This article develops a Bayesian semiparametric approach to the extended hazard model, with generalization to high-dimensional spatially grouped data. County-level spatial correlation is accommodated marginally through the normal transformation model of Li and Lin (2006, *Journal of the American Statistical Association* **101**, 591–603), using a correlation structure implied by an intrinsic conditionally autoregressive prior. Efficient Markov chain Monte Carlo algorithms are developed, especially applicable to fitting very large, highly censored areal survival data sets. Per-variable tests for proportional hazards, accelerated failure time, and accelerated hazards are efficiently carried out with and without spatial correlation through Bayes factors. The resulting reduced, interpretable spatial models can fit significantly better than a standard additive Cox model with spatial frailties.

Several statistical methods for meta-analysis of diagnostic accuracy studies have been discussed in the presence of a gold standard. However, in practice, the selected reference test may be imperfect due to measurement error, non-existence, invasive nature, or expensive cost of a gold standard. It has been suggested that treating an imperfect reference test as a gold standard can lead to substantial bias in the estimation of diagnostic test accuracy. Recently, two models have been proposed to account for imperfect reference test, namely, a multivariate generalized linear mixed model (MGLMM) and a hierarchical summary receiver operating characteristic (HSROC) model. Both models are very flexible in accounting for heterogeneity in accuracies of tests across studies as well as the dependence between tests. In this article, we show that these two models, although with different formulations, are closely related and are equivalent in the absence of study-level covariates. Furthermore, we provide the exact relations between the parameters of these two models and assumptions under which two models can be reduced to equivalent submodels. On the other hand, we show that some submodels of the MGLMM do not have corresponding equivalent submodels of the HSROC model, and vice versa. With three real examples, we illustrate the cases when fitting the MGLMM and HSROC models leads to equivalent submodels and hence identical inference, and the cases when the inferences from two models are slightly different. Our results generalize the important relations between the bivariate generalized linear mixed model and HSROC model when the reference test is a gold standard.

In the classic discriminant model of two multivariate normal distributions with equal variance matrices, the linear discriminant function is optimal both in terms of the log likelihood ratio and in terms of maximizing the standardized difference (the *t*-statistic) between the means of the two distributions. In a typical case–control study, normality may be sensible for the control sample but heterogeneity and uncertainty in diagnosis may suggest that a more flexible model is needed for the cases. We generalize the *t*-statistic approach by finding the linear function which maximizes a standardized difference but with data from one of the groups (the cases) filtered by a possibly nonlinear function *U*. We study conditions for consistency of the method and find the function *U* which is optimal in the sense of asymptotic efficiency. Optimality may also extend to other measures of discriminatory efficiency such as the area under the receiver operating characteristic curve. The optimal function *U* depends on a scalar probability density function which can be estimated non-parametrically using a standard numerical algorithm. A lasso-like version for variable selection is implemented by adding -regularization to the generalized *t*-statistic. Two microarray data sets in the study of asthma and various cancers are used as motivating examples.

Implementation study is an important tool for deploying state-of-the-art treatments from clinical efficacy studies into a treatment program, with the dual goals of learning about effectiveness of the treatments and improving the quality of care for patients enrolled into the program. In this article, we deal with the design of a treatment program of dynamic treatment regimens (DTRs) for patients with depression post-acute coronary syndrome. We introduce a novel adaptive randomization scheme for a sequential multiple assignment randomized trial of DTRs. Our approach adapts the randomization probabilities to favor treatment sequences having comparatively superior *Q*-functions used in *Q*-learning. The proposed approach addresses three main concerns of an implementation study: it allows incorporation of historical data or opinions, it includes randomization for learning purposes, and it aims to improve care via adaptation throughout the program. We demonstrate how to apply our method to design a depression treatment program using data from a previous study. By simulation, we illustrate that the inputs from historical data are important for the program performance measured by the expected outcomes of the enrollees, but also show that the adaptive randomization scheme is able to compensate poorly specified historical inputs by improving patient outcomes within a reasonable horizon. The simulation results also confirm that the proposed design allows efficient learning of the treatments by alleviating the curse of dimensionality.

Acar and Sun (2013, *Biometrics* **69**, 427–435) presented a generalized Kruskal–Wallis (GKW) test for genetic association studies that incorporated the genotype uncertainty and showed its robust and competitive performance compared to existing methods. We present another interesting way to derive the GKW test via a rank linear model.

We propose a novel statistical framework by supplementing case–control data with summary statistics on the population at risk for a subset of risk factors. Our approach is to first form two unbiased estimating equations, one based on the case–control data and the other on both the case data and the summary statistics, and then optimally combine them to derive another estimating equation to be used for the estimation. The proposed method is computationally simple and more efficient than standard approaches based on case–control data alone. We also establish asymptotic properties of the resulting estimator, and investigate its finite-sample performance through simulation. As a substantive application, we apply the proposed method to investigate risk factors for endometrial cancer, by using data from a recently completed population-based case–control study and summary statistics from the Behavioral Risk Factor Surveillance System, the Population Estimates Program of the US Census Bureau, and the Connecticut Department of Transportation.

In diverse fields of empirical research—including many in the biological sciences—attempts are made to decompose the effect of an exposure on an outcome into its effects via a number of different pathways. For example, we may wish to separate the effect of heavy alcohol consumption on systolic blood pressure (SBP) into effects via body mass index (BMI), via gamma-glutamyl transpeptidase (GGT), and via other pathways. Much progress has been made, mainly due to contributions from the field of causal inference, in understanding the precise nature of statistical estimands that capture such intuitive effects, the assumptions under which they can be identified, and statistical methods for doing so. These contributions have focused almost entirely on settings with a single mediator, or a set of mediators considered *en bloc*; in many applications, however, researchers attempt a much more ambitious decomposition into numerous path-specific effects through many mediators. In this article, we give counterfactual definitions of such path-specific estimands in settings with multiple mediators, when earlier mediators may affect later ones, showing that there are many ways in which decomposition can be done. We discuss the strong assumptions under which the effects are identified, suggesting a sensitivity analysis approach when a particular subset of the assumptions cannot be justified. These ideas are illustrated using data on alcohol consumption, SBP, BMI, and GGT from the Izhevsk Family Study. We aim to bridge the gap from “single mediator theory” to “multiple mediator practice,” highlighting the ambitious nature of this endeavor and giving practical suggestions on how to proceed.

