowed to depend on the value of the phenotype itself. Our starting point is a general formula for local correlation between two random variables. For estimation purposes, we use a multivariate Gaussian mixture, which is able to capture nonlinear dependence and respects certain distributional constraints. We derive an analytical expression for the associated correlation curve, and show how to decompose the correlation curve into genetic and environmental parts, for instance, a2(y) + c2(y) + e2(y) for the ACE model, where we estimate the components as functions of the phenotype y. Furthermore, our model allows switching, for instance, from the ACE model to the ADE model within the range of the same phenotype. When applied to birth weight (BW) data on Norwegian mother‐father‐child trios, we conclude from the model that low and high BW are less heritable traits than medium BW. We also demonstrate switching between the ACE and ADE model when studying body mass index in adult monozygotic and dizygotic twins.
Geir D. Berentsen,
Francesca Azzolini,
Hans J. Skaug,
Rolv T. Lie,
Håkon K. Gjessing
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8845?af=R
<p>Classical heritability models for family data split the phenotype variance into genetic and environmental components. For instance, the ACE model in twin studies assumes the phenotype variance decomposes as <span>
<i>a</i>
<sup>2</sup> + <i>c</i>
<sup>2</sup> + <i>e</i>
<sup>2</sup>
</span>, representing (additive) genetic effects, common (shared) environment, and residual environment, respectively. However, for some phenotypes it is biologically plausible that the genetic and environmental components may vary over the range of the phenotype. For instance, very large or small values of the phenotype may be caused by “sporadic” environmental factors, whereas the mid‐range phenotype variation may be more under the control of common genetic factors. This article introduces a “local” measure of heritability, where the genetic and environmental components are allowed to depend on the value of the phenotype itself. Our starting point is a general formula for local correlation between two random variables. For estimation purposes, we use a multivariate Gaussian mixture, which is able to capture nonlinear dependence and respects certain distributional constraints. We derive an analytical expression for the associated correlation curve, and show how to decompose the correlation curve into genetic and environmental parts, for instance, <span>
<i>a</i>
<sup>2</sup>(<i>y</i>) + <i>c</i>
<sup>2</sup>(<i>y</i>) + <i>e</i>
<sup>2</sup>(<i>y</i>)</span> for the ACE model, where we estimate the components as functions of the phenotype <i>y</i>. Furthermore, our model allows switching, for instance, from the ACE model to the ADE model within the range of the same phenotype. When applied to birth weight (BW) data on Norwegian mother‐father‐child trios, we conclude from the model that low and high BW are less heritable traits than medium BW. We also demonstrate switching between the ACE and ADE model when studying body mass index in adult monozygotic and dizygotic twins.</p>
Statistics in Medicine, EarlyView. Heritability curves: A local measure of heritability in family modelsdoi:10.1002/sim.8845Statistics in Medicine2020-12-17T11:13:58-08:00Statistics in Medicine10.1002/sim.8845https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8845?af=RRESEARCH ARTICLEAssessing environmental epidemiology questions in practice with a causal inference pipeline: An investigation of the air pollution‐multiple sclerosis relapses
relationship
When addressing environmental health‐related questions, most often, only observational data are collected for ethical or practical reasons. However, the lack of randomized exposure often prevents the comparison of similar groups of exposed and unexposed units. This design barrier leads the environmental epidemiology field to mainly estimate associations between environmental exposures and health outcomes. A recently developed causal inference pipeline was developed to guide researchers interested in estimating the effects of plausible hypothetical interventions for policy recommendations. This article illustrates how this multistaged pipeline can help environmental epidemiologists reconstruct and analyze hypothetical randomized experiments by investigating whether an air pollution reduction intervention decreases the risk of multiple sclerosis relapses in Alsace region, France. The epidemiology literature reports conflicted findings on the relationship between air pollution and multiple sclerosis. Some studies found significant associations, whereas others did not. Two case‐crossover studies reported significant associations between the risk of multiple sclerosis relapses and the exposure to air pollutants in the Alsace region. We use the same study population as these epidemiological studies to illustrate how appealing this causal inference approach is to estimate the effects of hypothetical, but plausible, environmental interventions.
Alice J. Sommer,
Emmanuelle Leray,
Young Lee,
Marie‐Abèle C. Bind
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8843?af=R
<p>When addressing environmental health‐related questions, most often, only observational data are collected for ethical or practical reasons. However, the lack of randomized exposure often prevents the comparison of similar groups of exposed and unexposed units. This design barrier leads the environmental epidemiology field to mainly estimate associations between environmental exposures and health outcomes. A recently developed causal inference pipeline was developed to guide researchers interested in estimating the effects of plausible hypothetical interventions for policy recommendations. This article illustrates how this multistaged pipeline can help environmental epidemiologists reconstruct and analyze hypothetical randomized experiments by investigating whether an air pollution reduction intervention decreases the risk of multiple sclerosis relapses in Alsace region, France. The epidemiology literature reports conflicted findings on the relationship between air pollution and multiple sclerosis. Some studies found significant associations, whereas others did not. Two case‐crossover studies reported significant associations between the risk of multiple sclerosis relapses and the exposure to air pollutants in the Alsace region. We use the same study population as these epidemiological studies to illustrate how appealing this causal inference approach is to estimate the effects of hypothetical, but plausible, environmental interventions.</p>
Statistics in Medicine, EarlyView. Assessing environmental epidemiology questions in practice with a causal inference pipeline: An investigation of the air pollution‐multiple sclerosis relapses
relationshipdoi:10.1002/sim.8843Statistics in Medicine2020-12-16T04:36:46-08:00Statistics in Medicine10.1002/sim.8843https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8843?af=RRESEARCH ARTICLEVector‐based kernel weighting: A simple estimator for improving precision and bias of average treatment effects in multiple treatment settings
Treatment effect estimation must account for observed confounding, in which factors affect treatment assignment and outcomes simultaneously. Ignoring observed confounding risks concluding that a helpful treatment is not beneficial or that a treatment is safe when actually harmful. Propensity score matching or weighting adjusts for observed confounding, but the best way to use propensity scores for multiple treatments is unknown. It is unclear when choice of a different weighting or matching strategy leads to divergent inferences. We used Monte Carlo simulations (1000 replications) to examine sensitivity of multivalued treatment inferences to propensity score weighting or matching strategies. We consider five variants of propensity score adjustment: inverse probability of treatment weights, generalized propensity score matching, kernel weights (KW), vector matching, and a new hybrid that is easily implemented—vector‐based kernel weighting (VBKW). VBKW matches observations with similar propensity score vectors, assigning greater KW to observations with similar probabilities within a given bandwidth. We varied degree of propensity score model misspecification, sample size, treatment effect heterogeneity, initial covariate imbalance, and sample distribution across treatment groups. We evaluated sensitivity of results to propensity score estimation technique (multinomial logit or multinomial probit). Across simulations, VBKW performed equally or better than the other methods in terms of bias, efficiency, and covariate balance measured via prognostic scores. Our simulations suggest that VBKW is amenable to full automation and is less sensitive to PS model misspecification than other methods used to account for observed confounding in multivalued treatment analyses.
