The case series method is useful in studying the relationship between time-varying exposures, such as infections, and acute events observed during the observation periods of individuals. It provides estimates of the relative incidences of events in risk periods (e.g., 30-day period after infections) relative to the baseline periods. When the times of exposure onsets are not known precisely, application of the case series model ignoring exposure onset measurement error leads to biased estimates. Bias-correction is necessary in order to understand the true directions and effect sizes associated with exposure risk periods, although uncorrected estimators have smaller variance. Thus, inference via hypothesis testing based on uncorrected test statistics, if valid, is potentially more powerful. Furthermore, the tests can be implemented in standard software and do not require additional auxiliary data. In this work, we examine the validity and power of naive hypothesis testing, based on applying the case series analysis to the imprecise data without correcting for the error. Based on simulation studies and theoretical calculations, we determine the validity and relative power of common hypothesis tests of interest in case series analysis. In particular, we illustrate that the tests for the global null hypothesis, the overall null hypotheses associated with all risk periods or all age effects are valid. However, tests of individual risk period parameters are not generally valid. Practical guidelines are provided and illustrated with data from patients on dialysis.

The classical accelerated failure time (AFT) model has been extensively investigated due to its direct interpretation of the covariate effects on the mean survival time in survival analysis. However, this classical AFT model and its associated methodologies are built on the fundamental assumption of data homoscedasticity. Consequently, when the homoscedasticity assumption is violated as often seen in the real applications, the estimators lose efficiency and the associated inference is not reliable. Furthermore, none of the existing methods can estimate the intercept consistently. To overcome these drawbacks, we propose a semiparametric approach in this article for both homoscedastic and heteroscedastic data. This approach utilizes a weighted least-squares equation with synthetic observations weighted by square root of their variances where the variances are estimated via the local polynomial regression. We establish the limiting distributions of the resulting coefficient estimators and prove that both slope parameters and the intercept can be consistently estimated. We evaluate the finite sample performance of the proposed approach through simulation studies and demonstrate its superiority through real example on its efficiency and reliability over the existing methods when the data is heteroscedastic.

In this article, we propose a generalized estimating equations (GEE) approach for correlated ordinal or nominal multinomial responses using a local odds ratios parameterization. Our motivation lies upon observing that: (i) modeling the dependence between correlated multinomial responses via the local odds ratios is meaningful both for ordinal and nominal response scales and (ii) ordinary GEE methods might not ensure the joint existence of the estimates of the marginal regression parameters and of the dependence structure. To avoid (ii), we treat the so-called “working” association vector as a “nuisance” parameter vector that defines the local odds ratios structure at the marginalized contingency tables after tabulating the responses without a covariate adjustment at each time pair. To estimate and simultaneously approximate adequately possible underlying dependence structures, we employ the family of association models proposed by Goodman. In simulations, the parameter estimators with the proposed GEE method for a marginal cumulative probit model appear to be less biased and more efficient than those with the independence “working” model, especially for studies having time-varying covariates and strong correlation.

We reexamine the subject of sample size determination (SSD) when testing logarithm of odds ratio (OR) against zero in two independent binomials. Four common approaches are considered: a closed-form SS formula based on the Wald test (), closed-form formulas that meet SS requirement by score and exact tests respectively ( and ), and a numerical approach to calculating SS based on likelihood ratio (LR) tests (). Several practically useful findings are presented. First, is a strictly convex function of OR for OR and OR , respectively, implying that SS calculated by does not necessarily decrease as OR gets further away from 1. However, minimum SS often occurs at OR values that are deemed relatively extreme and rare in real life. , and decrease monotonically as OR diverges from 1. Secondly, the optimal sampling ratio (OSR) between two independent binomials that yields maximum power for a given total SS is not always 1:1 but depends on the odds of outcome in each arm. benefits the most from the application of OSR in that total SS can be significantly reduced as compared to the commonly used 1:1 sampling ratio. Savings in SS by OSR in , and are relatively immaterial from a practical perspective. Finally, we use simulation studies to examine the power loyalty of each SS approach and explore penalized likelihood as a remedy for undermined power loyalty.

For testing stationarity of a given spatial point pattern, Guan (2008) proposed a model-free statistic, based on the deviations between observed and expected counts of points in expanding regions within the sampling window. This article extends his method to a general class of statistics by incorporating also such information when points are projected to the axes and by allowing different ways to construct regions in which the deviations are considered. The limiting distributions of the new statistics can be expressed in terms of integrals of a Brownian sheet and hence asymptotic critical values can be approximated. A simulation study shows that the new tests are always more powerful than that of Guan. When applied to the longleaf pine data where Guan's test gave an inconclusive answer, the new tests indicate a clear rejection of the stationarity hypothesis.

