Bayesian variable selection for latent class models

In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.     

Bayesian analysis and model selection for interval-censored survival data

Interval-censored data occur in survival analysis when the survival time of each patient is only known to be within an interval and these censoring intervals differ from patient to patient. For such data, we present some Bayesian discretized semiparametric models, incorporating proportional and nonproportional hazards structures, along with associated statistical analyses and tools for model selection using sampling-based methods. The scope of these methodologies is illustrated through a reanalysis of a breast cancer data set (Finkelstein, 1986, Biometrics 42, 845-854) to test whether the effect of covariate on survival changes over time.     

From mixed effects modeling to spike and slab variable selection: A Bayesian regression model for group testing data

Due to reductions in both time and cost, group testing is a popular alternative to individual-level testing for disease screening. These reductions are obtained by testing pooled biospecimens (eg, blood, urine, swabs, etc.) for the presence of an infectious agent. However, these reductions come at the expense of data complexity, making the task of conducting disease surveillance more tenuous when compared to using individual-level data. This is because an individual's disease status may be obscured by a group testing protocol and the effect of imperfect testing. Furthermore, unlike individual-level testing, a given participant could be involved in multiple testing outcomes and/or may never be tested individually. To circumvent these complexities and to incorporate all available information, we propose a Bayesian generalized linear mixed model that accommodates data arising from any group testing protocol, estimates unknown assay accuracy probabilities and accounts for potential heterogeneity in the covariate effects across population subgroups (eg, clinic sites, etc.); this latter feature is of key interest to practitioners tasked with conducting disease surveillance. To achieve model selection, our proposal uses spike and slab priors for both fixed and random effects. The methodology is illustrated through numerical studies and is applied to chlamydia surveillance data collected in Iowa.     

Bayesian variable selection and estimation in semiparametric joint models of multivariate longitudinal and survival data

This paper presents a novel semiparametric joint model for multivariate longitudinal and survival data (SJMLS) by relaxing the normality assumption of the longitudinal outcomes, leaving the baseline hazard functions unspecified and allowing the history of the longitudinal response having an effect on the risk of dropout. Using Bayesian penalized splines to approximate the unspecified baseline hazard function and combining the Gibbs sampler and the Metropolis–Hastings algorithm, we propose a Bayesian Lasso (BLasso) method to simultaneously estimate unknown parameters and select important covariates in SJMLS. Simulation studies are conducted to investigate the finite sample performance of the proposed techniques. An example from the International Breast Cancer Study Group (IBCSG) is used to illustrate the proposed methodologies.     

Improve survival prediction using principal components of gene expression data

The purpose of many microarray studies is to find the association between gene expression and sample characteristics such as treatment type or sample phenotype. There has been a surge of efforts developing different methods for delineating the association. Aside from the high dimensionality of microarray data, one well recognized challenge is the fact that genes could be complicatedly inter-related, thus making many statistical methods inappropriate to use directly on the expression data. Multivariate methods such as principal component analysis （PCA） and clustering are often used as a part of the effort to capture the gene correlation, and the derived components or clusters are used to describe the association between gene expression and sample phenotype. We propose a method for patient population dichotomization using maximally selected test statistics in combination with the PCA method, which shows favorable results. The proposed method is compared with a currently well-recognized method.     

Bayesian variable selection in searching for additive and dominant effects in genome-wide data

Although complex diseases and traits are thought to have multifactorial genetic basis, the common methods in genome-wide association analyses test each variant for association independent of the others. This computational simplification may lead to reduced power to identify variants with small effect sizes and requires correcting for multiple hypothesis tests with complex relationships. However, advances in computational methods and increase in computational resources are enabling the computation of models that adhere more closely to the theory of multifactorial inheritance. Here, a Bayesian variable selection and model averaging approach is formulated for searching for additive and dominant genetic effects. The approach considers simultaneously all available variants for inclusion as predictors in a linear genotype-phenotype mapping and averages over the uncertainty in the variable selection. This leads to naturally interpretable summary quantities on the significances of the variants and their contribution to the genetic basis of the studied trait. We first characterize the behavior of the approach in simulations. The results indicate a gain in the causal variant identification performance when additive and dominant variation are simulated, with a negligible loss of power in purely additive case. An application to the analysis of high- and low-density lipoprotein cholesterol levels in a dataset of 3895 Finns is then presented, demonstrating the feasibility of the approach at the current scale of single-nucleotide polymorphism data. We describe a Markov chain Monte Carlo algorithm for the computation and give suggestions on the specification of prior parameters using commonly available prior information. An open-source software implementing the method is available at http://www.lce.hut.fi/research/mm/bmagwa/ and https://github.com/to-mi/.     

Exploratory Bayesian model selection for serial genetics data

Characterizing the process by which molecular and cellular level changes occur over time will have broad implications for clinical decision making and help further our knowledge of disease etiology across many complex diseases. However, this presents an analytic challenge due to the large number of potentially relevant biomarkers and the complex, uncharacterized relationships among them. We propose an exploratory Bayesian model selection procedure that searches for model simplicity through independence testing of multiple discrete biomarkers measured over time. Bayes factor calculations are used to identify and compare models that are best supported by the data. For large model spaces, i.e., a large number of multi-leveled biomarkers, we propose a Markov chain Monte Carlo (MCMC) stochastic search algorithm for finding promising models. We apply our procedure to explore the extent to which HIV-1 genetic changes occur independently over time.     

Bayesian influence measures for joint models for longitudinal and survival data

Summary This article develops a variety of influence measures for carrying out perturbation (or sensitivity) analysis to joint models of longitudinal and survival data (JMLS) in Bayesian analysis. A perturbation model is introduced to characterize individual and global perturbations to the three components of a Bayesian model, including the data points, the prior distribution, and the sampling distribution. Local influence measures are proposed to quantify the degree of these perturbations to the JMLS. The proposed methods allow the detection of outliers or influential observations and the assessment of the sensitivity of inferences to various unverifiable assumptions on the Bayesian analysis of JMLS. Simulation studies and a real data set are used to highlight the broad spectrum of applications for our Bayesian influence methods.     