Melissa M. Garrido,
Jessica Lum,
Steven D. Pizer
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8836?af=R
<p>Treatment effect estimation must account for observed confounding, in which factors affect treatment assignment and outcomes simultaneously. Ignoring observed confounding risks concluding that a helpful treatment is not beneficial or that a treatment is safe when actually harmful. Propensity score matching or weighting adjusts for observed confounding, but the best way to use propensity scores for multiple treatments is unknown. It is unclear when choice of a different weighting or matching strategy leads to divergent inferences. We used Monte Carlo simulations (1000 replications) to examine sensitivity of multivalued treatment inferences to propensity score weighting or matching strategies. We consider five variants of propensity score adjustment: inverse probability of treatment weights, generalized propensity score matching, kernel weights (KW), vector matching, and a new hybrid that is easily implemented—vector‐based kernel weighting (VBKW). VBKW matches observations with similar propensity score vectors, assigning greater KW to observations with similar probabilities within a given bandwidth. We varied degree of propensity score model misspecification, sample size, treatment effect heterogeneity, initial covariate imbalance, and sample distribution across treatment groups. We evaluated sensitivity of results to propensity score estimation technique (multinomial logit or multinomial probit). Across simulations, VBKW performed equally or better than the other methods in terms of bias, efficiency, and covariate balance measured via prognostic scores. Our simulations suggest that VBKW is amenable to full automation and is less sensitive to PS model misspecification than other methods used to account for observed confounding in multivalued treatment analyses.</p>
Statistics in Medicine, EarlyView. Vector‐based kernel weighting: A simple estimator for improving precision and bias of average treatment effects in multiple treatment settingsdoi:10.1002/sim.8836Statistics in Medicine2020-12-16T04:34:04-08:00Statistics in Medicine10.1002/sim.8836https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8836?af=RRESEARCH ARTICLEAn overview and critique of the use of cumulative sum methods with surgical learning curve data
Cumulative sum (CUSUM) plots and methods have wide‐ranging applications in healthcare. We review and discuss some issues related to the analysis of surgical learning curve (LC) data with a focus on three types of CUSUM statistical approaches. The underlying assumptions, benefits, and weaknesses of each approach are given. Our primary conclusion is that two types of CUSUM methods are useful in providing visual aids, but are subject to overinterpretation due to the lack of well‐defined decision rules and performance metrics. The third type is based on plotting the CUSUM of the differences between observations and their average value. We show that this commonly applied retrospective method is frequently interpreted incorrectly and is thus unhelpful in the LC application. Curve‐fitting methods are more suitable for meeting many of the goals associated with the study of surgical LCs.
William H. Woodall,
George Rakovich,
Stefan H. Steiner
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8847?af=R
<p>Cumulative sum (CUSUM) plots and methods have wide‐ranging applications in healthcare. We review and discuss some issues related to the analysis of surgical learning curve (LC) data with a focus on three types of CUSUM statistical approaches. The underlying assumptions, benefits, and weaknesses of each approach are given. Our primary conclusion is that two types of CUSUM methods are useful in providing visual aids, but are subject to overinterpretation due to the lack of well‐defined decision rules and performance metrics. The third type is based on plotting the CUSUM of the differences between observations and their average value. We show that this commonly applied retrospective method is frequently interpreted incorrectly and is thus unhelpful in the LC application. Curve‐fitting methods are more suitable for meeting many of the goals associated with the study of surgical LCs.</p>
Statistics in Medicine, EarlyView. An overview and critique of the use of cumulative sum methods with surgical learning curve datadoi:10.1002/sim.8847Statistics in Medicine2020-12-14T04:54:50-08:00Statistics in Medicine10.1002/sim.8847https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8847?af=RRESEARCH ARTICLEEstimation of ascertainment bias and its effect on power in clinical trials with time‐to‐event outcomesWhile the gold standard for clinical trials is to blind all parties—participants, researchers, and evaluators—to treatment assignment, this is not always a possibility. When some or all of the above individuals know the treatment assignment, this leaves the study open to the introduction of postrandomization biases. In the Strategies to Reduce Injuries and Develop Confidence in Elders (STRIDE) trial, we were presented with the potential for the unblinded clinicians administering the treatment, as well as the individuals enrolled in the study, to introduce ascertainment bias into some but not all events comprising the primary outcome. In this article, we present ways to estimate the ascertainment bias for a time‐to‐event outcome, and discuss its impact on the overall power of a trial vs changing of the outcome definition to a more stringent unbiased definition that restricts attention to measurements less subject to potentially differential assessment. We found that for the majority of situations, it is better to revise the definition to a more stringent definition, as was done in STRIDE, even though fewer events may be observed.