Event-history studies of recurrent events are often conducted in fields such as demography, epidemiology, medicine, and social sciences (Cook and Lawless, 2007, The *Statistical Analysis of Recurrent Events*. New York: Springer-Verlag; Zhao et al., 2011, *Test* **20**, 1–42). For such analysis, two types of data have been extensively investigated: recurrent-event data and panel-count data. However, in practice, one may face a third type of data, mixed recurrent-event and panel-count data or mixed event-history data. Such data occur if some study subjects are monitored or observed continuously and thus provide recurrent-event data, while the others are observed only at discrete times and hence give only panel-count data. A more general situation is that each subject is observed continuously over certain time periods but only at discrete times over other time periods. There exists little literature on the analysis of such mixed data except that published by Zhu et al. (2013, *Statistics in Medicine* **32**, 1954–1963). In this article, we consider the regression analysis of mixed data using the additive rate model and develop some estimating equation-based approaches to estimate the regression parameters of interest. Both finite sample and asymptotic properties of the resulting estimators are established, and the numerical studies suggest that the proposed methodology works well for practical situations. The approach is applied to a Childhood Cancer Survivor Study that motivated this study.

Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for high-dimensional data. Methods are used in applications including high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep.

In clinical trials, minimum clinically important difference (MCID) has attracted increasing interest as an important supportive clinical and statistical inference tool. Many estimation methods have been developed based on various intuitions, while little theoretical justification has been established. This article proposes a new estimation framework of the MCID using both diagnostic measurements and patient-reported outcomes (PROs). The framework first formulates the population-based MCID as a large margin classification problem, and then extends to the personalized MCID to allow individualized thresholding value for patients whose clinical profiles may affect their PRO responses. More importantly, the proposed estimation framework is showed to be asymptotically consistent, and a finite-sample upper bound is established for its prediction accuracy compared against the ideal MCID. The advantage of our proposed method is also demonstrated in a variety of simulated experiments as well as two phase-3 clinical trials.

Multistate models are used to characterize individuals’ natural histories through diseases with discrete states. Observational data resources based on electronic medical records pose new opportunities for studying such diseases. However, these data consist of observations of the process at discrete sampling times, which may either be pre-scheduled and non-informative, or symptom-driven and informative about an individual's underlying disease status. We have developed a novel joint observation and disease transition model for this setting. The disease process is modeled according to a latent continuous-time Markov chain; and the observation process, according to a Markov-modulated Poisson process with observation rates that depend on the individual's underlying disease status. The disease process is observed at a combination of informative and non-informative sampling times, with possible misclassification error. We demonstrate that the model is computationally tractable and devise an expectation-maximization algorithm for parameter estimation. Using simulated data, we show how estimates from our joint observation and disease transition model lead to less biased and more precise estimates of the disease rate parameters. We apply the model to a study of secondary breast cancer events, utilizing mammography and biopsy records from a sample of women with a history of primary breast cancer.

The effect of a targeted agent on a cancer patient's clinical outcome putatively is mediated through the agent's effect on one or more early biological events. This is motivated by pre-clinical experiments with cells or animals that identify such events, represented by binary or quantitative biomarkers. When evaluating targeted agents in humans, central questions are whether the distribution of a targeted biomarker changes following treatment, the nature and magnitude of this change, and whether it is associated with clinical outcome. Major difficulties in estimating these effects are that a biomarker's distribution may be complex, vary substantially between patients, and have complicated relationships with clinical outcomes. We present a probabilistically coherent framework for modeling and estimation in this setting, including a hierarchical Bayesian nonparametric mixture model for biomarkers that we use to define a functional profile of pre-versus-post-treatment biomarker distribution change. The functional is similar to the receiver operating characteristic used in diagnostic testing. The hierarchical model yields clusters of individual patient biomarker profile functionals, and we use the profile as a covariate in a regression model for clinical outcome. The methodology is illustrated by analysis of a dataset from a clinical trial in prostate cancer using imatinib to target platelet-derived growth factor, with the clinical aim to improve progression-free survival time.

The N-mixture model is widely used to estimate the abundance of a population in the presence of unknown detection probability from only a set of counts subject to spatial and temporal replication (Royle, 2004, *Biometrics* **60**, 105–115). We explain and exploit the equivalence of N-mixture and multivariate Poisson and negative-binomial models, which provides powerful new approaches for fitting these models. We show that particularly when detection probability and the number of sampling occasions are small, infinite estimates of abundance can arise. We propose a sample covariance as a diagnostic for this event, and demonstrate its good performance in the Poisson case. Infinite estimates may be missed in practice, due to numerical optimization procedures terminating at arbitrarily large values. It is shown that the use of a bound, *K*, for an infinite summation in the N-mixture likelihood can result in underestimation of abundance, so that default values of *K* in computer packages should be avoided. Instead we propose a simple automatic way to choose *K*. The methods are illustrated by analysis of data on Hermann's tortoise *Testudo hermanni*.

Thanks to the growing interest in personalized medicine, joint modeling of longitudinal marker and time-to-event data has recently started to be used to derive dynamic individual risk predictions. Individual predictions are called dynamic because they are updated when information on the subject's health profile grows with time. We focus in this work on statistical methods for quantifying and comparing dynamic predictive accuracy of this kind of prognostic models, accounting for right censoring and possibly competing events. Dynamic area under the ROC curve (AUC) and Brier Score (BS) are used to quantify predictive accuracy. Nonparametric inverse probability of censoring weighting is used to estimate dynamic curves of AUC and BS as functions of the time at which predictions are made. Asymptotic results are established and both pointwise confidence intervals and simultaneous confidence bands are derived. Tests are also proposed to compare the dynamic prediction accuracy curves of two prognostic models. The finite sample behavior of the inference procedures is assessed via simulations. We apply the proposed methodology to compare various prediction models using repeated measures of two psychometric tests to predict dementia in the elderly, accounting for the competing risk of death. Models are estimated on the French Paquid cohort and predictive accuracies are evaluated and compared on the French Three-City cohort.