Spatially referenced binary data are common in epidemiology and public health. Owing to its elegant log-odds interpretation of the regression coefficients, a natural model for these data is logistic regression. To account for missing confounding variables that might exhibit a spatial pattern (say, socioeconomic, biological, or environmental conditions), it is customary to include a Gaussian spatial random effect. Conditioned on the spatial random effect, the coefficients may be interpreted as log odds ratios. However, marginally over the random effects, the coefficients no longer preserve the log-odds interpretation, and the estimates are hard to interpret and generalize to other spatial regions. To resolve this issue, we propose a new spatial random effect distribution through a copula framework which ensures that the regression coefficients maintain the log-odds interpretation both conditional on and marginally over the spatial random effects. We present simulations to assess the robustness of our approach to various random effects, and apply it to an interesting dataset assessing periodontal health of Gullah-speaking African Americans. The proposed methodology is flexible enough to handle areal or geo-statistical datasets, and hierarchical models with multiple random intercepts.

In clinical and observational studies, the event of interest can often recur on the same subject. In a more complicated situation, there exists a terminal event (e.g., death) which stops the recurrent event process. In many such instances, the terminal event is strongly correlated with the recurrent event process. We consider the recurrent/terminal event setting and model the dependence through a shared gamma frailty that is included in both the recurrent event rate and terminal event hazard functions. Conditional on the frailty, a model is specified only for the marginal recurrent event process, hence avoiding the strong Poisson-type assumptions traditionally used. Analysis is based on estimating functions that allow for estimation of covariate effects on the recurrent event rate and terminal event hazard. The method also permits estimation of the degree of association between the two processes. Closed-form asymptotic variance estimators are proposed. The proposed method is evaluated through simulations to assess the applicability of the asymptotic results in finite samples and the sensitivity of the method to its underlying assumptions. The methods can be extended in straightforward ways to accommodate multiple types of recurrent and terminal events. Finally, the methods are illustrated in an analysis of hospitalization data for patients in an international multi-center study of outcomes among dialysis patients.

To explore the nonlinear interactions between covariates and an index variable, partially linear proportional hazards models have been proposed for censored survival data. However, specification of the partially linear structure was usually carried out in an ad-hoc manner by first fitting a full varying-coefficient model and visually examining the resulting fit to identify the linear part. In this article, we consider the problem of coefficient estimation and constant coefficient identification based on a double shrinkage approach. Variable selection is also considered in a coherent estimation framework, resulting in a double-penalization procedure. Under the mild assumptions, we establish asymptotic properties for the procedure such as consistency, sparesistency, constansistency, and asymptotic normality. We evaluate the performance of the proposed method by numerical simulations and demonstrate its application using a breast cancer data set.

We propose semiparametric methods for estimating the effect of a time-dependent covariate on treatment-free survival. The data structure of interest consists of a longitudinal sequence of measurements and a potentially censored survival time. The factor of interest is time-dependent. Treatment-free survival is of interest and is dependently censored by the receipt of treatment. Patients may be removed from consideration for treatment, temporarily or permanently. The proposed methods combine landmark analysis and partly conditional hazard regression. A set of calendar time cross-sections is specified, and survival time (from cross-section date) is modeled through weighted Cox regression. The assumed model for death is marginal in the sense that time-varying covariates are taken as fixed at each landmark, with the mortality hazard function implicitly averaging across future covariate trajectories. Dependent censoring is overcome by a variant of inverse probability of censoring weighting (IPCW). The proposed estimators are shown to be consistent and asymptotically normal, with consistent covariance estimators provided. Simulation studies reveal that the proposed estimation procedures are appropriate for practical use. We apply the proposed methods to pre-transplant mortality among end-stage liver disease (ESLD) patients.

The natural direct effect (NDE), or the effect of an exposure on an outcome if an intermediate variable was set to the level it would have been in the absence of the exposure, is often of interest to investigators. In general, the statistical parameter associated with the NDE is difficult to estimate in the non-parametric model, particularly when the intermediate variable is continuous or high dimensional. In this article, we introduce a new causal parameter called the natural direct effect among the untreated, discus identifiability assumptions, propose a sensitivity analysis for some of the assumptions, and show that this new parameter is equivalent to the NDE in a randomized controlled trial. We also present a targeted minimum loss estimator (TMLE), a locally efficient, double robust substitution estimator for the statistical parameter associated with this causal parameter. The TMLE can be applied to problems with continuous and high dimensional intermediate variables, and can be used to estimate the NDE in a randomized controlled trial with such data. Additionally, we define and discuss the estimation of three related causal parameters: the natural direct effect among the treated, the indirect effect among the untreated and the indirect effect among the treated.