Erich J. Greene,
Peter Peduzzi,
James Dziura,
Can Meng,
Michael E. Miller,
Thomas G. Travison,
Denise Esserman
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8842?af=R
<p>While the gold standard for clinical trials is to blind all parties—participants, researchers, and evaluators—to treatment assignment, this is not always a possibility. When some or all of the above individuals know the treatment assignment, this leaves the study open to the introduction of postrandomization biases. In the Strategies to Reduce Injuries and Develop Confidence in Elders (STRIDE) trial, we were presented with the potential for the unblinded clinicians administering the treatment, as well as the individuals enrolled in the study, to introduce ascertainment bias into some but not all events comprising the primary outcome. In this article, we present ways to estimate the ascertainment bias for a time‐to‐event outcome, and discuss its impact on the overall power of a trial vs changing of the outcome definition to a more stringent unbiased definition that restricts attention to measurements less subject to potentially differential assessment. We found that for the majority of situations, it is better to revise the definition to a more stringent definition, as was done in STRIDE, even though fewer events may be observed.</p>
Statistics in Medicine, EarlyView. Estimation of ascertainment bias and its effect on power in clinical trials with time‐to‐event outcomesdoi:10.1002/sim.8842Statistics in Medicine2020-12-14T12:00:00-08:00Statistics in Medicine10.1002/sim.8842https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8842?af=RRESEARCH ARTICLEModeling the mean time to interval cancer after negative results of periodic cancer screening
Interval cancers are cancers detected symptomatically between screens or after the last screen. A mathematical model for the development of interval cancers can provide useful information for evaluating cancer screening. In this regard a useful quantity is MIC, the mean duration in years of progressive preclinical cancer (PPC) that leads to interval cancers. Estimation of MIC involved extending a previous model to include three negative screens, invoking the multinomial‐Poisson transformation to avoid estimating background cancer trends, and varying screening test sensitivity. Simulations show that when the true MIC is 0.5, the method yields a reasonably narrow range of estimated MICs over the range of screening test sensitivities from 0.5 to 1.0. If the lower bound on the screening test sensitivity is 0.7, the method performs considerably better even for larger MICs. The application of the method involved annual lung cancer screening in the Prostate, Lung, Colorectal, and Ovarian trial. Assuming a normal distribution for PPC duration, the estimated MIC (95% confidence interval) ranged from 0.00 (0.00 to 0.34) at a screening test sensitivity of 1.0 to 0.54 (0.03, 1.00) at a screening test sensitivity of 0.5 Assuming an exponential distribution for PPC duration, which did not fit as well, the estimated MIC ranged from 0.27 (0.08, 0.49) at a screening test sensitivity of 0.5 to 0.73 (0.32, 1.26) at a screen test sensitivity of 1.0 Based on these results, investigators may wish to investigate more frequent lung cancer screening.
Stuart G. Baker
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8849?af=R
<p>Interval cancers are cancers detected symptomatically between screens or after the last screen. A mathematical model for the development of interval cancers can provide useful information for evaluating cancer screening. In this regard a useful quantity is MIC, the mean duration in years of progressive preclinical cancer (PPC) that leads to interval cancers. Estimation of MIC involved extending a previous model to include three negative screens, invoking the multinomial‐Poisson transformation to avoid estimating background cancer trends, and varying screening test sensitivity. Simulations show that when the true MIC is 0.5, the method yields a reasonably narrow range of estimated MICs over the range of screening test sensitivities from 0.5 to 1.0. If the lower bound on the screening test sensitivity is 0.7, the method performs considerably better even for larger MICs. The application of the method involved annual lung cancer screening in the Prostate, Lung, Colorectal, and Ovarian trial. Assuming a normal distribution for PPC duration, the estimated MIC (95% confidence interval) ranged from 0.00 (0.00 to 0.34) at a screening test sensitivity of 1.0 to 0.54 (0.03, 1.00) at a screening test sensitivity of 0.5 Assuming an exponential distribution for PPC duration, which did not fit as well, the estimated MIC ranged from 0.27 (0.08, 0.49) at a screening test sensitivity of 0.5 to 0.73 (0.32, 1.26) at a screen test sensitivity of 1.0 Based on these results, investigators may wish to investigate more frequent lung cancer screening.</p>
Statistics in Medicine, EarlyView. Modeling the mean time to interval cancer after negative results of periodic cancer screeningdoi:10.1002/sim.8849Statistics in Medicine2020-12-13T09:14:34-08:00Statistics in Medicine10.1002/sim.8849https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8849?af=RRESEARCH ARTICLEModel diagnostics for censored regression via randomized survival probabilitiesResiduals in normal regression are used to assess a model's goodness‐of‐fit (GOF) and discover directions for improving the model. However, there is a lack of residuals with a characterized reference distribution for censored regression. In this article, we propose to diagnose censored regression with normalized randomized survival probabilities (RSP). The key idea of RSP is to replace the survival probability (SP) of a censored failure time with a uniform random number between 0 and the SP of the censored time. We prove that RSPs always have the uniform distribution on (0, 1) under the true model with the true generating parameters. Therefore, we can transform RSPs into normally distributed residuals with the normal quantile function. We call such residuals by normalized RSP (NRSP residuals). We conduct simulation studies to investigate the sizes and powers of statistical tests based on NRSP residuals in detecting the incorrect choice of distribution family and nonlinear effect in covariates. Our simulation studies show that, although the GOF tests with NRSP residuals are not as powerful as a traditional GOF test method, a nonlinear test based on NRSP residuals has significantly higher power in detecting nonlinearity. We also compared these model diagnostics methods with a breast‐cancer recurrent‐free time dataset. The results show that the NRSP residual diagnostics successfully captures a subtle nonlinear relationship in the dataset, which is not detected by the graphical diagnostics with CS residuals and existing GOF tests.