Multi-site time series studies have reported evidence of an association between short term exposure to particulate matter (PM) and adverse health effects, but the effect size varies across the United States. Variability in the effect may partially be due to differing community level exposure and health characteristics, but also due to the chemical composition of PM which is known to vary greatly by location and time. The objective of this article is to identify particularly harmful components of this chemical mixture. Because of the large number of highly-correlated components, we must incorporate some regularization into a statistical model. We assume that, at each spatial location, the regression coefficients come from a mixture model with the flavor of stochastic search variable selection, but utilize a copula to share information about variable inclusion and effect magnitude across locations. The model differs from current spatial variable selection techniques by accommodating both local and global variable selection. The model is used to study the association between fine PM (PM 2.5m) components, measured at 115 counties nationally over the period 2000–2008, and cardiovascular emergency room admissions among Medicare patients.

Recent advances in genomics and biotechnologies have accelerated the development of molecularly targeted treatments and accompanying markers to predict treatment responsiveness. However, it is common at the initiation of a definitive phase III clinical trial that there is no compelling biological basis or early trial data for a candidate marker regarding its capability in predicting treatment effects. In this case, it is reasonable to include all patients as eligible for randomization but to plan for prospective subgroup analysis based on the marker. One analysis plan in such all-comers designs is the so-called fallback approach that first tests for overall treatment efficacy and then proceeds to test in a biomarker-positive subgroup if the first test is not significant. In this approach, owing to the adaptive nature of the analysis and a correlation between the two tests, a bias will arise in estimating the treatment effect in the biomarker-positive subgroup after a non-significant first overall test. In this article, we formulate the bias function and show a difficulty in obtaining unbiased estimators for a whole range of an associated parameter. To address this issue, we propose bias-corrected estimation methods, including those based on an approximation of the bias function under a bounded range of the parameter using polynomials. We also provide an interval estimation method based on a bivariate doubly truncated normal distribution. Simulation experiments demonstrated a success in bias reduction. Application to a phase III trial for lung cancer is provided.

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, *Journal of the Royal Statistical Society, Series B* **74**, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

Instrumental variable (IV) methods are popular in non-experimental studies to estimate the causal effects of medical interventions. These approaches allow for the consistent estimation of treatment effects even if important confounding factors are unobserved. Despite the increasing use of these methods, there have been few extensions of IV methods to censored data problems. In this article, we discuss challenges in applying IV techniques to the proportional hazards model and demonstrate the utility of the additive hazards formulation for IV analyses with censored data. Assuming linear structural equation models for the hazard function, we develop a closed-form, two-stage estimator for the causal effect in the additive hazard model. The methods permit both continuous and discrete exposures, and enable the estimation of causal relative survival measures. The asymptotic properties of the estimators are derived and the resulting inferences are shown to perform well in simulation studies and in an application to a data set on the effectiveness of a novel chemotherapeutic agent for colon cancer.

We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a “full” model. We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso. We show the resulting method, here called the LSA method, to be an (asymptotically) oracle model selection method. The finite sample performance of the proposed LSA method is investigated with Monte Carlo simulations, in which we examine the percentage of selecting true ODE models, the efficiency of the parameter estimation compared to simply using the full and true models, and coverage probabilities of the estimated confidence intervals for ODE parameters, all of which have satisfactory performances. Our method is also demonstrated by selecting the best predator-prey ODE to model a lynx and hare population dynamical system among some well-known and biologically interpretable ODE models.

We present a simple general method for combining two one-sample confidence procedures to obtain inferences in the two-sample problem. Some applications give striking connections to established methods; for example, combining exact binomial confidence procedures gives new confidence intervals on the difference or ratio of proportions that match inferences using Fisher's exact test, and numeric studies show the associated confidence intervals bound the type I error rate. Combining exact one-sample Poisson confidence procedures recreates standard confidence intervals on the ratio, and introduces new ones for the difference. Combining confidence procedures associated with one-sample *t*-tests recreates the Behrens–Fisher intervals. Other applications provide new confidence intervals with fewer assumptions than previously needed. For example, the method creates new confidence intervals on the difference in medians that do not require shift and continuity assumptions. We create a new confidence interval for the difference between two survival distributions at a fixed time point when there is independent censoring by combining the recently developed beta product confidence procedure for each single sample. The resulting interval is designed to guarantee coverage regardless of sample size or censoring distribution, and produces equivalent inferences to Fisher's exact test when there is no censoring. We show theoretically that when combining intervals asymptotically equivalent to normal intervals, our method has asymptotically accurate coverage. Importantly, all situations studied suggest guaranteed nominal coverage for our new interval whenever the original confidence procedures themselves guarantee coverage.

The increasing cost of drug development has raised the demand for surrogate endpoints when evaluating new drugs in clinical trials. However, over the years, it has become clear that surrogate endpoints need to be statistically evaluated and deemed valid, before they can be used as substitutes of “true” endpoints in clinical studies. Nowadays, two paradigms, based on causal-inference and meta-analysis, dominate the scene. Nonetheless, although the literature emanating from these paradigms is wide, till now the relationship between them has largely been left unexplored. In the present work, we discuss the conceptual framework underlying both approaches and study the relationship between them using theoretical elements and the analysis of a real case study. Furthermore, we show that the meta-analytic approach can be embedded within a causal-inference framework on the one hand and that it can be heuristically justified why surrogate endpoints successfully evaluated using this approach will often be appealing from a causal-inference perspective as well, on the other. A newly developed and user friendly R package *Surrogate* is provided to carry out the evaluation exercise.

The Northern Humboldt Current System (NHCS) is the world's most productive ecosystem in terms of fish. In particular, the Peruvian anchovy (Engraulis ringens) is the major prey of the main top predators, like seabirds, fish, humans, and other mammals. In this context, it is important to understand the dynamics of the anchovy distribution to preserve it as well as to exploit its economic capacities. Using the data collected by the “Instituto del Mar del Perú” (IMARPE) during a scientific survey in 2005, we present a statistical analysis that has as main goals: (i) to adapt to the characteristics of the sampled data, such as spatial dependence, high proportions of zeros and big size of samples; (ii) to provide important insights on the dynamics of the anchovy population; and (iii) to propose a model for estimation and prediction of anchovy biomass in the NHCS offshore from Perú. These data were analyzed in a Bayesian framework using the integrated nested Laplace approximation (INLA) method. Further, to select the best model and to study the predictive power of each model, we performed model comparisons and predictive checks, respectively. Finally, we carried out a Bayesian spatial influence diagnostic for the preferred model.