We describe a Bayesian technique to (a) perform a sparse joint selection of significant predictor variables and significant inverse covariance matrix elements of the response variables in a high-dimensional linear Gaussian sparse seemingly unrelated regression (SSUR) setting and (b) perform an association analysis between the high-dimensional sets of predictors and responses in such a setting. To search the high-dimensional model space, where both the number of predictors and the number of possibly correlated responses can be larger than the sample size, we demonstrate that a marginalization-based collapsed Gibbs sampler, in combination with spike and slab type of priors, offers a computationally feasible and efficient solution. As an example, we apply our method to an expression quantitative trait loci (eQTL) analysis on publicly available single nucleotide polymorphism (SNP) and gene expression data for humans where the primary interest lies in finding the significant associations between the sets of SNPs and possibly correlated genetic transcripts. Our method also allows for inference on the sparse interaction network of the transcripts (response variables) after accounting for the effect of the SNPs (predictor variables). We exploit properties of Gaussian graphical models to make statements concerning conditional independence of the responses. Our method compares favorably to existing Bayesian approaches developed for this purpose.

In this article, we consider two-phase sampling in the situation in which all covariates are categorical. Two-phase designs are appealing from an efficiency perspective since they allow sampling to be concentrated in informative cells. A number of likelihood-based methods have been developed for the analysis of two-phase data, but we describe a Bayesian approach which has previously been unavailable. The methods are first compared with existing approaches via a simulation study, and are then applied to data collected on Wilms tumor. The benefits of a Bayesian approach include relaxation of the reliance on asymptotic inference, particularly in sparse data situations, and the potential to model data with complex dependencies, for example, via the introduction of random effects. The sparse data situation is illustrated via a simulated example.

Directed acyclic graphical (DAG) models are increasingly employed in the study of physical and biological systems to model direct influences between variables. Identifying the graph from data is a challenging endeavor, which can be more reasonably tackled if the variables are assumed to satisfy a given ordering; in this case we simply have to estimate the presence or absence of each potential edge. Working under this assumption, we propose an objective Bayesian method for searching the space of Gaussian DAG models, which provides a rich output from minimal input. We base our analysis on non-local parameter priors, which are especially suited for learning sparse graphs, because they allow a faster learning rate, relative to ordinary local parameter priors, when the true unknown sampling distribution belongs to a simple model. We implement an efficient stochastic search algorithm, which deals effectively with data sets having sample size smaller than the number of variables, and apply our method to a variety of simulated and real data sets. Our approach compares favorably, in terms of the ROC curve for edge hit rate versus false alarm rate, to current state-of-the-art frequentist methods relying on the assumption of ordered variables; under this assumption it exhibits a competitive advantage over the PC-algorithm, which can be considered as a frequentist benchmark for unordered variables. Importantly, we find that our method is still at an advantage for learning the skeleton of the DAG, when the ordering of the variables is only moderately mis-specified. Prospectively, our method could be coupled with a strategy to learn the order of the variables, thus dropping the known ordering assumption.

Feature (variable) selection has become a fundamentally important problem in recent statistical literature. Sometimes, in applications, many variables are introduced to reduce possible modeling biases, but the number of variables a model can accommodate is often limited by the amount of data available. In other words, the number of variables considered depends on the sample size, which reflects the estimability of the parametric model. In this article, we consider the problem of feature selection in finite mixture of regression models when the number of parameters in the model can increase with the sample size. We propose a penalized likelihood approach for feature selection in these models. Under certain regularity conditions, our approach leads to consistent variable selection. We carry out extensive simulation studies to evaluate the performance of the proposed approach under controlled settings. We also applied the proposed method to two real data. The first is on telemonitoring of Parkinson's disease (PD), where the problem concerns whether dysphonic features extracted from the patients’ speech signals recorded at home can be used as surrogates to study PD severity and progression. The second is on breast cancer prognosis, in which one is interested in assessing whether cell nuclear features may offer prognostic values on long-term survival of breast cancer patients. Our analysis in each of the application revealed a mixture structure in the study population and uncovered a unique relationship between the features and the response variable in each of the mixture component.

We consider the problem of testing each of m null hypotheses with a sequential permutation procedure in which the number of draws from the permutation distribution of each test statistic is a random variable. Each sequential permutation p-value has a null distribution that is nonuniform on a discrete support. We show how to use a collection of such p-values to estimate the number of true null hypotheses m₀ among the m null hypotheses tested and how to estimate the false discovery rate (FDR) associated with p-value significance thresholds. We use real data analyses and simulation studies to evaluate and illustrate the performance of our proposed approach relative to standard, more computationally intensive strategies. We find that our sequential approach produces similar results with far less computational expense in a variety of scenarios.

Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method.

This article deals with jointly modeling a large number of geographically referenced outcomes observed over a very large number of locations. We seek to capture associations among the variables as well as the strength of spatial association for each variable. In addition, we reckon with the common setting where not all the variables have been observed over all locations, which leads to spatial misalignment. Dimension reduction is needed in two aspects: (i) the length of the vector of outcomes, and (ii) the very large number of spatial locations. Latent variable (factor) models are usually used to address the former, although low-rank spatial processes offer a rich and flexible modeling option for dealing with a large number of locations. We merge these two ideas to propose a class of hierarchical low-rank spatial factor models. Our framework pursues stochastic selection of the latent factors without resorting to complex computational strategies (such as reversible jump algorithms) by utilizing certain identifiability characterizations for the spatial factor model. A Markov chain Monte Carlo algorithm is developed for estimation that also deals with the spatial misalignment problem. We recover the full posterior distribution of the missing values (along with model parameters) in a Bayesian predictive framework. Various additional modeling and implementation issues are discussed as well. We illustrate our methodology with simulation experiments and an environmental data set involving air pollutants in California.