Longhai Li,
Tingxuan Wu,
Cindy Feng
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8852?af=R
<p>Residuals in normal regression are used to assess a model's goodness‐of‐fit (GOF) and discover directions for improving the model. However, there is a lack of residuals with a characterized reference distribution for censored regression. In this article, we propose to diagnose censored regression with normalized randomized survival probabilities (RSP). The key idea of RSP is to replace the survival probability (SP) of a censored failure time with a uniform random number between 0 and the SP of the censored time. We prove that RSPs always have the uniform distribution on <span>(0, 1)</span> under the true model with the true generating parameters. Therefore, we can transform RSPs into normally distributed residuals with the normal quantile function. We call such residuals by normalized RSP (NRSP residuals). We conduct simulation studies to investigate the sizes and powers of statistical tests based on NRSP residuals in detecting the incorrect choice of distribution family and nonlinear effect in covariates. Our simulation studies show that, although the GOF tests with NRSP residuals are not as powerful as a traditional GOF test method, a nonlinear test based on NRSP residuals has significantly higher power in detecting nonlinearity. We also compared these model diagnostics methods with a breast‐cancer recurrent‐free time dataset. The results show that the NRSP residual diagnostics successfully captures a subtle nonlinear relationship in the dataset, which is not detected by the graphical diagnostics with CS residuals and existing GOF tests.</p>
Statistics in Medicine, EarlyView. Model diagnostics for censored regression via randomized survival probabilitiesdoi:10.1002/sim.8852Statistics in Medicine2020-12-13T03:49:34-08:00Statistics in Medicine10.1002/sim.8852https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8852?af=RRESEARCH ARTICLEPropensity score stratification methods for continuous treatments
Continuous treatments propensity scoring remains understudied as the majority of methods are focused on the binary treatment setting. Current propensity score methods for continuous treatments typically rely on weighting in order to produce causal estimates. It has been shown that in some continuous treatment settings, weighting methods can result in worse covariate balance than had no adjustments been made to the data. Furthermore, weighting is not always stable, and resultant estimates may be unreliable due to extreme weights. These issues motivate the current development of novel propensity score stratification techniques to be used with continuous treatments. Specifically, the generalized propensity score cumulative distribution function (GPS‐CDF) and the nonparametric GPS‐CDF approaches are introduced. Empirical CDFs are used to stratify subjects based on pretreatment confounders in order to produce causal estimates. A detailed simulation study shows superiority of these new stratification methods based on the empirical CDF, when compared with standard weighting techniques. The proposed methods are applied to the “Mexican‐American Tobacco use in Children” study to determine the causal relationship between continuous exposure to smoking imagery in movies, and smoking behavior among Mexican‐American adolescents. These promising results provide investigators with new options for implementing continuous treatment propensity scoring.
Derek W. Brown,
Thomas J. Greene,
Michael D. Swartz,
Anna V. Wilkinson,
Stacia M. DeSantis
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8835?af=R
<p>Continuous treatments propensity scoring remains understudied as the majority of methods are focused on the binary treatment setting. Current propensity score methods for continuous treatments typically rely on weighting in order to produce causal estimates. It has been shown that in some continuous treatment settings, weighting methods can result in worse covariate balance than had no adjustments been made to the data. Furthermore, weighting is not always stable, and resultant estimates may be unreliable due to extreme weights. These issues motivate the current development of novel propensity score stratification techniques to be used with continuous treatments. Specifically, the generalized propensity score cumulative distribution function (GPS‐CDF) and the nonparametric GPS‐CDF approaches are introduced. Empirical CDFs are used to stratify subjects based on pretreatment confounders in order to produce causal estimates. A detailed simulation study shows superiority of these new stratification methods based on the empirical CDF, when compared with standard weighting techniques. The proposed methods are applied to the “Mexican‐American Tobacco use in Children” study to determine the causal relationship between continuous exposure to smoking imagery in movies, and smoking behavior among Mexican‐American adolescents. These promising results provide investigators with new options for implementing continuous treatment propensity scoring.</p>
Statistics in Medicine, EarlyView. Propensity score stratification methods for continuous treatmentsdoi:10.1002/sim.8835Statistics in Medicine2020-12-10T09:09:08-08:00Statistics in Medicine10.1002/sim.8835https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8835?af=RRESEARCH ARTICLEMean comparisons and power calculations to ensure reproducibility in preclinical drug discovery
Abstract
In the pharmaceutical industry, in vivo animal experiments are conducted to test the effects of novel preclinical drug compounds. Well‐planned animal studies involve a sample size and statistical power analysis to provide a basis for the number of animals allocated into comparator arms of a future study. These calculations require approximate values for the parameters of a statistical model that will be applied to the future data and used to test for differences via statistical hypotheses. If the prestudy parameter estimates are nearly correct, the power analysis guarantees that a difference will be detected from the study data, up to a prespecified probability. Traditional power computations, however, are not calculated with reproducibility in mind. In this work, the issue of reproducibility in drug discovery is tackled from the point of view that study‐to‐study variability is not included in a typical sample size and power analysis. Three proposed methods that yield a reproducible mean‐comparison analysis are derived and compared.