In many scientific and engineering applications, covariates are naturally grouped. When the group structures are available among covariates, people are usually interested in identifying both important groups and important variables within the selected groups. Among existing successful group variable selection methods, some methods fail to conduct the within group selection. Some methods are able to conduct both group and within group selection, but the corresponding objective functions are non-convex. Such a non-convexity may require extra numerical effort. In this article, we propose a novel Log-Exp-Sum(LES) penalty for group variable selection. The LES penalty is strictly convex. It can identify important groups as well as select important variables within the group. We develop an efficient group-level coordinate descent algorithm to fit the model. We also derive non-asymptotic error bounds and asymptotic group selection consistency for our method in the high-dimensional setting where the number of covariates can be much larger than the sample size. Numerical results demonstrate the good performance of our method in both variable selection and prediction. We applied the proposed method to an American Cancer Society breast cancer survivor dataset. The findings are clinically meaningful and may help design intervention programs to improve the qualify of life for breast cancer survivors.

Ecological studies that make use of data on groups of individuals, rather than on the individuals themselves, are subject to numerous biases that cannot be resolved without some individual-level data. In the context of a rare outcome, the hybrid design for ecological inference efficiently combines group-level data with individual-level case-control data. Unfortunately, except in relatively simple settings, use of the design in practice is limited since evaluation of the hybrid likelihood is computationally prohibitively expensive. In this article we first propose and develop an alternative representation of the hybrid likelihood. Second, based on this new representation, a series of approximations are proposed that drastically reduce computational burden. A comprehensive simulation shows that, in a broad range of scenarios, estimators based on the approximate hybrid likelihood exhibit the same operating characteristics as the exact hybrid likelihood, without any penalty in terms of increased bias or reduced efficiency. Third, in settings where the approximations may not hold, a pragmatic estimation and inference strategy is developed that uses the approximate form for some likelihood contributions and the exact form for others. The strategy gives researchers the ability to balance computational tractability with accuracy in their own settings. Finally, as a by-product of the development, we provide the first explicit characterization of the hybrid aggregate data design which combines data from an aggregate data study (Prentice and Sheppard, 1995, *Biometrika* 82, 113–125) with case–control samples. The methods are illustrated using data from North Carolina on births between 2007 and 2009.

Mixed latent Markov (MLM) models represent an important tool of analysis of longitudinal data when response variables are affected by time-fixed and time-varying unobserved heterogeneity, in which the latter is accounted for by a hidden Markov chain. In order to avoid bias when using a model of this type in the presence of informative drop-out, we propose an event-history (EH) extension of the latent Markov approach that may be used with multivariate longitudinal data, in which one or more outcomes of a different nature are observed at each time occasion. The EH component of the resulting model is referred to the interval-censored drop-out, and bias in MLM modeling is avoided by correlated random effects, included in the different model components, which follow common latent distributions. In order to perform maximum likelihood estimation of the proposed model by the expectation–maximization algorithm, we extend the usual forward-backward recursions of Baum and Welch. The algorithm has the same complexity as the one adopted in cases of non-informative drop-out. We illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest, one continuous and the other binary.

A recent article (Zhang et al., 2012, *Biometrics* **168**, 1010–1018) compares regression based and inverse probability based methods of estimating an optimal treatment regime and shows for a small number of covariates that inverse probability weighted methods are more robust to model misspecification than regression methods. We demonstrate that using models that fit the data better reduces the concern about non-robustness for the regression methods. We extend the simulation study of Zhang et al. (2012, *Biometrics* **168**, 1010–1018), also considering the situation of a larger number of covariates, and show that incorporating random forests into both regression and inverse probability weighted based methods improves their properties.

Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects is essential for practical data analysis. Simultaneous selection of variables in both longitudinal and survival components functions as a necessary safeguard against model misspecification. However, variable selection in such models has not been studied. No existing computational tools, to the best of our knowledge, have been made available to practitioners. In this article, we describe a penalized likelihood method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for simultaneous selection of fixed and random effects in joint models. To perform selection in variance components of random effects, we reparameterize the variance components using a Cholesky decomposition; in doing so, a penalty function of group shrinkage is introduced. To reduce the estimation bias resulted from penalization, we propose a two-stage selection procedure in which the magnitude of the bias is ameliorated in the second stage. The penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. Simulation study showed excellent selection results in the first stage and small estimation biases in the second stage. To illustrate, we analyzed a longitudinally observed clinical marker and patient survival in a cohort of patients with heart failure.

Pooling of controls under nested-case control settings can produce substantial efficiency gains compared to standard time-matched analysis using the Mantel–Haenszel method or conditional logistic regression. In the context of possible adverse effects of early childhood vaccinations, we propose pooling of the information from the controls to estimate the population exposure prevalence as a parametric or nonparametric function of time, and possibly other factors. This function in turn may be used as a plug-in estimate to control for confounding in the subsequent estimation of rate ratios. We derive standard errors for the resulting two-step estimators, demonstrate through simulations the efficiency gains compared to standard matched analysis, and propose a novel graphical presentation of the vaccination and adverse event time data. We formulate the methods in the general framework of case-base sampling, which subsumes the different case-control and case-only methods.

Ordinal outcomes arise frequently in clinical studies when each subject is assigned to a category and the categories have a natural order. Classification rules for ordinal outcomes may be developed with commonly used regression models such as the full continuation ratio (CR) model (fCR), which allows the covariate effects to differ across all continuation ratios, and the CR model with a proportional odds structure (pCR), which assumes the covariate effects to be constant across all continuation ratios. For settings where the covariate effects differ between some continuation ratios but not all, fitting either fCR or pCR may lead to suboptimal prediction performance. In addition, these standard models do not allow for nonlinear covariate effects. In this article, we propose a sparse CR kernel machine (KM) regression method for ordinal outcomes where we use the KM framework to incorporate nonlinearity and impose sparsity on the overall differences between the covariate effects of continuation ratios to control for overfitting. In addition, we provide data driven rule to select an optimal kernel to maximize the prediction accuracy. Simulation results show that our proposed procedures perform well under both linear and nonlinear settings, especially when the true underlying model is in-between fCR and pCR models. We apply our procedures to develop a prediction model for levels of anti-CCP among rheumatoid arthritis patients and demonstrate the advantage of our method over other commonly used methods.

