Empirical Bayes methods have been extensively used for microarray data analysis by modeling the large number of unknown parameters as random effects. Empirical Bayes allows borrowing information across genes and can automatically adjust for multiple testing and selection bias. However, the standard empirical Bayes model can perform poorly if the assumed working prior deviates from the true prior. This paper proposes a new rank-conditioned inference in which the shrinkage and confidence intervals are based on the distribution of the error conditioned on rank of the data. Our approach is in contrast to a Bayesian posterior, which conditions on the data themselves. The new method is almost as efficient as standard Bayesian methods when the working prior is close to the true prior, and it is much more robust when the working prior is not close. In addition, it allows a more accurate (but also more complex) non-parametric estimate of the prior to be easily incorporated, resulting in improved inference. The new method's prior robustness is demonstrated via simulation experiments. Application to a breast cancer gene expression microarray dataset is presented. Our R package rank.Shrinkage provides a ready-to-use implementation of the proposed methodology.

This paper considers the problem of choosing between competing models for infectious disease final outcome data in a population that is partitioned into households. The epidemic models are stochastic individual-based transmission models of the susceptible-infective-removed type. The main focus is on various algorithms for the estimation of Bayes factors, of which a path sampling-based algorithm is seen to give the best results. We also explore theoretical properties in the case where the within-model prior distributions become increasingly uninformative, which show the need for caution when using Bayes factors as a model choice tool. A suitable form of deviance information criterion is also considered for comparison. The theory and methods are illustrated with both artificial data, and influenza data from the Tecumseh study of illness.

A major challenge in cancer epidemiologic studies, especially those of rare cancers, is observing enough cases. To address this, researchers often join forces by bringing multiple studies together to achieve large sample sizes, allowing for increased power in hypothesis testing, and improved efficiency in effect estimation. Combining studies, however, renders the analysis difficult owing to the presence of heterogeneity in the pooled data. In this article, motivated by a collaborative nested case-control (NCC) study of ovarian cancer in three cohorts from United States, Sweden, and Italy, we investigate the use of penalty regularized partial likelihood estimation in the context of pooled NCC studies to achieve two goals. First, we propose an adaptive group lasso (gLASSO) penalized approach to simultaneously identify important variables and estimate their effects. Second, we propose a composite agLASSO penalized approach to identify variables with heterogeneous effects. Both methods are readily implemented with the group coordinate gradient decent algorithm and shown to enjoy the oracle property. We conduct simulation studies to evaluate the performance of our proposed approaches in finite samples under various heterogeneity settings, and apply them to the pooled ovarian cancer study.

Modern medicine has graduated from broad spectrum treatments to targeted therapeutics. New drugs recognize the recently discovered heterogeneity of many diseases previously considered to be fairly homogeneous. These treatments attack specific genetic pathways which are only dysregulated in some smaller subset of patients with the disease. Often this subset is only rudimentarily understood until well into large-scale clinical trials. As such, standard practice has been to enroll a broad range of patients and run post hoc subset analysis to determine those who may particularly benefit. This unnecessarily exposes many patients to hazardous side effects, and may vastly decrease the efficiency of the trial (especially if only a small subset of patients benefit). In this manuscript, we propose a class of adaptive enrichment designs that allow the eligibility criteria of a trial to be adaptively updated during the trial, restricting entry to patients likely to benefit from the new treatment. We show that our designs both preserve the type 1 error, and in a variety of cases provide a substantial increase in power.

Random effects models are commonly used to analyze longitudinal categorical data. Marginalized random effects models are a class of models that permit direct estimation of marginal mean parameters and characterize serial correlation for longitudinal categorical data via random effects (Heagerty, 1999). Marginally specified logistic-normal models for longitudinal binary data. Biometrics 55, 688-698; Lee and Daniels, 2008. Marginalized models for longitudinal ordinal data with application to quality of life studies. Statistics in Medicine 27, 4359-4380). In this paper, we propose a Kronecker product (KP) covariance structure to capture the correlation between processes at a given time and the correlation within a process over time (serial correlation) for bivariate longitudinal ordinal data. For the latter, we consider a more general class of models than standard (first-order) autoregressive correlation models, by re-parameterizing the correlation matrix using partial autocorrelations (Daniels and Pourahmadi, 2009). Modeling covariance matrices via partial autocorrelations. Journal of Multivariate Analysis 100, 2352-2363). We assess the reasonableness of the KP structure with a score test. A maximum marginal likelihood estimation method is proposed utilizing a quasi-Newton algorithm with quasi-Monte Carlo integration of the random effects. We examine the effects of demographic factors on metabolic syndrome and C-reactive protein using the proposed models.