Steven Novick,
Tianhui Zhang
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8848?af=R
<h2>Abstract</h2>
<p>In the pharmaceutical industry, in vivo animal experiments are conducted to test the effects of novel preclinical drug compounds. Well‐planned animal studies involve a sample size and statistical power analysis to provide a basis for the number of animals allocated into comparator arms of a future study. These calculations require approximate values for the parameters of a statistical model that will be applied to the future data and used to test for differences via statistical hypotheses. If the prestudy parameter estimates are nearly correct, the power analysis guarantees that a difference will be detected from the study data, up to a prespecified probability. Traditional power computations, however, are not calculated with reproducibility in mind. In this work, the issue of reproducibility in drug discovery is tackled from the point of view that study‐to‐study variability is not included in a typical sample size and power analysis. Three proposed methods that yield a reproducible mean‐comparison analysis are derived and compared.</p>
Statistics in Medicine, EarlyView. Mean comparisons and power calculations to ensure reproducibility in preclinical drug discoverydoi:10.1002/sim.8848Statistics in Medicine2020-12-09T05:04:07-08:00Statistics in Medicine10.1002/sim.8848https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8848?af=RRESEARCH ARTICLEJoint analysis of mixed types of outcomes with latent variablesWe propose a joint modeling approach to investigating the observed and latent risk factors of mixed types of outcomes. The proposed model comprises three parts. The first part is an exploratory factor analysis model that summarizes latent factors through multiple observed variables. The second part is a proportional hazards model that examines the observed and latent risk factors of multivariate time‐to‐event outcomes. The third part is a linear regression model that investigates the determinants of a continuous outcome. We develop a Bayesian approach coupled with MCMC methods to determine the number of latent factors, the association between latent and observed variables, and the important risk factors of different types of outcomes. A modified stochastic search item selection algorithm, which introduces normal‐mixture‐inverse gamma priors to factor loadings and regression coefficients, is developed for simultaneous model selection and parameter estimation. The proposed method is subjected to simulation studies for empirical performance assessment and then applied to a study concerning the risk factors of type 2 diabetes and the associated complications.
Deng Pan,
Yingying Wei,
Xinyuan Song
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8840?af=R
<p>We propose a joint modeling approach to investigating the observed and latent risk factors of mixed types of outcomes. The proposed model comprises three parts. The first part is an exploratory factor analysis model that summarizes latent factors through multiple observed variables. The second part is a proportional hazards model that examines the observed and latent risk factors of multivariate time‐to‐event outcomes. The third part is a linear regression model that investigates the determinants of a continuous outcome. We develop a Bayesian approach coupled with MCMC methods to determine the number of latent factors, the association between latent and observed variables, and the important risk factors of different types of outcomes. A modified stochastic search item selection algorithm, which introduces normal‐mixture‐inverse gamma priors to factor loadings and regression coefficients, is developed for simultaneous model selection and parameter estimation. The proposed method is subjected to simulation studies for empirical performance assessment and then applied to a study concerning the risk factors of type 2 diabetes and the associated complications.</p>
Statistics in Medicine, EarlyView. Joint analysis of mixed types of outcomes with latent variablesdoi:10.1002/sim.8840Statistics in Medicine2020-12-09T04:34:49-08:00Statistics in Medicine10.1002/sim.8840https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8840?af=RRESEARCH ARTICLELongitudinal multivariate normative comparisonsMotivated by the Multicenter AIDS Cohort Study (MACS), we develop classification procedures for cognitive impairment based on longitudinal measures. To control family‐wise error, we adapt the cross‐sectional multivariate normative comparisons (MNC) method to the longitudinal setting. The cross‐sectional MNC was proposed to control family‐wise error by measuring the distance between multiple domain scores of a participant and the norms of healthy controls and specifically accounting for intercorrelations among all domain scores. However, in a longitudinal setting where domain scores are recorded multiple times, applying the cross‐sectional MNC at each visit will still have inflated family‐wise error rate due to multiple testing over repeated visits. Thus, we propose longitudinal MNC procedures that are constructed based on multivariate mixed effects models. A χ2 test procedure is adapted from the cross‐sectional MNC to classify impairment on longitudinal multivariate normal data. Meanwhile, a permutation procedure is proposed to handle skewed data. Through simulations we show that our methods can effectively control family‐wise error at a predetermined level. A dataset from a neuropsychological substudy of the MACS is used to illustrate the applications of our proposed classification procedures.
Zheng Wang,
Yu Cheng,
Eric C. Seaberg,
Leah H. Rubin,
Andrew J. Levine,
James T. Becker,
Neuropsychology Working Group of the MACS
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8850?af=R
<p>Motivated by the Multicenter AIDS Cohort Study (MACS), we develop classification procedures for cognitive impairment based on longitudinal measures. To control family‐wise error, we adapt the cross‐sectional multivariate normative comparisons (MNC) method to the longitudinal setting. The cross‐sectional MNC was proposed to control family‐wise error by measuring the distance between multiple domain scores of a participant and the norms of healthy controls and specifically accounting for intercorrelations among all domain scores. However, in a longitudinal setting where domain scores are recorded multiple times, applying the cross‐sectional MNC at each visit will still have inflated family‐wise error rate due to multiple testing over repeated visits. Thus, we propose longitudinal MNC procedures that are constructed based on multivariate mixed effects models. A χ2 test procedure is adapted from the cross‐sectional MNC to classify impairment on longitudinal multivariate normal data. Meanwhile, a permutation procedure is proposed to handle skewed data. Through simulations we show that our methods can effectively control family‐wise error at a predetermined level. A dataset from a neuropsychological substudy of the MACS is used to illustrate the applications of our proposed classification procedures.</p>
Statistics in Medicine, EarlyView. Longitudinal multivariate normative comparisonsdoi:10.1002/sim.8850Statistics in Medicine2020-12-09T03:53:35-08:00Statistics in Medicine10.1002/sim.8850https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8850?af=RRESEARCH ARTICLERegression analysis of mixed panel count data with informative indicator processesPanel count data occur often in event history studies and in these situations, one observes only incomplete information, the number of events rather than the occurrence times of each event, about the point processes of interest.2 Sometimes one may have to face a more complicated type of panel count data, mixed panel count data in which instead of the number of events, one only knows if there is an occurrence of an event.3 Furthermore, this may depend on the underlying point process of interest or in other words, the point process of interest and the observation type process may be related. To address this, a sieve maximum likelihood estimation approach is proposed with the use of Bernstein polynomials, and for the implementation, an EM algorithm is developed. To assess the finite sample performance of the proposed approach, a simulation study is conducted and suggests that it works well for practical situations. The method is then applied to a motivating example about cancer survivors.