We propose a method for high-dimensional curve clustering in the presence of interindividual variability. Curve clustering has longly been studied especially using splines to account for functional random effects. However, splines are not appropriate when dealing with high-dimensional data and can not be used to model irregular curves such as peak-like data. Our method is based on a wavelet decomposition of the signal for both fixed and random effects. We propose an efficient dimension reduction step based on wavelet thresholding adapted to multiple curves and using an appropriate structure for the random effect variance, we ensure that both fixed and random effects lie in the same functional space even when dealing with irregular functions that belong to Besov spaces. In the wavelet domain our model resumes to a linear mixed-effects model that can be used for a model-based clustering algorithm and for which we develop an EM-algorithm for maximum likelihood estimation. The properties of the overall procedure are validated by an extensive simulation study. Then, we illustrate our method on mass spectrometry data and we propose an original application of functional data analysis on microarray comparative genomic hybridization (CGH) data. Our procedure is available through the R package curvclust which is the first publicly available package that performs curve clustering with random effects in the high dimensional framework (available on the CRAN).

Functional principal components (FPC) analysis is widely used to decompose and express functional observations. Curve estimates implicitly condition on basis functions and other quantities derived from FPC decompositions; however these objects are unknown in practice. In this article, we propose a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions. Additionally, pointwise and simultaneous confidence intervals that account for both model- and decomposition-based variability are constructed. Standard mixed model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition. Iterated expectation and variance formulas combine model-based conditional estimates across the distribution of decompositions. A bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities. Our method compares favorably to competing approaches in simulation studies that include both densely and sparsely observed functions. We apply our method to sparse observations of CD4 cell counts and to dense white-matter tract profiles. Code for the analyses and simulations is publicly available, and our method is implemented in the R package refund on CRAN.

This article studies a semiparametric accelerated failure time mixture model for estimation of a biological treatment effect on a latent subgroup of interest with a time-to-event outcome in randomized clinical trials. Latency is induced because membership is observable in one arm of the trial and unidentified in the other. This method is useful in randomized clinical trials with all-or-none noncompliance when patients in the control arm have no access to active treatment and in, for example, oncology trials when a biopsy used to identify the latent subgroup is performed only on subjects randomized to active treatment. We derive a computational method to estimate model parameters by iterating between an expectation step and a weighted Buckley–James optimization step. The bootstrap method is used for variance estimation, and the performance of our method is corroborated in simulation. We illustrate our method through an analysis of a multicenter selective lymphadenectomy trial for melanoma.

In order to monitor a medical center's survival outcomes using simple plots, we introduce a risk-adjusted Observed–Expected (O–E) Cumulative SUM (CUSUM) along with monitoring bands as decision criterion.The proposed monitoring bands can be used in place of a more traditional but complicated V-shaped mask or the simultaneous use of two one-sided CUSUMs. The resulting plot is designed to simultaneously monitor for failure time outcomes that are “worse than expected” or “better than expected.” The slopes of the O–E CUSUM provide direct estimates of the relative risk (as compared to a standard or expected failure rate) for the data being monitored. Appropriate rejection regions are obtained by controlling the false alarm rate (type I error) over a period of given length. Simulation studies are conducted to illustrate the performance of the proposed method. A case study is carried out for 58 liver transplant centers. The use of CUSUM methods for quality improvement is stressed.

When faced with categorical predictors and a continuous response, the objective of an analysis often consists of two tasks: finding which factors are important and determining which levels of the factors differ significantly from one another. Often times, these tasks are done separately using Analysis of Variance (ANOVA) followed by a post hoc hypothesis testing procedure such as Tukey's Honestly Significant Difference test. When interactions between factors are included in the model the collapsing of levels of a factor becomes a more difficult problem. When testing for differences between two levels of a factor, claiming no difference would refer not only to equality of main effects, but also to equality of each interaction involving those levels. This structure between the main effects and interactions in a model is similar to the idea of heredity used in regression models. This article introduces a new method for accomplishing both of the common analysis tasks simultaneously in an interaction model while also adhering to the heredity-type constraint on the model. An appropriate penalization is constructed that encourages levels of factors to collapse and entire factors to be set to zero. It is shown that the procedure has the oracle property implying that asymptotically it performs as well as if the exact structure were known beforehand. We also discuss the application to estimating interactions in the unreplicated case. Simulation studies show the procedure outperforms post hoc hypothesis testing procedures as well as similar methods that do not include a structural constraint. The method is also illustrated using a real data example.