Frequentist concepts, such as the control of the type I error or the false discovery rate, are well established in the medical literature and often required by regulators. Most Bayesian designs are defined without explicit considerations of frequentist characteristics. Once the Bayesian design is structured, statisticians use simulations and adjust tuning parameters to comply with a set of targeted operating characteristics. These adjustments affect the use of prior information and utility functions. Here we consider a Bayesian decision theoretic approach for experimental designs with explicit frequentist requisites. We define optimal designs under a set of constraints required by a regulator. Our approach combines the use of interpretable utility functions with frequentist criteria, and selects an optimal design that satisfies a set of required operating characteristics. We illustrate the approach using a group-sequential multi-arm Phase II trial and a bridging trial.

Pocock et al. (2012, *European Heart Journal* **33**, 176–182) proposed a win ratio approach to analyzing composite endpoints comprised of outcomes with different clinical priorities. In this article, we establish a statistical framework for this approach. We derive the null hypothesis and propose a closed-form variance estimator for the win ratio statistic in all pairwise matching situation. Our simulation study shows that the proposed variance estimator performs well regardless of the magnitude of treatment effect size and the type of the joint distribution of the outcomes.

Motivated by field sampling of DNA fragments, we describe a general model for capture–recapture modeling of samples drawn one at a time in continuous-time. Our model is based on Poisson sampling where the sampling time may be unobserved. We show that previously described models correspond to partial likelihoods from our Poisson model and their use may be justified through arguments concerning *S*- and Bayes-ancillarity of discarded information. We demonstrate a further link to continuous-time capture–recapture models and explain observations that have been made about this class of models in terms of partial ancillarity. We illustrate application of our models using data from the European badger (*Meles meles*) in which genotyping of DNA fragments was subject to error.

Research in the field of nonparametric shape constrained regression has been intensive. However, only few publications explicitly deal with unimodality although there is need for such methods in applications, for example, in dose–response analysis. In this article, we propose unimodal spline regression methods that make use of Bernstein–Schoenberg splines and their shape preservation property. To achieve unimodal and smooth solutions we use penalized splines, and extend the penalized spline approach toward penalizing against general parametric functions, instead of using just difference penalties. For tuning parameter selection under a unimodality constraint a restricted maximum likelihood and an alternative Bayesian approach for unimodal regression are developed. We compare the proposed methodologies to other common approaches in a simulation study and apply it to a dose–response data set. All results suggest that the unimodality constraint or the combination of unimodality and a penalty can substantially improve estimation of the functional relationship.

We develop a linear mixed regression model where both the response and the predictor are functions. Model parameters are estimated by maximizing the log likelihood via the ECME algorithm. The estimated variance parameters or covariance matrices are shown to be positive or positive definite at each iteration. In simulation studies, the approach outperforms in terms of the fitting error and the MSE of estimating the “regression coefficients.”

Motivated by objective measurements of physical activity, we take a functional data approach to longitudinal data with simultaneous measurement of a continuous and a binary outcomes. The regression structures are specified as smooth curves measured at various time-points with random effects that have a hierarchical correlation structure. The random effect curves for each variable are summarized using a few important principal components, and the association of the two longitudinal variables is modeled through the association of the principal component scores. We use penalized splines to model the mean curves and the principal component curves, and cast the proposed model into a mixed effects model framework for model fitting, prediction and inference. Via a quasilikelihood type approximation for the binary component, we develop an algorithm to fit the model. Data-based transformation of the continuous variable and selection of the number of principal components are incorporated into the algorithm. The method is applied to the motivating physical activity data and is evaluated empirically by a simulation study. Extensions for different types of outcomes are also discussed.

Studying the interactions between different brain regions is essential to achieve a more complete understanding of brain function. In this article, we focus on identifying functional co-activation patterns and undirected functional networks in neuroimaging studies. We build a functional brain network, using a sparse covariance matrix, with elements representing associations between region-level peak activations. We adopt a penalized likelihood approach to impose sparsity on the covariance matrix based on an extended multivariate Poisson model. We obtain penalized maximum likelihood estimates via the expectation-maximization (EM) algorithm and optimize an associated tuning parameter by maximizing the predictive log-likelihood. Permutation tests on the brain co-activation patterns provide region pair and network-level inference. Simulations suggest that the proposed approach has minimal biases and provides a coverage rate close to 95% of covariance estimations. Conducting a meta-analysis of 162 functional neuroimaging studies on emotions, our model identifies a functional network that consists of connected regions within the basal ganglia, limbic system, and other emotion-related brain regions. We characterize this network through statistical inference on region-pair connections as well as by graph measures.

We consider the problem of robust estimation of the regression relationship between a response and a covariate based on sample in which precise measurements on the covariate are not available but error-prone surrogates for the unobserved covariate are available for each sampled unit. Existing methods often make restrictive and unrealistic assumptions about the density of the covariate and the densities of the regression and the measurement errors, for example, normality and, for the latter two, also homoscedasticity and thus independence from the covariate. In this article we describe Bayesian semiparametric methodology based on mixtures of B-splines and mixtures induced by Dirichlet processes that relaxes these restrictive assumptions. In particular, our models for the aforementioned densities adapt to asymmetry, heavy tails and multimodality. The models for the densities of regression and measurement errors also accommodate conditional heteroscedasticity. In simulation experiments, our method vastly outperforms existing methods. We apply our method to data from nutritional epidemiology.

Mediation analysis is important for understanding the mechanisms whereby one variable causes changes in another. Measurement error could obscure the ability of the potential mediator to explain such changes. This article focuses on developing correction methods for measurement error in the mediator with failure time outcomes. We consider a broad definition of measurement error, including technical error, and error associated with temporal variation. The underlying model with the “true” mediator is assumed to be of the Cox proportional hazards model form. The induced hazard ratio for the observed mediator no longer has a simple form independent of the baseline hazard function, due to the conditioning event. We propose a mean-variance regression calibration approach and a follow-up time regression calibration approach, to approximate the partial likelihood for the induced hazard function. Both methods demonstrate value in assessing mediation effects in simulation studies. These methods are generalized to multiple biomarkers and to both case-cohort and nested case-control sampling designs. We apply these correction methods to the Women's Health Initiative hormone therapy trials to understand the mediation effect of several serum sex hormone measures on the relationship between postmenopausal hormone therapy and breast cancer risk.

