Stroke patients with orthostatic hypertensive responses that are one of the blood pressure regulation problems can easily fall down while doing rehabilitation, which may result in prolonged hospitalization and delayed treatment and recovery. This may result in increasing the medical cost and burden. In turn, developing a diagnostic test for the orthostatic hypertension (OH) is clinically important for patients who are suffering from stroke. Clinically, a patient needs to have a tilt testing that requires measuring the change of blood pressures and heart rate at all angles to determine whether a stroke patient has OH. It takes lots of time and effort to perform the test. Assuming there exist measurement errors when obtaining the blood pressures and heart rate at all angles, this paper proposes using multiple mixed-effect models to obtain the true trajectories of these measurements, which take into account the measurement error and the possible correlation among multiple measurements, and a logistic regression uses these true trajectories at a given time and other fixed-effect covariates as predictors to predict the status of OH. The joint likelihood function is derived to estimate parameters and the area under the receiver operating characteristics curve is used to estimate the predictive power of the model. Monte Carlo simulations are performed to evaluate the feasibility of the proposed methods. Also, the proposed model is implemented in the real data and provides an acceptable predictive power.

]]>Meta-analysis of rare event studies has recently become a subject of controversy and debate. We will argue and demonstrate in this paper that the occurrence of zero events in clinical trials or cohort studies, even if zeros occur in both arms (the case of a double-zero trial), is less problematic, at least from a statistical perspective, if the available statistical tools are applied in the appropriate way. In particular, it is neither necessary nor advisable to exclude studies with zero events from the meta-analysis. In terms of statistical tools, we will focus here on Mantel–Haenszel techniques, mixed Poisson regression and related regression models.

]]>We describe a mixed-effects model for nonnegative continuous cross-sectional data in a two-part modelling framework. A potentially endogenous binary variable is included in the model specification and association between the outcomes is modeled through a (discrete) latent structure. We show how model parameters can be estimated in a finite mixture context, allowing for skewness, multivariate association between random effects and endogeneity. The model behavior is investigated through a large-scale simulation experiment. The proposed model is computationally parsimonious and seems to produce acceptable results even if the underlying random effects structure follows a continuous parametric (e.g. Gaussian) distribution. The proposed approach is motivated by the analysis of a sample taken from the Medical Expenditure Panel Survey. The analyzed outcome, that is ambulatory health expenditure, is a mixture of zeros and continuous values. The effects of socio-demographic characteristics on health expenditure are investigated and, as a by-product of the estimation procedure, two subpopulations (i.e. high and low users) are identified.

]]>Although there are many suggested measures of explained variation for single-event survival data, there has been little attention to explained variation for recurrent event data. We describe an existing rank-based measure and we investigate a new statistic based on observed and expected event count processes. Both methods can be used for all models. Adjustments for missing data are proposed and demonstrated through simulation to be effective. We compare the population values of the two statistics and illustrate their use in comparing an array of non-nested models for data on recurrent episodes of infant diarrhoea.

]]>Covariate measurement error may cause biases in parameters of regression coefficients in generalized linear models. The influence of measurement error on interaction parameters has, however, only rarely been investigated in depth, and if so, attenuation effects were reported. In this paper, we show that also reverse attenuation of interaction effects may emerge, namely when heteroscedastic measurement error or sampling variances of a mismeasured covariate are present, which are not unrealistic scenarios in practice. Theoretical findings are illustrated with simulations. A Bayesian approach employing integrated nested Laplace approximations is suggested to model the heteroscedastic measurement error and covariate variances, and an application shows that the method is able to reveal approximately correct parameter estimates.

]]>The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zero-inflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about mean-variance relationships *a priori*. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.

A surrogate endpoint is intended to replace a clinical endpoint for the evaluation of new treatments when it can be measured more cheaply, more conveniently, more frequently, or earlier than that clinical endpoint. A surrogate endpoint is expected to predict clinical benefit, harm, or lack of these. Besides the biological plausibility of a surrogate, a quantitative assessment of the strength of evidence for surrogacy requires the demonstration of the prognostic value of the surrogate for the clinical outcome, and evidence that treatment effects on the surrogate reliably predict treatment effects on the clinical outcome. We focus on these two conditions, and outline the statistical approaches that have been proposed to assess the extent to which these conditions are fulfilled. When data are available from a single trial, one can assess the “individual level association” between the surrogate and the true endpoint. When data are available from several trials, one can additionally assess the “trial level association” between the treatment effect on the surrogate and the treatment effect on the true endpoint. In the latter case, the “surrogate threshold effect” can be estimated as the minimum effect on the surrogate endpoint that predicts a statistically significant effect on the clinical endpoint. All these concepts are discussed in the context of randomized clinical trials in oncology, and illustrated with two meta-analyses in gastric cancer.