Many regression analyses involve explanatory variables that are measured with error, and failing to account for this error is well known to lead to biased point and interval estimates of the regression coefficients. We present here a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski–Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation. We develop the theory in the setting of classical likelihood models; this setting covers, for example, linear regression, nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not involving assumptions on the distribution of the true covariate. We discuss the theoretical properties of the method and present simulation results in the logistic regression setting (univariate and multivariate). For illustration, we apply the method to data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer.

In ROC analysis, covariate adjustment is advocated when the covariates impact the magnitude or accuracy of the test under study. Meanwhile, for many large scale screening tests, the true condition status may be subject to missingness because it is expensive and/or invasive to ascertain the disease status. The complete-case analysis may end up with a biased inference, also known as “verification bias.” To address the issue of covariate adjustment with verification bias in ROC analysis, we propose several estimators for the area under the covariate-specific and covariate-adjusted ROC curves (AUC_x and AAUC). The AUC_x is directly modeled in the form of binary regression, and the estimating equations are based on the U statistics. The AAUC is estimated from the weighted average of AUC_x over the covariate distribution of the diseased subjects. We employ reweighting and imputation techniques to overcome the verification bias problem. Our proposed estimators are initially derived assuming that the true disease status is missing at random (MAR), and then with some modification, the estimators can be extended to the not missing at random (NMAR) situation. The asymptotic distributions are derived for the proposed estimators. The finite sample performance is evaluated by a series of simulation studies. Our method is applied to a data set in Alzheimer's disease research.

Most current Bayesian SEIR (Susceptible, Exposed, Infectious, Removed (or Recovered)) models either use exponentially distributed latent and infectious periods, allow for a single distribution on the latent and infectious period, or make strong assumptions regarding the quantity of information available regarding time distributions, particularly the time spent in the exposed compartment. Many infectious diseases require a more realistic assumption on the latent and infectious periods. In this article, we provide an alternative model allowing general distributions to be utilized for both the exposed and infectious compartments, while avoiding the need for full latent time data. The alternative formulation is a path-specific SEIR (PS SEIR) model that follows individual paths through the exposed and infectious compartments, thereby removing the need for an exponential assumption on the latent and infectious time distributions. We show how the PS SEIR model is a stochastic analog to a general class of deterministic SEIR models. We then demonstrate the improvement of this PS SEIR model over more common population averaged models via simulation results and perform a new analysis of the Iowa mumps epidemic from 2006.

The estimation of future prevalences of chronic diseases is essential for public health policy. Using incidence estimates from cohort data and demographic projections for general mortality and population sizes, we propose a method based on a general illness–death model to make prevalence projections for chronic diseases. In contrast to previously published methods, we account for differences between global mortality and mortality of healthy subjects and compare two assumptions regarding the secular trend for mortality of diseased subjects. Then we develop a methodology to estimate changes in future disease prevalences resulting from prevention campaign to reduce the frequency or the excess risk associated with a risk factor. The methods are applied for estimating dementia prevalence in France between 2010 and 2030.

In an observational study, one treated subject may be matched for observed covariates to either one or several untreated controls. The common motivation for using several controls rather than one is to increase the power of a test of no effect under the doubtful assumption that matching for observed covariates suffices to remove bias from nonrandom treatment assignment. Does the choice between one or several matched controls affect the sensitivity of conclusions to violations of this doubtful assumption? With continuous responses, it is known that reducing the heterogeneity of matched pair differences reduces sensitivity to unmeasured biases, but increasing the sample size has a highly circumscribed effect on sensitivity to bias. Is the use of several controls rather than one analogous to a reduction in heterogeneity or to an increase in sample size? The issue is examined for Huber's m-statistics, including the t-test, the examination having three components: an example, asymptotic calculations using design sensitivity, and a simulation. Use of multiple controls with continuous responses yields a nontrivial reduction in sensitivity to unmeasured biases. An example looks at lead and cadmium in the blood of smokers from the 2008 National Health and Nutrition Examination Survey. A by-product of the discussion is a new result giving the design sensitivity for the permutation distribution of m-statistics.

A primary objective in the application of postmarketing drug safety surveillance is to ascertain the relationship between time-varying drug exposures and recurrent adverse events (AEs) related to health outcomes. The self-controlled case series (SCCS) method is one approach to analysis in this context. It is based on a conditional Poisson regression model, which assumes that events at different time points are conditionally independent given the covariate process. This requirement is problematic when the occurrence of an event can alter the future event risk. In a clinical setting, for example, patients who have a first myocardial infarction (MI) may be at higher subsequent risk for a second. In this work, we propose the positive dependence self-controlled case series (PD-SCCS) method: a generalization of SCCS that allows the occurrence of an event to increase the future event risk, yet maintains the advantages of the original model by controlling for fixed baseline covariates and relying solely on data from cases. As in the SCCS model, individual-level baseline parameters drop out of the PD-SCCS likelihood. Data sources used for postmarketing surveillance can contain tens of millions of people, so in this situation it is particularly advantageous that PD-SCCS avoids doing a costly estimation of individual parameters. We develop expressions for large sample inference and optimization for PD-SCCS and compare the results of our generalized model with the more restrictive SCCS approach.