Nested case–control sampling is a popular design for large epidemiological cohort studies due to its cost effectiveness. A number of methods have been developed for the estimation of the proportional hazards model with nested case–control data; however, the evaluation of modeling assumption is less attended. In this article, we propose a class of goodness-of-fit test statistics for testing the proportional hazards assumption based on nested case–control data. The test statistics are constructed based on asymptotically mean-zero processes derived from Samuelsen's maximum pseudo-likelihood estimation method. In addition, we develop an innovative resampling scheme to approximate the asymptotic distribution of the test statistics while accounting for the dependent sampling scheme of nested case–control design. Numerical studies are conducted to evaluate the performance of our proposed approach, and an application to the Wilms' Tumor Study is given to illustrate the methodology.

When estimating the effect of an exposure or treatment on an outcome it is important to select the proper subset of confounding variables to include in the model. Including too many covariates increases mean square error on the effect of interest while not including confounding variables biases the exposure effect estimate. We propose a decision-theoretic approach to confounder selection and effect estimation. We first estimate the full standard Bayesian regression model and then post-process the posterior distribution with a loss function that penalizes models omitting important confounders. Our method can be fit easily with existing software and in many situations without the use of Markov chain Monte Carlo methods, resulting in computation on the order of the least squares solution. We prove that the proposed estimator has attractive asymptotic properties. In a simulation study we show that our method outperforms existing methods. We demonstrate our method by estimating the effect of fine particulate matter (PM) exposure on birth weight in Mecklenburg County, North Carolina.

Variable screening has emerged as a crucial first step in the analysis of high-throughput data, but existing procedures can be computationally cumbersome, difficult to justify theoretically, or inapplicable to certain types of analyses. Motivated by a high-dimensional censored quantile regression problem in multiple myeloma genomics, this article makes three contributions. First, we establish a score test-based screening framework, which is widely applicable, extremely computationally efficient, and relatively simple to justify. Secondly, we propose a resampling-based procedure for selecting the number of variables to retain after screening according to the principle of reproducibility. Finally, we propose a new iterative score test screening method which is closely related to sparse regression. In simulations we apply our methods to four different regression models and show that they can outperform existing procedures. We also apply score test screening to an analysis of gene expression data from multiple myeloma patients using a censored quantile regression model to identify high-risk genes.

Recent advance in biotechnology and its wide applications have led to the generation of many high-dimensional gene expression data sets that can be used to address similar biological questions. Meta-analysis plays an important role in summarizing and synthesizing scientific evidence from multiple studies. When the dimensions of datasets are high, it is desirable to incorporate variable selection into meta-analysis to improve model interpretation and prediction. According to our knowledge, all existing methods conduct variable selection with meta-analyzed data in an “all-in-or-all-out” fashion, that is, a gene is either selected in all of studies or not selected in any study. However, due to data heterogeneity commonly exist in meta-analyzed data, including choices of biospecimens, study population, and measurement sensitivity, it is possible that a gene is important in some studies while unimportant in others. In this article, we propose a novel method called meta-lasso for variable selection with high-dimensional meta-analyzed data. Through a hierarchical decomposition on regression coefficients, our method not only borrows strength across multiple data sets to boost the power to identify important genes, but also keeps the selection flexibility among data sets to take into account data heterogeneity. We show that our method possesses the gene selection consistency, that is, when sample size of each data set is large, with high probability, our method can identify all important genes and remove all unimportant genes. Simulation studies demonstrate a good performance of our method. We applied our meta-lasso method to a meta-analysis of five cardiovascular studies. The analysis results are clinically meaningful.

Integrative genomics offers a promising approach to more powerful genetic association studies. The hope is that combining outcome and genotype data with other types of genomic information can lead to more powerful SNP detection. We present a new association test based on a statistical model that explicitly assumes that genetic variations affect the outcome through perturbing gene expression levels. It is shown analytically that the proposed approach can have more power to detect SNPs that are associated with the outcome through transcriptional regulation, compared to tests using the outcome and genotype data alone, and simulations show that our method is relatively robust to misspecification. We also provide a strategy for applying our approach to high-dimensional genomic data. We use this strategy to identify a potentially new association between a SNP and a yeast cell's response to the natural product tomatidine, which standard association analysis did not detect.

Treatment-selection markers predict an individual's response to different therapies, thus allowing for the selection of a therapy with the best predicted outcome. A good marker-based treatment-selection rule can significantly impact public health through the reduction of the disease burden in a cost-effective manner. Our goal in this article is to use data from randomized trials to identify optimal linear and nonlinear biomarker combinations for treatment selection that minimize the total burden to the population caused by either the targeted disease or its treatment. We frame this objective into a general problem of minimizing a weighted sum of 0-1 loss and propose a novel penalized minimization method that is based on the difference of convex functions algorithm (DCA). The corresponding estimator of marker combinations has a kernel property that allows flexible modeling of linear and nonlinear marker combinations. We compare the proposed methods with existing methods for optimizing treatment regimens such as the logistic regression model and the weighted support vector machine. Performances of different weight functions are also investigated. The application of the proposed method is illustrated using a real example from an HIV vaccine trial: we search for a combination of Fc receptor genes for recommending vaccination in preventing HIV infection.

Semi-parametric regression models for the joint estimation of marginal mean and within-cluster pairwise association parameters are used in a variety of settings for population-averaged modeling of multivariate categorical outcomes. Recently, a formulation of alternating logistic regressions based on orthogonalized, marginal residuals has been introduced for correlated binary data. Unlike the original procedure based on conditional residuals, its covariance estimator is invariant to the ordering of observations within clusters. In this article, the orthogonalized residuals method is extended to model correlated ordinal data with a global odds ratio, and shown in a simulation study to be more efficient and less biased with regards to estimating within-cluster association parameters than an existing extension to ordinal data of alternating logistic regressions based on conditional residuals. Orthogonalized residuals are used to estimate a model for three correlated ordinal outcomes measured repeatedly in a longitudinal clinical trial of an intervention to improve recovery of patients' perception of altered sensation following jaw surgery.

Auxiliary covariates are often encountered in biomedical research settings where the primary exposure variable is measured only for a subgroup of study subjects. This article is concerned with generalized linear mixed models in the presence of auxiliary covariate information for clustered data. We propose a novel semiparametric estimation method based on a pairwise likelihood function and develop an estimating equation-based inference procedure by treating both the error structure and random effects as nuisance parameters. This method is robust against misspecification of either error structure or random-effects distribution and allows for dependence between random effects and covariates. We show that the resulting estimators are consistent and asymptotically normal. Extensive simulation studies evaluate the finite sample performance of the proposed estimators and demonstrate their advantage over the validation set based method and the existing method. We illustrate the method with two real data examples.