Lei Ge,
Liang Zhu,
Jianguo Sun
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8839?af=R
<p>Panel count data occur often in event history studies and in these situations, one observes only incomplete information, the number of events rather than the occurrence times of each event, about the point processes of interest.<span>
<sup>2</sup>
</span> Sometimes one may have to face a more complicated type of panel count data, mixed panel count data in which instead of the number of events, one only knows if there is an occurrence of an event.<span>
<sup>3</sup>
</span> Furthermore, this may depend on the underlying point process of interest or in other words, the point process of interest and the observation type process may be related. To address this, a sieve maximum likelihood estimation approach is proposed with the use of Bernstein polynomials, and for the implementation, an EM algorithm is developed. To assess the finite sample performance of the proposed approach, a simulation study is conducted and suggests that it works well for practical situations. The method is then applied to a motivating example about cancer survivors.</p>
Statistics in Medicine, EarlyView. Regression analysis of mixed panel count data with informative indicator processesdoi:10.1002/sim.8839Statistics in Medicine2020-12-03T07:24:26-08:00Statistics in Medicine10.1002/sim.8839https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8839?af=RRESEARCH ARTICLEConfidence intervals for difference in proportions for matched pairs compatible with exact McNemar's or sign testsFor testing with paired data (eg, twins randomized between two treatments), a simple test is the sign test, where we test if the distribution of the sign of the differences in responses between the two treatments within pairs is more often positive (favoring one treatment) or negative (favoring the other). When the responses are binary, this reduces to a McNemar‐type test, and the calculations are the same. Although it is easy to calculate an exact P‐value by conditioning on the total number of discordant pairs, the accompanying confidence interval on a parameter of interest (proportion positive minus proportion negative) is not straightforward. Effect estimates and confidence intervals are important for interpretation because it is possible that the treatment helps a very small proportion of the population yet gives a highly significant effect. We construct a confidence interval that is compatible with an exact sign test, meaning the 100(1−α)% interval excludes the null hypothesis of equality of proportions if and only if the associated exact sign test rejects at level α. We conjecture that the proposed confidence intervals guarantee nominal coverage, and we support that conjecture with extensive numerical calculations, but we have no mathematical proof to show guaranteed coverage. We have written and made available the function mcnemarExactDP in the exact2x2 R package and the function signTest in the asht R package to perform the methods described in this article.
Michael P. Fay,
Keith Lumbard
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8829?af=R
<p>For testing with paired data (eg, twins randomized between two treatments), a simple test is the sign test, where we test if the distribution of the sign of the differences in responses between the two treatments within pairs is more often positive (favoring one treatment) or negative (favoring the other). When the responses are binary, this reduces to a McNemar‐type test, and the calculations are the same. Although it is easy to calculate an exact <i>P</i>‐value by conditioning on the total number of discordant pairs, the accompanying confidence interval on a parameter of interest (proportion positive minus proportion negative) is not straightforward. Effect estimates and confidence intervals are important for interpretation because it is possible that the treatment helps a very small proportion of the population yet gives a highly significant effect. We construct a confidence interval that is compatible with an exact sign test, meaning the 100(1−α)% interval excludes the null hypothesis of equality of proportions if and only if the associated exact sign test rejects at level α. We conjecture that the proposed confidence intervals guarantee nominal coverage, and we support that conjecture with extensive numerical calculations, but we have no mathematical proof to show guaranteed coverage. We have written and made available the function <span style="font-family:sans-serif">mcnemarExactDP</span> in the <span style="font-family:sans-serif">exact2x2</span> R package and the function <span style="font-family:sans-serif">signTest</span> in the <span style="font-family:sans-serif">asht</span> R package to perform the methods described in this article.</p>
Statistics in Medicine, EarlyView. Confidence intervals for difference in proportions for matched pairs compatible with exact McNemar's or sign testsdoi:10.1002/sim.8829Statistics in Medicine2020-12-01T06:25:46-08:00Statistics in Medicine10.1002/sim.8829https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8829?af=RRESEARCH ARTICLEDesign and analysis of three‐arm parallel cluster randomized trials with small numbers of clusters
In this article, we review and evaluate a number of methods used in the design and analysis of small three‐arm parallel cluster randomized trials. We conduct a simulation‐based study to evaluate restricted randomization methods including covariate‐constrained randomization and a novel method for matched‐group cluster randomization. We also evaluate the appropriate modelling of the data and small sample inferential methods for a variety of treatment effects relevant to three‐arm trials. Our results indicate that small‐sample corrections are required for high (0.05) but not low (0.001) values of the intraclass correlation coefficient and their performance can depend on trial design, number of clusters, and the nature of the hypothesis being tested. The Satterthwaite correction generally performed best at an ICC of 0.05 with a nominal type I error rate for single‐period trials, and in trials with repeated measures type I error rates were between 0.04 and 0.06. Restricted randomization methods produce little benefit in trials with repeated measures but in trials with single post‐intervention design can provide relatively large gains in power when compared to the most unbalanced possible allocations. Matched‐group randomization improves power but is not as effective as covariate‐constrained randomization. For model‐based analysis, adjusting for fewer covariates than were used in a restricted randomization process under any design can produce non‐nominal type I error rates and reductions in power. Where comparisons to two‐arm cluster trials are possible, the performance of the methods is qualitatively very similar.