Testing homogeneity of dispersions may be of its own scientific interest as well as an important auxiliary step verifying assumptions of a main analysis. The problem is that many biological and ecological data are highly skewed and zero-inflated. Also the number of variables often exceeds the sample size. Thus data analysts often do not rely on parametric assumptions, but use a particular dissimilarity measure to calculate a matrix of pairwise differences. This matrix is then the basis for further statistical inference. Anderson (2006) proposed a distance-based test of homogeneity of multivariate dispersions for a one-way ANOVA design, for which a matrix of pairwise dissimilarities can be taken as an input. The key idea, like in Levene's test, is to replace each observation with its distance to an estimated group center. In this paper we suggest an alternative approach that is based on the means of within-group distances and does not require group centre calculations to obtain the test statistic. We show that this approach can have theoretical as well as practical advantages. A permutation procedure that gives type I error close to the prescribed value even in small samples is described.

Many animal monitoring studies seek to estimate the proportion of a study area occupied by a target population. The study area is divided into spatially distinct sites where the detected presence or absence of the population is recorded, and this is repeated in time for multiple seasons. However, when occupied sites are detected with probability p < 1, the lack of a detection does not imply lack of occupancy. MacKenzie et al. (2003, Ecology 84, 2200–2207) developed a multiseason model for estimating seasonal site occupancy (ψ_t) while accounting for unknown p. Their model performs well when observations are collected according to the robust design, where multiple sampling occasions occur during each season; the repeated sampling aids in the estimation p. However, their model does not perform as well when the robust design is lacking. In this paper, we propose an alternative likelihood model that yields improved seasonal estimates of p and Ψ_t in the absence of the robust design. We construct the marginal likelihood of the observed data by conditioning on, and summing out, the latent number of occupied sites during each season. A simulation study shows that in cases without the robust design, the proposed model estimates p with less bias than the MacKenzie et al. model and hence improves the estimates of Ψ_t. We apply both models to a data set consisting of repeated presence–absence observations of American robins (Turdus migratorius) with yearly survey periods. The two models are compared to a third estimator available when the repeated counts (from the same study) are considered, with the proposed model yielding estimates of Ψ_t closest to estimates from the point count model.

This article is motivated by an interest in comparing inferences made when using a Bayesian or frequentist statistical approach. The article addresses the study of one-sided superiority and noninferiority Bayesian tests. These tests are stated in terms of the posterior probability that the null hypothesis is true for the binomial distribution and in terms of one-sided credible limits. We restrict our considerations to conjugate beta priors with integer parameters. Under this assumption, the posterior probabilities of tested hypotheses can be transformed into the frequentist probabilities of Bernoulli trials with an adjusted number of events and population sizes. The method resembles a standard frequentist problem formulation. By using an appropriate choice of prior parameters, the posterior probabilities of the null hypothesis can be made smaller or larger than the p-values of frequentist tests.

While the population-based case-control approach is the popular study design for association mapping of complex genetic traits because of ease of data collection and statistical analyses, it suffers from the inherent problem of population stratification. There have been methodological developments for adjusting these studies for population substructure, but efficient estimation of the number of subpopulations (K), which has evolutionary significance, remains a statistical challenge. In this article, we propose a Bayesian semiparametric approach to estimate population substructure under the assumption that K is random. Using extensive simulations, we find that our proposed method is not only computationally much faster than an existing Bayesian approach Structure, but also estimates the number of subpopulations more accurately, and thus, yields more power in detecting association in case-control studies.

We discuss inference for a human phage display experiment with three stages. The data are tripeptide counts by tissue and stage. The primary aim of the experiment is to identify ligands that bind with high affinity to a given tissue. We formalize the research question as inference about the monotonicity of mean counts over stages. The inference goal is then to identify a list of peptide–tissue pairs with significant increase over stages. We use a semiparametric Dirichlet process mixture of Poisson model. The posterior distribution under this model allows the desired inference about the monotonicity of mean counts. However, the desired inference summary as a list of peptide–tissue pairs with significant increase involves a massive multiplicity problem. We consider two alternative approaches to address this multiplicity issue. First we propose an approach based on the control of the posterior expected false discovery rate. We notice that the implied solution ignores the relative size of the increase. This motivates a second approach based on a utility function that includes explicit weights for the size of the increase.

This article considers linear regression models with long memory errors. These models have been proven useful for application in many areas, such as medical imaging, signal processing, and econometrics. Wavelets, being self-similar, have a strong connection to long memory data. Here we employ discrete wavelet transforms as whitening filters to simplify the dense variance–covariance matrix of the data. We then adopt a Bayesian approach for the estimation of the model parameters. Our inferential procedure uses exact wavelet coefficients variances and leads to accurate estimates of the model parameters. We explore performances on simulated data and present an application to an fMRI data set. In the application we produce posterior probability maps (PPMs) that aid interpretation by identifying voxels that are likely activated with a given confidence.