]]>When performing single arm meta-analyses of rare events in small populations, if the outcome of interest is incidence, it is not uncommon to have at least one study with zero events, especially in the presence of competing risks. In this paper, we address the problem of how to include studies with zero events in inverse variance meta-analyses when individual patient data are not available, going beyond the naïve approach of not including the study or the use of a continuity correction. The proposed solution is the arcsine transformation of the crude cumulative incidence as its approximate variance, which is inversely proportional to the sample size, can be calculated also for studies with a zero estimate. As an alternative, generalized linear mixed models (GLMM) can be used. Simulations were performed to compare the results from inverse variance method meta-analyses of the arcsine transformed cumulative incidence to those obtained from meta-analyses of the cumulative incidence itself and of the logit transformation of the cumulative incidence. The comparisons have been carried out for different scenarios of heterogeneity, incidence, and censoring and for competing and not competing risks. The arcsine transformation showed the smallest bias and the highest coverage among models assuming within study normality. At the same time, the GLMM model had the best performance at very low incidences. The proposed method was applied to the clinical context that motivated this work, i.e. a meta-analysis of 5-year crude cumulative incidence of central nervous system recurrences in children treated for acute lymphoblastic leukemia.

]]>Multiple imputation can be used as a tool in the process of constructing prediction models in medical and epidemiological studies with missing covariate values. Such models can be used to make predictions for model performance assessment, but the task is made more complicated by the multiple imputation structure. We summarize various predictions constructed from covariates, including multiply imputed covariates, and either the set of imputation-specific prediction model coefficients or the pooled prediction model coefficients. We further describe approaches for using the predictions to assess model performance. We distinguish between *ideal model performance* and *pragmatic model performance*, where the former refers to the model's performance in an ideal clinical setting where all individuals have fully observed predictors and the latter refers to the model's performance in a real-world clinical setting where some individuals have missing predictors. The approaches are compared through an extensive simulation study based on the UK700 trial. We determine that measures of ideal model performance can be estimated within imputed datasets and subsequently pooled to give an overall measure of model performance. Alternative methods to evaluate pragmatic model performance are required and we propose constructing predictions either from a second set of covariate imputations which make no use of observed outcomes, or from a set of partial prediction models constructed for each potential observed pattern of covariate. Pragmatic model performance is generally lower than ideal model performance. We focus on model performance within the derivation data, but describe how to extend all the methods to a validation dataset.

Quantitative decision models such as multiple criteria decision analysis (MCDA) can be used in benefit-risk assessment to formalize trade-offs between benefits and risks, providing transparency to the assessment process. There is however no well-established method for propagating uncertainty of treatment effects data through such models to provide a sense of the variability of the benefit-risk balance. Here, we present a Bayesian statistical method that directly models the outcomes observed in randomized placebo-controlled trials and uses this to infer indirect comparisons between competing active treatments. The resulting treatment effects estimates are suitable for use within the MCDA setting, and it is possible to derive the distribution of the overall benefit-risk balance through Markov Chain Monte Carlo simulation. The method is illustrated using a case study of natalizumab for relapsing-remitting multiple sclerosis.

]]>While benefit-risk assessment is a key component of the drug development and maintenance process, it is often described in a narrative. In contrast, structured benefit-risk assessment builds on established ideas from decision analysis and comprises a qualitative framework and quantitative methodology. We compare two such frameworks, applying multi-criteria decision-analysis (MCDA) within the PrOACT-URL framework and weighted net clinical benefit (wNCB), within the BRAT framework. These are applied to a case study of natalizumab for the treatment of relapsing remitting multiple sclerosis. We focus on the practical considerations of applying these methods and give recommendations for visual presentation of results. In the case study, we found structured benefit-risk analysis to be a useful tool for structuring, quantifying, and communicating the relative benefit and safety profiles of drugs in a transparent, rational and consistent way. The two frameworks were similar. MCDA is a generic and flexible methodology that can be used to perform a structured benefit-risk in any common context. wNCB is a special case of MCDA and is shown to be equivalent to an extension of the number needed to treat (NNT) principle. It is simpler to apply and understand than MCDA and can be applied when all outcomes are measured on a binary scale.