Samuel I. Watson,
Alan Girling,
Karla Hemming
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8828?af=R
<p>In this article, we review and evaluate a number of methods used in the design and analysis of small three‐arm parallel cluster randomized trials. We conduct a simulation‐based study to evaluate restricted randomization methods including covariate‐constrained randomization and a novel method for matched‐group cluster randomization. We also evaluate the appropriate modelling of the data and small sample inferential methods for a variety of treatment effects relevant to three‐arm trials. Our results indicate that small‐sample corrections are required for high (0.05) but not low (0.001) values of the intraclass correlation coefficient and their performance can depend on trial design, number of clusters, and the nature of the hypothesis being tested. The Satterthwaite correction generally performed best at an ICC of 0.05 with a nominal type I error rate for single‐period trials, and in trials with repeated measures type I error rates were between 0.04 and 0.06. Restricted randomization methods produce little benefit in trials with repeated measures but in trials with single post‐intervention design can provide relatively large gains in power when compared to the most unbalanced possible allocations. Matched‐group randomization improves power but is not as effective as covariate‐constrained randomization. For model‐based analysis, adjusting for fewer covariates than were used in a restricted randomization process under any design can produce non‐nominal type I error rates and reductions in power. Where comparisons to two‐arm cluster trials are possible, the performance of the methods is qualitatively very similar.</p>
Statistics in Medicine, EarlyView. Design and analysis of three‐arm parallel cluster randomized trials with small numbers of clustersdoi:10.1002/sim.8828Statistics in Medicine2020-11-30T11:19:33-08:00Statistics in Medicine10.1002/sim.8828https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8828?af=RRESEARCH ARTICLEA simplified approach for establishing estimable functions in fixed effect age‐period‐cohort multiple classification models
Estimable functions play an important role in learning about certain aspects of the impact of ages, periods, and cohorts in age‐period‐cohort multiple classification (APCMC) models. The advantage of these estimates is that they are unbiased estimates of, for example, the deviations of age, period, and cohort effects from their linear trends, or changes in the linear trends of cohort effects within cohorts, or the residuals of fixed effect APCMC models. If the fixed effect APCMC model contains the relevant variables (is well specified), these estimable functions are unbiased estimates of functions of the parameters that generated the dependent variable data, even though the parameters that generated that data are not identified. I provide a simplified approach to establishing which functions are estimable in fixed effect APCMC models that provides an intuitive understanding of estimable functions by showing clearly and simply why they are estimable. This approach involves the partitioning of the age, period, and cohort effects into linear components and deviations from the linear components; the use of the “line of solutions”; and of the “extended null vector.”
Robert M. O'Brien
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8831?af=R
<p>Estimable functions play an important role in learning about certain aspects of the impact of ages, periods, and cohorts in age‐period‐cohort multiple classification (APCMC) models. The advantage of these estimates is that they are unbiased estimates of, for example, the deviations of age, period, and cohort effects from their linear trends, or changes in the linear trends of cohort effects within cohorts, or the residuals of fixed effect APCMC models. If the fixed effect APCMC model contains the relevant variables (is well specified), these estimable functions are unbiased estimates of functions of the parameters that generated the dependent variable data, even though the parameters that generated that data are not identified. I provide a simplified approach to establishing which functions are estimable in fixed effect APCMC models that provides an intuitive understanding of estimable functions by showing clearly and simply why they are estimable. This approach involves the partitioning of the age, period, and cohort effects into linear components and deviations from the linear components; the use of the “line of solutions”; and of the “extended null vector.”</p>
Statistics in Medicine, EarlyView. A simplified approach for establishing estimable functions in fixed effect age‐period‐cohort multiple classification modelsdoi:10.1002/sim.8831Statistics in Medicine2020-11-30T08:45:15-08:00Statistics in Medicine10.1002/sim.8831https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8831?af=RRESEARCH ARTICLEGeneralizing randomized trial findings to a target population using complex survey population dataRandomized trials are considered the gold standard for estimating causal effects. Trial findings are often used to inform policy and programming efforts, yet their results may not generalize well to a relevant target population due to potential differences in effect moderators between the trial and population. Statistical methods have been developed to improve generalizability by combining trials and population data, and weighting the trial to resemble the population on baseline covariates. Large‐scale surveys in fields such as health and education with complex survey designs are a logical source for population data; however, there is currently no best practice for incorporating survey weights when generalizing trial findings to a complex survey. We propose and investigate ways to incorporate survey weights in this context. We examine the performance of our proposed estimator through simulations in comparison to estimators that ignore the complex survey design. We then apply the methods to generalize findings from two trials—a lifestyle intervention for blood pressure reduction and a web‐based intervention to treat substance use disorders—to their respective target populations using population data from complex surveys. The work highlights the importance in properly accounting for the complex survey design when generalizing trial findings to a population represented by a complex survey sample.