Assessment of evaluation criteria for survival prediction from genomic data

Survival prediction from high-dimensional genomic data is dependent on a proper regularization method. With an increasing number of such methods proposed in the literature, comparative studies are called for and some have been performed. However, there is currently no consensus on which prediction assessment criterion should be used for time-to-event data. Without a firm knowledge about whether the choice of evaluation criterion may affect the conclusions made as to which regularization method performs best, these comparative studies may be of limited value. In this paper, four evaluation criteria are investigated: the log-rank test for two groups, the area under the time-dependent ROC curve (AUC), an R2-measure based on the Cox partial likelihood, and an R2-measure based on the Brier score. The criteria are compared according to how they rank six widely used regularization methods that are based on the Cox regression model, namely univariate selection, principal components regression (PCR), supervised PCR, partial least squares regression, ridge regression, and the lasso. Based on our application to three microarray gene expression data sets, we find that the results obtained from the widely used log-rank test deviate from the other three criteria studied. For future studies, where one also might want to include non-likelihood or non-model-based regularization methods, we argue in favor of AUC and the R2-measure based on the Brier score, as these do not suffer from the arbitrary splitting into two groups nor depend on the Cox partial likelihood.     

Multitrait Bayesian shrinkage and variable selection models with the BGLR-R package

The BGLR-R package implements various types of single-trait shrinkage/variable selection Bayesian regressions. The package was first released in 2014, since then it has become a software very often used in genomic studies. We recently develop functionality for multitrait models. The implementation allows users to include an arbitrary number of random-effects terms. For each set of predictors, users can choose diffuse, Gaussian, and Gaussian–spike–slab multivariate priors. Unlike other software packages for multitrait genomic regressions, BGLR offers many specifications for (co)variance parameters (unstructured, diagonal, factor analytic, and recursive). Samples from the posterior distribution of the models implemented in the multitrait function are generated using a Gibbs sampler, which is implemented by combining code written in the R and C programming languages. In this article, we provide an overview of the models and methods implemented BGLR’s multitrait function, present examples that illustrate the use of the package, and benchmark the performance of the software.     

Bayesian prediction of spatial count data using generalized linear mixed models

Spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a Bayesian approach and Markov chain Monte Carlo. Informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling. Furthermore, we demonstrate that so-called Langevin-Hastings updates are useful for efficient simulation of the posterior distributions, and we discuss computational issues concerning prediction.     

A Bayesian semiparametric joint hierarchical model for longitudinal and survival data

This article proposes a new semiparametric Bayesian hierarchical model for the joint modeling of longitudinal and survival data. We relax the distributional assumptions for the longitudinal model using Dirichlet process priors on the parameters defining the longitudinal model. The resulting posterior distribution of the longitudinal parameters is free of parametric constraints, resulting in more robust estimates. This type of approach is becoming increasingly essential in many applications, such as HIV and cancer vaccine trials, where patients' responses are highly diverse and may not be easily modeled with known distributions. An example will be presented from a clinical trial of a cancer vaccine where the survival outcome is time to recurrence of a tumor. Immunologic measures believed to be predictive of tumor recurrence were taken repeatedly during follow-up. We will present an analysis of this data using our new semiparametric Bayesian hierarchical joint modeling methodology to determine the association of these longitudinal immunologic measures with time to tumor recurrence.     

Additive risk models for survival data with high-dimensional covariates

As a useful alternative to Cox's proportional hazard model, the additive risk model assumes that the hazard function is the sum of the baseline hazard function and the regression function of covariates. This article is concerned with estimation and prediction for the additive risk models with right censored survival data, especially when the dimension of the covariates is comparable to or larger than the sample size. Principal component regression is proposed to give unique and numerically stable estimators. Asymptotic properties of the proposed estimators, component selection based on the weighted bootstrap, and model evaluation techniques are discussed. This approach is illustrated with analysis of the primary biliary cirrhosis clinical data and the diffuse large B-cell lymphoma genomic data. It is shown that this methodology is numerically stable and effective in dimension reduction, while still being able to provide satisfactory prediction and classification results.     

Generalized conjugate priors for Bayesian analysis of risk and survival regressions

Conjugate priors for Bayesian analyses of relative risks can be quite restrictive, because their shape depends on their location. By introducing a separate location parameter, however, these priors generalize to allow modeling of a broad range of prior opinions, while still preserving the computational simplicity of conjugate analyses. The present article illustrates the resulting generalized conjugate analyses using examples from case-control studies of the association of residential wire codes and magnetic fields with childhood leukemia.     

Bayesian adaptive regression splines for hierarchical data

This article considers methodology for hierarchical functional data analysis, motivated by studies of reproductive hormone profiles in the menstrual cycle. Current methods standardize the cycle lengths and ignore the timing of ovulation within the cycle, both of which are biologically informative. Methods are needed that avoid standardization, while flexibly incorporating information on covariates and the timing of reference events, such as ovulation and onset of menses. In addition, it is necessary to account for within-woman dependency when data are collected for multiple cycles. We propose an approach based on a hierarchical generalization of Bayesian multivariate adaptive regression splines. Our formulation allows for an unknown set of basis functions characterizing the population-averaged and woman-specific trajectories in relation to covariates. A reversible jump Markov chain Monte Carlo algorithm is developed for posterior computation. Applying the methods to data from the North Carolina Early Pregnancy Study, we investigate differences in urinary progesterone profiles between conception and nonconception cycles.