Several statistical approaches for the analysis of longitudinal data require that models be correctly specified for the association between a current outcome and the full history of past outcomes and time-dependent exposures. It is empirically challenging to determine the specific aspects of the outcome and/or exposure history that are predictive of a current outcome because the potential number of variables representing the history can be quite large. The purpose of this article is to outline statistical methods that can characterize lagged effects and to provide a structured approach for data analysis with the goal of appropriate model development. One of the main contributions of the article is to emphasize the possibility that in practice transition models may frequently require more than simple additive and linear models for the predictors representing the history of the outcome and covariate processes. We illustrate the concepts using an example from anemia treatment for dialysis patients and show how linear models can be specified with flexible dependence on exposure and/or outcome histories.

Patients who were previously treated for prostate cancer with radiation therapy are monitored at regular intervals using a laboratory test called Prostate Specific Antigen (PSA). If the value of the PSA test starts to rise, this is an indication that the prostate cancer is more likely to recur, and the patient may wish to initiate new treatments. Such patients could be helped in making medical decisions by an accurate estimate of the probability of recurrence of the cancer in the next few years. In this article, we describe the methodology for giving the probability of recurrence for a new patient, as implemented on a web-based calculator. The methods use a joint longitudinal survival model. The model is developed on a training dataset of 2386 patients and tested on a dataset of 846 patients. Bayesian estimation methods are used with one Markov chain Monte Carlo (MCMC) algorithm developed for estimation of the parameters from the training dataset and a second quick MCMC developed for prediction of the risk of recurrence that uses the longitudinal PSA measures from a new patient.

Longitudinal behavioral intervention trials to reduce HIV transmission risk collect complex multilevel and multivariate data longitudinally for each subject with important correlation structures across time, level, and variables. Accurately assessing the effects of these trials are critical for determining which interventions are effective. Both numbers of partners and numbers of sex acts with each partner are reported at each time point. Sex acts with each partner are further differentiated into protected and unprotected acts with correspondingly differing risks of HIV/STD transmission. These trials generally also have eligibility criteria limiting enrollment to participants with some minimal level of risky sexual behavior tied directly to the outcome of interest. The combination of these factors makes it difficult to quantify sexual behaviors and the effects of intervention. We propose a multivariate multilevel count model that simultaneously models the number of partners, acts within partners, and accounts for recruitment eligibility. Our methods are useful in the evaluation of intervention trials and provide a more accurate and complete model for sexual behavior. We illustrate the contributions of our model by examining seroadaptive behavior defined as risk reducing behavior that depends on the serostatus of the partner. Several forms of seroadaptive risk reducing behavior are quantified and distinguished from nonseroadaptive risk reducing behavior.

This article reports an analysis that aims to quantify the effect of fingolimod, an oral treatment for relapsing remitting multiple sclerosis (MS), on disability progression. The standard approach utilizes survival analysis methods, which may be problematic for MS studies that assess disability at only a few time points and include as a cardinal feature both relapses and remissions. Instead, a Markov transition model, originally developed in the framework of longitudinal data, is fit, and its special probabilistic properties are used to estimate survival curves for time to disability progression. The transition approach models the whole disability process and uses all available transition data for inference, while survival methods concentrate on a single event of interest and use only time to event data. This article compares the transition model approach to survival analysis methods, and discusses the differences in the interpretations of the estimated parameters. It applies both models to data obtained from two phase 3 clinical trials and finds that both yield positive effects for the new treatment compared to placebo, and provide similar estimates for the probability of disability progression over time. The transition model enables calculation of covariate-specific transition matrices that describe the short-term effect of treatment and other covariates on the disability process.

Evaluating vaccine efficacy for protection against colonization with bacterial pathogens is an area of growing interest. Colonization of the nasopharynx is an asymptomatic carrier state responsible for person-to-person transmission. It differs from most clinical outcomes in that it is common, recurrent, and observed only in its prevalent state. To estimate rates of acquisition and clearance of colonization requires repeated active sampling of the same individuals over time, an expensive and invasive undertaking. Motivated by feasibility constraints in efficacy trials with colonization endpoints, investigators have been estimating vaccine efficacy from cross-sectional studies without principled methods. We present two examples of vaccine studies estimating vaccine efficacy from cross-sectional data on nasopharyngeal colonization by Streptococcus pneumoniae (pneumococcus). This study presents a framework for defining and estimating strain-specific and overall vaccine efficacy for susceptibility to acquisition of colonization () when there is a large number of strains with mutual interactions and recurrent dynamics of colonization. We develop estimators based on one observation of the current status per study subject, evaluate their robustness, and re-analyze the two vaccine trials. Methodologically, the proposed estimators are closely related to case–control studies with prevalent cases, with appropriate consideration of the at-risk time in choosing the controls.