Benjamin Ackerman,
Catherine R. Lesko,
Juned Siddique,
Ryoko Susukida,
Elizabeth A. Stuart
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8822?af=R
<p>Randomized trials are considered the gold standard for estimating causal effects. Trial findings are often used to inform policy and programming efforts, yet their results may not generalize well to a relevant target population due to potential differences in effect moderators between the trial and population. Statistical methods have been developed to improve generalizability by combining trials and population data, and weighting the trial to resemble the population on baseline covariates. Large‐scale surveys in fields such as health and education with complex survey designs are a logical source for population data; however, there is currently no best practice for incorporating survey weights when generalizing trial findings to a complex survey. We propose and investigate ways to incorporate survey weights in this context. We examine the performance of our proposed estimator through simulations in comparison to estimators that ignore the complex survey design. We then apply the methods to generalize findings from two trials—a lifestyle intervention for blood pressure reduction and a web‐based intervention to treat substance use disorders—to their respective target populations using population data from complex surveys. The work highlights the importance in properly accounting for the complex survey design when generalizing trial findings to a population represented by a complex survey sample.</p>
Statistics in Medicine, EarlyView. Generalizing randomized trial findings to a target population using complex survey population datadoi:10.1002/sim.8822Statistics in Medicine2020-11-26T01:21:17-08:00Statistics in Medicine10.1002/sim.8822https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8822?af=RRESEARCH ARTICLESimulation model of disease incidence driven by diagnostic activityIt is imperative to understand the effects of early detection and treatment of chronic diseases, such as prostate cancer, regarding incidence, overtreatment and mortality. Previous simulation models have emulated clinical trials, and relied on extensive assumptions on the natural history of the disease. In addition, model parameters were typically calibrated to a variety of data sources. We propose a model designed to emulate real‐life scenarios of chronic disease using a proxy for the diagnostic activity without explicitly modeling the natural history of the disease and properties of clinical tests. Our model was applied to Swedish nation‐wide population‐based prostate cancer data, and demonstrated good performance in terms of reconstructing observed incidence and mortality. The model was used to predict the number of prostate cancer diagnoses with a high or limited diagnostic activity between 2017 and 2060. In the long term, high diagnostic activity resulted in a substantial increase in the number of men diagnosed with lower risk disease, fewer men with metastatic disease, and decreased prostate cancer mortality. The model can be used for prediction of outcome, to guide decision‐making, and to evaluate diagnostic activity in real‐life settings with respect to overdiagnosis and prostate cancer mortality.
Marcus Westerberg,
Rolf Larsson,
Lars Holmberg,
Pär Stattin,
Hans Garmo
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8833?af=R
<p>It is imperative to understand the effects of early detection and treatment of chronic diseases, such as prostate cancer, regarding incidence, overtreatment and mortality. Previous simulation models have emulated clinical trials, and relied on extensive assumptions on the natural history of the disease. In addition, model parameters were typically calibrated to a variety of data sources. We propose a model designed to emulate real‐life scenarios of chronic disease using a proxy for the diagnostic activity without explicitly modeling the natural history of the disease and properties of clinical tests. Our model was applied to Swedish nation‐wide population‐based prostate cancer data, and demonstrated good performance in terms of reconstructing observed incidence and mortality. The model was used to predict the number of prostate cancer diagnoses with a high or limited diagnostic activity between 2017 and 2060. In the long term, high diagnostic activity resulted in a substantial increase in the number of men diagnosed with lower risk disease, fewer men with metastatic disease, and decreased prostate cancer mortality. The model can be used for prediction of outcome, to guide decision‐making, and to evaluate diagnostic activity in real‐life settings with respect to overdiagnosis and prostate cancer mortality.</p>
Statistics in Medicine, EarlyView. Simulation model of disease incidence driven by diagnostic activitydoi:10.1002/sim.8833Statistics in Medicine2020-11-25T07:30:25-08:00Statistics in Medicine10.1002/sim.8833https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8833?af=RRESEARCH ARTICLEA unified approach to sample size and power determination for testing parameters in generalized linear and time‐to‐event regression modelsTo ensure that a study can properly address its research aims, the sample size and power must be determined appropriately. Covariate adjustment via regression modeling permits more precise estimation of the effect of a primary variable of interest at the expense of increased complexity in sample size/power calculation. The presence of correlation between the main variable and other covariates, commonly seen in observational studies and non‐randomized clinical trials, further complicates this process. Though sample size and power specification methods have been obtained to accommodate specific covariate distributions and models, most existing approaches rely on either simple approximations lacking theoretical support or complex procedures that are difficult to apply at the design stage. The current literature lacks a general, coherent theory applicable to a broader class of regression models and covariate distributions. We introduce succinct formulas for sample size and power determination with the generalized linear, Cox, and Fine‐Gray models that account for correlation between a main effect and other covariates. Extensive simulations demonstrate that this method produces studies that are appropriately sized to meet their type I error rate and power specifications, particularly offering accurate sample size/power estimation in the presence of correlated covariates.
Michael J. Martens,
Brent R. Logan
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8823?af=R
<p>To ensure that a study can properly address its research aims, the sample size and power must be determined appropriately. Covariate adjustment via regression modeling permits more precise estimation of the effect of a primary variable of interest at the expense of increased complexity in sample size/power calculation. The presence of correlation between the main variable and other covariates, commonly seen in observational studies and non‐randomized clinical trials, further complicates this process. Though sample size and power specification methods have been obtained to accommodate specific covariate distributions and models, most existing approaches rely on either simple approximations lacking theoretical support or complex procedures that are difficult to apply at the design stage. The current literature lacks a general, coherent theory applicable to a broader class of regression models and covariate distributions. We introduce succinct formulas for sample size and power determination with the generalized linear, Cox, and Fine‐Gray models that account for correlation between a main effect and other covariates. Extensive simulations demonstrate that this method produces studies that are appropriately sized to meet their type I error rate and power specifications, particularly offering accurate sample size/power estimation in the presence of correlated covariates.</p>
Statistics in Medicine, EarlyView. A unified approach to sample size and power determination for testing parameters in generalized linear and time‐to‐event regression modelsdoi:10.1002/sim.8823Statistics in Medicine2020-11-18T07:50:36-08:00Statistics in Medicine10.1002/sim.8823https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8823?af=RRESEARCH ARTICLE