]]>Discrimination statistics describe the ability of a survival model to assign higher risks to individuals who experience earlier events: examples are Harrell's C-index and Royston and Sauerbrei's D, which we call the D-index. Prognostic covariates whose distributions are controlled by the study design (e.g. age and sex) influence discrimination and can make it difficult to compare model discrimination between studies. Although covariate adjustment is a standard procedure for quantifying disease-risk factor associations, there are no covariate adjustment methods for discrimination statistics in censored survival data.

To develop extensions of the C-index and D-index that describe the prognostic ability of a model adjusted for one or more covariate(s).

We define a covariate-adjusted C-index and D-index for censored survival data, propose several estimators, and investigate their performance in simulation studies and in data from a large individual participant data meta-analysis, the Emerging Risk Factors Collaboration.

The proposed methods perform well in simulations. In the Emerging Risk Factors Collaboration data, the age-adjusted C-index and D-index were substantially smaller than unadjusted values. The study-specific standard deviation of baseline age was strongly associated with the unadjusted C-index and D-index but not significantly associated with the age-adjusted indices.

The proposed estimators improve meta-analysis comparisons, are easy to implement and give a more meaningful clinical interpretation.

In many areas of science where empirical data are analyzed, a task is often to identify important variables with influence on an outcome. Most often this is done by using a variable selection strategy in the context of a multivariable regression model. Using a study on ozone effects in children (*n* = 496, 24 covariates), we will discuss aspects relevant for deriving a suitable model. With an emphasis on model stability, we will explore and illustrate differences between predictive models and explanatory models, the key role of stopping criteria, and the value of bootstrap resampling (with and without replacement). Bootstrap resampling will be used to assess variable selection stability, to derive a predictor that incorporates model uncertainty, check for influential points, and visualize the variable selection process. For the latter two tasks we adapt and extend recent approaches, such as stability paths, to serve our purposes. Based on earlier experiences and on results from the example, we will argue for simpler models and that predictions are usually very similar, irrespective of the selection method used. Important differences exist for the corresponding variances, and the model uncertainty concept helps to protect against serious underestimation of the variance of a predictor-derived data dependently. Results of stability investigations illustrate severe difficulties in the task of deriving a suitable explanatory model. It seems possible to identify a small number of variables with an important and probably true influence on the outcome, but too often several variables are included whose selection may be a result of chance or may depend on a small number of observations.

We develop an asymptotic likelihood ratio test for multivariate lognormal data with a point mass at zero in each dimension. The test generalizes Wilks' lambda and Hotelling *T*-test to the case of semicontinuous data. Simulations show that the resulting test statistic attains the nominal Type I error rate and has good power for reasonable alternatives. We conclude with an application to exploration of ecological niches of trees of South Africa.

New markers may improve prediction of diagnostic and prognostic outcomes. We aimed to review options for graphical display and summary measures to assess the predictive value of markers over standard, readily available predictors. We illustrated various approaches using previously published data on 3264 participants from the Framingham Heart Study, where 183 developed coronary heart disease (10-year risk 5.6%). We considered performance measures for the incremental value of adding HDL cholesterol to a prediction model. An initial assessment may consider statistical significance (HR = 0.65, 95% confidence interval 0.53 to 0.80; likelihood ratio *p* < 0.001), and distributions of predicted risks (densities or box plots) with various summary measures. A range of decision thresholds is considered in predictiveness and receiver operating characteristic curves, where the area under the curve (AUC) increased from 0.762 to 0.774 by adding HDL. We can furthermore focus on reclassification of participants with and without an event in a reclassification graph, with the continuous net reclassification improvement (NRI) as a summary measure. When we focus on one particular decision threshold, the changes in sensitivity and specificity are central. We propose a net reclassification risk graph, which allows us to focus on the number of reclassified persons and their event rates. Summary measures include the binary AUC, the two-category NRI, and decision analytic variants such as the net benefit (NB). Various graphs and summary measures can be used to assess the incremental predictive value of a marker. Important insights for impact on decision making are provided by a simple graph for the net reclassification risk.

A method for simultaneously assessing noninferiority with respect to efficacy and superiority with respect to another endpoint in two-arm noninferiority trials is presented. The procedure controls both the average type I error rate for the intersection-union test problem and the frequentist type I error rate for the noninferiority test by α while allowing an increased level for the superiority test. For normally distributed outcomes, two methods are presented to deal with the uncertainty about the correlation between the endpoints which defines the adjusted levels. The operating characteristics of these procedures are investigated. Furthermore, the sample size required when applying the proposed method is compared with that of alternative procedures. Application of the method in the situation of binary endpoints and mixed normal and binary endpoints, respectively, is sketched. An illustrative example is provided demonstrating implementation of the proposed approach in a clinical trial.