The basic reproduction number of an infection in a given population, R0, is inflated by individual heterogeneity in contact rates. Recently, new methods for estimating R0 using social contact data and serological survey data have been proposed. These methods, like most of their predecessors, ignore individual heterogeneity, and are sensitive to perturbation of the contact function. Using a frailty framework, we derive expressions for R0 in the presence of age-varying heterogeneity. In this case, R0 is the spectral radius of a population version of the next generation operator, which involves the variance function of the age-dependent frailty. This variance can be estimated within a shared frailty framework from paired data on two infections transmitted by the same route. We propose two estimators of R0 for infections in endemic equilibrium. We investigate their performance by simulation, and find that one is generally less efficient but more robust than the other to perturbation of the effective contact function. These methods are applied to data on varicella zoster virus infection from two European countries.

In the case-cohort studies conducted within the Atherosclerosis Risk in Communities (ARIC) study, it is of interest to assess and compare the effect of high-sensitivity C-reactive protein (hs-CRP) on the increased risks of incident coronary heart disease and incident ischemic stroke. Empirical cumulative hazards functions for different levels of hs-CRP reveal an additive structure for the risks for each disease outcome. Additionally, we are interested in estimating the difference in the risk for the different hs-CRP groups. Motivated by this, we consider fitting marginal additive hazards regression models for case-cohort studies with multiple disease outcomes. We consider a weighted estimating equations approach for the estimation of model parameters. The asymptotic properties of the proposed estimators are derived and their finite-sample properties are assessed via simulation studies. The proposed method is applied to analyze the ARIC Study.

The transmission dynamics of infectious diseases have been traditionally described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance following the Sellke construction. Here we focus on a generalization using Weibull individual tolerance thresholds under the susceptible-exposed-infectious-removed class of models which is widely employed in epidemics. Applications with experimental foot-and-mouth disease and historical smallpox data are discussed, and simulation results are presented. Inference is carried out using Markov chain Monte Carlo methods following a Bayesian approach. Model evaluation is performed, where the adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, and comparison between 2 candidate models is also considered using a latent likelihood ratio-type test that avoids problems encountered with relevant methods based on Bayes factors.

Space-time modeling of small area data is often used in epidemiology for mapping chronic disease rates and by government statistical agencies for producing local estimates of, for example, unemployment or crime rates. Although there is typically a general temporal trend, which affects all areas similarly, abrupt changes may occur in a particular area, e.g. due to emergence of localized predictors/risk factor(s) or impact of a new policy. Detection of areas with "unusual" temporal patterns is therefore important as a screening tool for further investigations. In this paper, we propose BaySTDetect, a novel detection method for short-time series of small area data using Bayesian model choice between two competing space-time models. The first model is a multiplicative decomposition of the area effect and the temporal effect, assuming one common temporal pattern across the whole study region. The second model estimates the time trends independently for each area. For each area, the posterior probability of belonging to the common trend model is calculated, which is then used to classify the local time trend as unusual or not. Crucial to any detection method, we provide a Bayesian estimate of the false discovery rate (FDR). A comprehensive simulation study has demonstrated the consistent good performance of BaySTDetect in detecting various realistic departure patterns in addition to estimating well the FDR. The proposed method is applied retrospectively to mortality data on chronic obstructive pulmonary disease (COPD) in England and Wales between 1990 and 1997 (a) to test a hypothesis that a government policy increased the diagnosis of COPD and (b) to perform surveillance. While results showed no evidence supporting the hypothesis regarding the policy, an identified unusual district (Tower Hamlets in inner London) was later recognized to have higher than national rates of hospital readmission and mortality due to COPD by the National Health Service, which initiated various local enhanced services to tackle the problem. Our method would have led to an early detection of this local health issue.

Risk mapping in epidemiology enables areas with a low or high risk of disease contamination to be localized and provides a measure of risk differences between these regions. Risk mapping models for pooled data currently used by epidemiologists focus on the estimated risk for each geographical unit. They are based on a Poisson log-linear mixed model with a latent intrinsic continuous hidden Markov random field (HMRF) generally corresponding to a Gaussian autoregressive spatial smoothing. Risk classification, which is necessary to draw clearly delimited risk zones (in which protection measures may be applied), generally must be performed separately. We propose a method for direct classified risk mapping based on a Poisson log-linear mixed model with a latent discrete HMRF. The discrete hidden field (HF) corresponds to the assignment of each spatial unit to a risk class. The risk values attached to the classes are parameters and are estimated. When mapping risk using HMRFs, the conditional distribution of the observed field is modeled with a Poisson rather than a Gaussian distribution as in image segmentation. Moreover, abrupt changes in risk levels are rare in disease maps. The spatial hidden model should favor smoothed out risks, but conventional discrete Markov random fields (e.g. the Potts model) do not impose this. We therefore propose new potential functions for the HF that take into account class ordering. We use a Monte Carlo version of the expectation-maximization algorithm to estimate parameters and determine risk classes. We illustrate the method's behavior on simulated and real data sets. Our method appears particularly well adapted to localize high-risk regions and estimate the corresponding risk levels.