A popular way to model overdispersed count data, such as the number of falls reported during intervention studies, is by means of the negative binomial (NB) distribution. Classical estimating methods are well-known to be sensitive to model misspecifications, taking the form of patients falling much more than expected in such intervention studies where the NB regression model is used. We extend in this article two approaches for building robust *M*-estimators of the regression parameters in the class of generalized linear models to the NB distribution. The first approach achieves robustness in the response by applying a bounded function on the Pearson residuals arising in the maximum likelihood estimating equations, while the second approach achieves robustness by bounding the unscaled deviance components. For both approaches, we explore different choices for the bounding functions. Through a unified notation, we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately, and provide the asymptotic distributions of the resulting estimators. Moreover, we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter, specific to the NB distribution. Simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model, and this for both approaches. We present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from Parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference.

Complex computer models play a crucial role in air quality research. These models are used to evaluate potential regulatory impacts of emission control strategies and to estimate air quality in areas without monitoring data. For both of these purposes, it is important to calibrate model output with monitoring data to adjust for model biases and improve spatial prediction. In this article, we propose a new spectral method to study and exploit complex relationships between model output and monitoring data. Spectral methods allow us to estimate the relationship between model output and monitoring data separately at different spatial scales, and to use model output for prediction only at the appropriate scales. The proposed method is computationally efficient and can be implemented using standard software. We apply the method to compare Community Multiscale Air Quality (CMAQ) model output with ozone measurements in the United States in July 2005. We find that CMAQ captures large-scale spatial trends, but has low correlation with the monitoring data at small spatial scales.

There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the binary data, and may influence the dependence relationships. Motivated by such a dataset on genomic instability collected from tumor samples of several types, we propose a sparse covariate dependent Ising model to study both the conditional dependency within the binary data and its relationship with the additional covariates. This results in subject-specific Ising models, where the subject's covariates influence the strength of association between the genes. As in all exploratory data analysis, interpretability of results is important, and we use penalties to induce sparsity in the fitted graphs and in the number of selected covariates. Two algorithms to fit the model are proposed and compared on a set of simulated data, and asymptotic results are established. The results on the tumor dataset and their biological significance are discussed in detail.

In observational microarray studies, issues of confounding invariably arise. One approach to account for measured confounders is to include them as covariates in a multivariate linear model. For this model, however, the application of permutation-based multiple testing procedures is problematic because exchangeability of responses, in general, does not hold. Nevertheless, it is possible to achieve rotatability of transformed responses at the cost of a distributional assumption. We argue that rotation-based multiple testing, by allowing for adjustments for confounding, represents an important extension of permutation-based multiple testing procedures. The proposed methodology is illustrated with a microarray observational study on breast cancer tumors. Software to perform the procedure described in this article is available in the flip R package.

We investigate model for abundance estimation in closed-population capture–recapture studies, where animals are identified from natural marks such as DNA profiles or photographs of distinctive individual features. Model extends the classical model to accommodate errors in identification, by specifying that each sample identification is correct with probability and false with probability . Information about misidentification is gained from a surplus of capture histories with only one entry, which arise from false identifications. We derive an exact closed-form expression for the likelihood for model and show that it can be computed efficiently, in contrast to previous studies which have held the likelihood to be computationally intractable. Our fast computation enables us to conduct a thorough investigation of the statistical properties of the maximum likelihood estimates. We find that the indirect approach to error estimation places high demands on data richness, and good statistical properties in terms of precision and bias require high capture probabilities or many capture occasions. When these requirements are not met, abundance is estimated with very low precision and negative bias, and at the extreme better properties can be obtained by the naive approach of ignoring misidentification error. We recommend that model be used with caution and other strategies for handling misidentification error be considered. We illustrate our study with genetic and photographic surveys of the New Zealand population of southern right whale (*Eubalaena australis*).

In the context of state-space modeling, conventional usage of the deviance information criterion (DIC) evaluates the ability of the model to predict an observation at time *t* given the underlying state at time *t*. Motivated by the failure of conventional DIC to clearly choose between competing multivariate nonlinear Bayesian state-space models for coho salmon population dynamics, and the computational challenge of alternatives, this work proposes a one-step-ahead DIC, , where prediction is conditional on the state at the previous time point. Simulations revealed that worked well for choosing between state-space models with different process or observation equations. In contrast, conventional DIC could be grossly misleading, with a strong preference for the wrong model. This can be explained by its failure to account for inflated estimates of process error arising from the model mis-specification. is not based on a true conditional likelihood, but is shown to have interpretation as a pseudo-DIC in which the compensatory behavior of the inflated process errors is eliminated. It can be easily calculated using the DIC monitors within popular BUGS software when the process and observation equations are conjugate. The improved performance of is demonstrated by application to the multi-stage modeling of coho salmon abundance in Lobster Creek, Oregon.

There has been an increasing interest in the analysis of spatially distributed multivariate binary data motivated by a wide range of research problems. Two types of correlations are usually involved: the correlation between the multiple outcomes at one location and the spatial correlation between the locations for one particular outcome. The commonly used regression models only consider one type of correlations while ignoring or modeling inappropriately the other one. To address this limitation, we adopt a Bayesian nonparametric approach to jointly modeling multivariate spatial binary data by integrating both types of correlations. A multivariate probit model is employed to link the binary outcomes to Gaussian latent variables; and Gaussian processes are applied to specify the spatially correlated random effects. We develop an efficient Markov chain Monte Carlo algorithm for the posterior computation. We illustrate the proposed model on simulation studies and a multidrug-resistant tuberculosis case study.

A Bayesian approach to the prediction of occurred-but-not-yet-reported events is developed for application in real-time public health surveillance. The motivation was the prediction of the daily number of hospitalizations for the hemolytic-uremic syndrome during the large May–July 2011 outbreak of Shiga toxin-producing *Escherichia coli* (STEC) O104:H4 in Germany. Our novel Bayesian approach addresses the count data nature of the problem using negative binomial sampling and shows that right-truncation of the reporting delay distribution under an assumption of time-homogeneity can be handled in a conjugate prior-posterior framework using the generalized Dirichlet distribution. Since, in retrospect, the true number of hospitalizations is available, proper scoring rules for count data are used to evaluate and compare the predictive quality of the procedures during the outbreak. The results show that it is important to take the count nature of the time series into account and that changes in the delay distribution occurred due to intervention measures. As a consequence, we extend the Bayesian analysis to a hierarchical model, which combines a discrete time survival regression model for the delay distribution with a penalized spline for the dynamics of the epidemic curve. Altogether, we conclude that in emerging and time-critical outbreaks, nowcasting approaches are a valuable tool to gain information about current trends.