]]>Survey data often contain measurements for variables that are semicontinuous in nature, i.e. they either take a single fixed value (we assume this is zero) or they have a continuous, often skewed, distribution on the positive real line. Standard methods for small area estimation (SAE) based on the use of linear mixed models can be inefficient for such variables. We discuss SAE techniques for semicontinuous variables under a two part random effects model that allows for the presence of excess zeros as well as the skewed nature of the nonzero values of the response variable. In particular, we first model the excess zeros via a generalized linear mixed model fitted to the probability of a nonzero, i.e. strictly positive, value being observed, and then model the response, given that it is strictly positive, using a linear mixed model fitted on the logarithmic scale. Empirical results suggest that the proposed method leads to efficient small area estimates for semicontinuous data of this type. We also propose a parametric bootstrap method to estimate the MSE of the proposed small area estimator. These bootstrap estimates of the MSE are compared to the true MSE in a simulation study.

]]>In randomized clinical trials where the times to event of two treatment groups are compared under a proportional hazards assumption, it has been established that omitting prognostic factors from the model entails an underestimation of the hazards ratio. Heterogeneity due to unobserved covariates in cancer patient populations is a concern since genomic investigations have revealed molecular and clinical heterogeneity in these populations. In HIV prevention trials, heterogeneity is unavoidable and has been shown to decrease the treatment effect over time. This article assesses the influence of trial duration on the bias of the estimated hazards ratio resulting from omitting covariates from the Cox analysis. The true model is defined by including an unobserved random frailty term in the individual hazard that reflects the omitted covariate. Three frailty distributions are investigated: gamma, log-normal, and binary, and the asymptotic bias of the hazards ratio estimator is calculated. We show that the attenuation of the treatment effect resulting from unobserved heterogeneity strongly increases with trial duration, especially for continuous frailties that are likely to reflect omitted covariates, as they are often encountered in practice. The possibility of interpreting the long-term decrease in treatment effects as a bias induced by heterogeneity and trial duration is illustrated by a trial in oncology where adjuvant chemotherapy in stage 1B NSCLC was investigated.

]]>Caries infiltration is a novel treatment option for proximal caries lesions. The idea is to build a diffusion barrier inside the lesion to slow down or stop the caries progression. If a lesion still reaches a critical size, restorative treatment is required. Clinical trials investigating caries infiltration thus produce multiple censored ordinal data. Standard statistical models do not take into account this censoring, and we therefore propose the Multiple Ordered Tobit (MOT) model. The model is implemented in R and compared with standard approaches. Simulation studies demonstrate that for all sample sizes and scenarios the MOT model has the largest statistical power among all methods compared, and it is robust against heteroscedasticity to some extent. Finally, a comparison with dichotomous and ordinal scaled models shows that the use of metric data for the lesion size reduces the required sample size considerably.

]]>When the efficacy of a new medical drug is compared against that of an established competitor in a randomized controlled trial, the difference in patient-relevant outcomes, such as mortality, is usually measured directly. In diagnostic research, however, the impact of diagnostic procedures is of an indirect nature as test results do influence downstream clinical decisions, but test performance (as characterized by sensitivity, specificity, and the predictive values of a procedure) is, at best, only a surrogate endpoint for patient outcome and does not necessarily translate into it. Not many randomized controlled trials have been conducted so far in diagnostic research, and, hence, we need alternative approaches to close the gap between test characteristics and patient outcomes. Several informal approaches have been suggested in order to close this gap, and decision modeling has been advocated as a means of obtaining formal approaches. Recently, the expected benefit has been proposed as a quantity that allows a simple formal approach, and we take up this suggestion in this paper. We regard the expected benefit as an estimation problem and consider two approaches to statistical inference. Moreover, using data from a previously published study, we illustrate the possible insights to be gained from the application of formal inference techniques to determine the expected benefit.

]]>To reduce the lengthy duration of a crossover trial for comparing three treatments, the incomplete block design has been often considered. A sample size calculation procedure for testing nonequality between either of the two experimental treatments and a placebo under such a design is developed. To evaluate the performance of the proposed sample size calculation procedure, Monte Carlo simulation is employed. The accuracy of the sample size calculation procedure developed here is demonstrated in a variety of situations. As compared with the parallel groups design, a substantial proportional reduction in the total minimum required sample size in use of the incomplete block crossover design is found. A crossover trial comparing two different doses of formoterol with a placebo on the forced expiratory volume is applied to illustrate the use of the sample size calculation procedure.