False-positive test results are among the most common harms of screening tests and may lead to more invasive and expensive diagnostic testing procedures. Estimating the cumulative risk of a false-positive screening test result after repeat screening rounds is, therefore, important for evaluating potential screening regimens. Existing estimators of the cumulative false-positive risk are limited by strong assumptions about censoring mechanisms and parametric assumptions about variation in risk across screening rounds. To address these limitations, we propose a semiparametric censoring bias model for cumulative false-positive risk that allows for dependent censoring without specifying a fixed functional form for variation in risk across screening rounds. Simulation studies demonstrated that the censoring bias model performs similarly to existing models under independent censoring and can largely eliminate bias under dependent censoring. We used the existing and newly proposed models to estimate the cumulative false-positive risk and variation in risk as a function of baseline age and family history of breast cancer after 10 years of annual screening mammography using data from the Breast Cancer Surveillance Consortium. Ignoring potential dependent censoring in this context leads to underestimation of the cumulative risk of false-positive results. Models that provide accurate estimates under dependent censoring are critical for providing appropriate information for evaluating screening tests.

Safety analysis to estimate the effect of a treatment on an adverse event poses a challenging statistical problem even in randomized controlled trials because these events are typically rare, so studies originally powered for efficacy are underpowered for safety outcomes. A meta-analysis of data pooled across multiple studies may increase power, but missingness in the outcome or failed randomization can introduce bias. This article illustrates how targeted maximum likelihood estimation (TMLE) can be applied in a meta-analysis to reduce bias in causal effect estimates, and compares performance with other estimators in the literature. A simulation study in which missingness in the outcome is at random or completely at random highlights the differences in estimators with respect to the potential gains in bias and efficiency. Risk difference, relative risk, and odds ratio of the effect of treatment on 30-daymortality are estimated from data from eight randomized controlled trials. When an outcome event is rare there may be little opportunity to improve efficiency, and associations between covariates and the outcome may be hard to detect. TMLE attempts to exploit the available information to either meet or exceed the performance of a less sophisticated estimator.

Methods based on the propensity score comprise one set of valuable tools for comparative effectiveness research and for estimating causal effects more generally. These methods typically consist of two distinct stages: (1) a propensity score stage where a model is fit to predict the propensity to receive treatment (the propensity score), and (2) an outcome stage where responses are compared in treated and untreated units having similar values of the estimated propensity score. Traditional techniques conduct estimation in these two stages separately; estimates from the first stage are treated as fixed and known for use in the second stage. Bayesian methods have natural appeal in these settings because separate likelihoods for the two stages can be combined into a single joint likelihood, with estimation of the two stages carried out simultaneously. One key feature of joint estimation in this context is “feedback” between the outcome stage and the propensity score stage, meaning that quantities in a model for the outcome contribute information to posterior distributions of quantities in the model for the propensity score. We provide a rigorous assessment of Bayesian propensity score estimation to show that model feedback can produce poor estimates of causal effects absent strategies that augment propensity score adjustment with adjustment for individual covariates. We illustrate this phenomenon with a simulation study and with a comparative effectiveness investigation of carotid artery stenting versus carotid endarterectomy among 123,286 Medicare beneficiaries hospitlized for stroke in 2006 and 2007.

Modeling the spatial distribution of a species is a fundamental problem in ecology. A number of modeling methods have been developed, an extremely popular one being MAXENT, a maximum entropy modeling approach. In this article, we show that MAXENT is equivalent to a Poisson regression model and hence is related to a Poisson point process model, differing only in the intercept term, which is scale-dependent in MAXENT. We illustrate a number of improvements to MAXENT that follow from these relations. In particular, a point process model approach facilitates methods for choosing the appropriate spatial resolution, assessing model adequacy, and choosing the LASSO penalty parameter, all currently unavailable to MAXENT. The equivalence result represents a significant step in the unification of the species distribution modeling literature.

In the context of randomized trials, Rosenblum and van der Laan (2009, Biometrics 63, 937–945) considered the null hypothesis of no treatment effect on the mean outcome within strata of baseline variables. They showed that hypothesis tests based on linear regression models and generalized linear regression models are guaranteed to have asymptotically correct Type I error regardless of the actual data generating distribution, assuming the treatment assignment is independent of covariates. We consider another important outcome in randomized trials, the time from randomization until failure, and the null hypothesis of no treatment effect on the survivor function conditional on a set of baseline variables. By a direct application of arguments in Rosenblum and van der Laan (2009), we show that hypothesis tests based on multiplicative hazards models with an exponential link, i.e., proportional hazards models, and multiplicative hazards models with linear link functions where the baseline hazard is parameterized, are asymptotically valid under model misspecification provided that the censoring distribution is independent of the treatment assignment given the covariates. In the case of the Cox model and linear link model with unspecified baseline hazard function, the arguments in Rosenblum and van der Laan (2009) cannot be applied to show the robustness of a misspecified model. Instead, we adopt an approach used in previous literature (Struthers and Kalbfleisch, 1986, Biometrika 73, 363–369) to show that hypothesis tests based on these models, including models with interaction terms, have correct type I error.