In many biomedical studies, patients may experience the same type of recurrent event repeatedly over time, such as bleeding, multiple infections and disease. In this article, we propose a Bayesian design to a pivotal clinical trial in which lower risk myelodysplastic syndromes (MDS) patients are treated with MDS disease modifying therapies. One of the key study objectives is to demonstrate the investigational product (treatment) effect on reduction of platelet transfusion and bleeding events while receiving MDS therapies. In this context, we propose a new Bayesian approach for the design of superiority clinical trials using recurrent events frailty regression models. Historical recurrent events data from an already completed phase 2 trial are incorporated into the Bayesian design via the partial borrowing power prior of Ibrahim et al. (2012, *Biometrics* **68**, 578–586). An efficient Gibbs sampling algorithm, a predictive data generation algorithm, and a simulation-based algorithm are developed for sampling from the fitting posterior distribution, generating the predictive recurrent events data, and computing various design quantities such as the type I error rate and power, respectively. An extensive simulation study is conducted to compare the proposed method to the existing frequentist methods and to investigate various operating characteristics of the proposed design.

We address estimation of intervention effects in experimental designs in which (a) interventions are assigned at the cluster level; (b) clusters are selected to form pairs, matched on observed characteristics; and (c) intervention is assigned to one cluster at random within each pair. One goal of policy interest is to estimate the average outcome if all clusters in all pairs are assigned control versus if all clusters in all pairs are assigned to intervention. In such designs, inference that ignores individual level covariates can be imprecise because cluster-level assignment can leave substantial imbalance in the covariate distribution between experimental arms within each pair. However, most existing methods that adjust for covariates have estimands that are not of policy interest. We propose a methodology that explicitly balances the observed covariates among clusters in a pair, and retains the original estimand of interest. We demonstrate our approach through the evaluation of the Guided Care program.

Historical information is always relevant for clinical trial design. Additionally, if incorporated in the analysis of a new trial, historical data allow to reduce the number of subjects. This decreases costs and trial duration, facilitates recruitment, and may be more ethical. Yet, under prior-data conflict, a too optimistic use of historical data may be inappropriate. We address this challenge by deriving a Bayesian meta-analytic-predictive prior from historical data, which is then combined with the new data. This prospective approach is equivalent to a meta-analytic-combined analysis of historical and new data if parameters are exchangeable across trials. The prospective Bayesian version requires a good approximation of the meta-analytic-predictive prior, which is not available analytically. We propose two- or three-component mixtures of standard priors, which allow for good approximations and, for the one-parameter exponential family, straightforward posterior calculations. Moreover, since one of the mixture components is usually vague, mixture priors will often be heavy-tailed and therefore robust. Further robustness and a more rapid reaction to prior-data conflicts can be achieved by adding an extra weakly-informative mixture component. Use of historical prior information is particularly attractive for adaptive trials, as the randomization ratio can then be changed in case of prior-data conflict. Both frequentist operating characteristics and posterior summaries for various data scenarios show that these designs have desirable properties. We illustrate the methodology for a phase II proof-of-concept trial with historical controls from four studies. Robust meta-analytic-predictive priors alleviate prior-data conflicts ' they should encourage better and more frequent use of historical data in clinical trials.

Receiver operating characteristic (ROC) analysis is widely used to evaluate the performance of diagnostic tests with continuous or ordinal responses. A popular study design for assessing the accuracy of diagnostic tests involves multiple readers interpreting multiple diagnostic test results, called the multi-reader, multi-test design. Although several different approaches to analyzing data from this design exist, few methods have discussed the sample size and power issues. In this article, we develop a power formula to compare the correlated areas under the ROC curves (AUC) in a multi-reader, multi-test design. We present a nonparametric approach to estimate and compare the correlated AUCs by extending DeLong et al.'s (1988, *Biometrics* **44**, 837–845) approach. A power formula is derived based on the asymptotic distribution of the nonparametric AUCs. Simulation studies are conducted to demonstrate the performance of the proposed power formula and an example is provided to illustrate the proposed procedure.

The performance of diagnostic tests for disease classification is often measured by accuracy (e.g., sensitivity or specificity); however, costs of the diagnostic test are a concern as well. Combinations of multiple diagnostic tests may improve accuracy, but incur additional costs. Here, we consider serial testing approaches that maintain accuracy while controlling costs of the diagnostic tests. We present a serial risk score classification approach. The basic idea is to sequentially test with additional diagnostic tests just until persons are classified. In this way, it is not necessary to test all persons with all tests. The methods are studied in simulations and compared with logistic regression. We applied the methods to data from HIV cohort studies to identify HIV infected individuals who are recently infected (1 year) by testing with assays for multiple biomarkers. We find that the serial risk score classification approach can maintain accuracy while achieving a reduction in cost compared to testing all individuals with all assays.

In some longitudinal studies the initiation time of the process is not clearly defined, yet it is important to make inference or do predictions about the longitudinal process. The application of interest in this article is to provide a framework for modeling individualized labor curves (longitudinal cervical dilation measurements) where the start of labor is not clearly defined. This is a well-known problem in obstetrics where the benchmark reference time is often chosen as the end of the process (individuals are fully dilated at 10 cm) and time is run backwards. This approach results in valid and efficient inference unless subjects are censored before the end of the process, or if we are focused on prediction. Providing dynamic individualized predictions of the longitudinal labor curve prospectively (where backwards time is unknown) is of interest to aid obstetricians to determine if a labor is on a suitable trajectory. We propose a model for longitudinal labor dilation that uses a random-effects model with unknown time-zero and a random change point. We present a maximum likelihood approach for parameter estimation that uses adaptive Gaussian quadrature for the numerical integration. Further, we propose a Monte Carlo approach for dynamic prediction of the future longitudinal dilation trajectory from past dilation measurements. The methodology is illustrated with longitudinal cervical dilation data from the Consortium of Safe Labor Study.