]]>Instead of assessing the overall fit of candidate models like the traditional model selection criteria, the focused information criterion focuses attention directly on the parameter of the primary interest and aims to select the model with the minimum estimated mean squared error for the estimate of the focused parameter. In this article we apply the focused information criterion for personalized medicine. By using individual-level information from clinical observations, demographics, and genetics, we obtain the personalized predictive models to make the prognosis and diagnosis individually. The consideration of the heterogeneity among the individuals helps reduce the prediction uncertainty and improve the prediction accuracy. Two real data examples from biomedical research are studied as illustrations.

]]>In observational studies with dichotomous outcome of a population, researchers usually report treatment effect alone, although both baseline risk and treatment effect are needed to evaluate the significance of the treatment effect to the population. In this article, we study point and interval estimates including confidence region of baseline risk and treatment effect based on logistic model, where baseline risk is the risk of outcome of the population under control treatment while treatment effect is measured by the risk difference between outcomes of the population under active versus control treatments. Using approximate normal distribution of the maximum-likelihood (ML) estimate of the model parameters, we obtain an approximate joint distribution of the ML estimate of the baseline risk and the treatment effect. Using the approximate joint distribution, we obtain point estimate and confidence region of the baseline risk and the treatment effect as well as point estimate and confidence interval of the treatment effect when the ML estimate of the baseline risk falls into specified range. These interval estimates reflect nonnormality of the joint distribution of the ML estimate of the baseline risk and the treatment effect. The method can be easily implemented by using any software that generates normal distribution. The method can also be used to obtain point and interval estimates of baseline risk and any other measure of treatment effect such as risk ratio and the number needed to treat. The method can also be extended from logistic model to other models such as log-linear model.

]]>Using the conditional likelihood, a model-specific score test can be derived under a given genetic model to test genetic association for case-parents triad family data. When the underlying genetic model is correctly specified, the score test is most powerful. However, it can lose substantial power when the model is misspecified. Several robust tests have been proposed to deal with the problem, such as the maximum test statistic, the maximin efficiency robust test, and the constrained likelihood ratio test. These tests have been shown to be robust against model misspecification compared with those model-specific score tests, but they are either time-consuming in computation or not sufficiently high in power robustness under some situations. In this study, a data-driven procedure is proposed to construct two adaptive robust genetic association tests *W*_{MERT} and *W*_{MAX}. The *W*_{MERT} is simple in calculation and has fairly high power robustness. The empirical power of *W*_{MAX} is quite stable and close to those of the model-specific score tests. The two proposed tests should be beneficial to practical genetic association studies. A real dataset consisting of neural tube defect triad families is used for illustration of the methods. R-scripts are also provided for numerical calculation of the proposed methods in practical studies.

This paper proposes a semiparametric methodology for modeling multivariate and conditional distributions. We first build a multivariate distribution whose dependence structure is induced by a Gaussian copula and whose marginal distributions are estimated nonparametrically via mixtures of B-spline densities. The conditional distribution of a given variable is obtained in closed form from this multivariate distribution. We take a Bayesian approach, using Markov chain Monte Carlo methods for inference. We study the frequentist properties of the proposed methodology via simulation and apply the method to estimation of conditional densities of summary statistics, used for computing conditional local false discovery rates, from genetic association studies of schizophrenia and cardiovascular disease risk factors.

]]>We consider modelling the movements of larvae using individual bioassays in which data are collected at a high-frequency rate of five observations per second. The aim is to characterize the behaviour of the larvae when exposed to attractant and repellent compounds. Mixtures of diffusion processes, as well as Hidden Markov models, are proposed as models of larval movement. These models account for directed and localized movements, and successfully distinguish between the behaviour of larvae exposed to attractant and repellent compounds. A simulation study illustrates the advantage of using a Hidden Markov model rather than a simpler mixture model. Practical aspects of model estimation and inference are considered on extensive data collected in a study of novel approaches for the management of cabbage root fly.

]]>Shape analysis is of great importance in many fields of medical imaging and computational biology. In this paper, we consider the shape space as the set of smooth planar immersed curves in (parameterized curves) and, using the property of being isometric to a classical manifold immersed in a Euclidean space, we introduce a new extrinsic sample mean and a new extrinsic variance for a finite set of shapes, which are not necessarily star shaped. This is a fundamental tool in medical image analysis, for instance, to assess uncertainties that arise in locating anatomical structures such as the prostate and the bladder. We apply it to a dataset consisting of parallel planar axial CT sections of human prostate, in order to study the variability between boundaries that have been manually delineated by several observers.

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