Tree-informed Bayesian multi-source domain adaptation: cross-population probabilistic cause-of-death assignment using verbal autopsy.

Determining causes of deaths (CODs) occurred outside of civil registration and vital statistics systems is challenging. A technique called verbal autopsy (VA) is widely adopted to gather information on deaths in practice. A VA consists of interviewing relatives of a deceased person about symptoms of the deceased in the period leading to the death, often resulting in multivariate binary responses. While statistical methods have been devised for estimating the cause-specific mortality fractions (CSMFs) for a study population, continued expansion of VA to new populations (or "domains") necessitates approaches that recognize between-domain differences while capitalizing on potential similarities. In this article, we propose such a domain-adaptive method that integrates external between-domain similarity information encoded by a prespecified rooted weighted tree. Given a cause, we use latent class models to characterize the conditional distributions of the responses that may vary by domain. We specify a logistic stick-breaking Gaussian diffusion process prior along the tree for class mixing weights with node-specific spike-and-slab priors to pool information between the domains in a data-driven way. The posterior inference is conducted via a scalable variational Bayes algorithm. Simulation studies show that the domain adaptation enabled by the proposed method improves CSMF estimation and individual COD assignment. We also illustrate and evaluate the method using a validation dataset. The article concludes with a discussion of limitations and future directions.

A modeling framework for detecting and leveraging node-level information in Bayesian network inference.

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected alongside the data of primary interest constitutes an opportunity to mitigate these difficulties by guiding the detection of dependence structures. For instance, gene network inference may be informed by the use of publicly available summary statistics on the regulation of genes by genetic variants. Here we present a novel Gaussian graphical modeling framework to identify and leverage information on the centrality of nodes in conditional independence graphs. Specifically, we consider a fully joint hierarchical model to simultaneously infer (i) sparse precision matrices and (ii) the relevance of node-level information for uncovering the sought-after network structure. We encode such information as candidate auxiliary variables using a spike-and-slab submodel on the propensity of nodes to be hubs, which allows hypothesis-free selection and interpretation of a sparse subset of relevant variables. As efficient exploration of large posterior spaces is needed for real-world applications, we develop a variational expectation conditional maximization algorithm that scales inference to hundreds of samples, nodes and auxiliary variables. We illustrate and exploit the advantages of our approach in simulations and in a gene network study which identifies hub genes involved in biological pathways relevant to immune-mediated diseases.

A non-negative spike-and-slab lasso generalized linear stacking prediction modeling method for high-dimensional omics data.

BACKGROUND: High-dimensional omics data are increasingly utilized in clinical and public health research for disease risk prediction. Many previous sparse methods have been proposed that using prior knowledge, e.g., biological group structure information, to guide the model-building process. However, these methods are still based on a single model, offen leading to overconfident inferences and inferior generalization. RESULTS: We proposed a novel stacking strategy based on a non-negative spike-and-slab Lasso (nsslasso) generalized linear model (GLM) for disease risk prediction in the context of high-dimensional omics data. Briefly, we used prior biological knowledge to segment omics data into a set of sub-data. Each sub-model was trained separately using the features from the group via a proper base learner. Then, the predictions of sub-models were ensembled by a super learner using nsslasso GLM. The proposed method was compared to several competitors, such as the Lasso, grlasso, and gsslasso, using simulated data and two open-access breast cancer data. As a result, the proposed method showed robustly superior prediction performance to the optimal single-model method in high-noise simulated data and real-world data. Furthermore, compared to the traditional stacking method, the proposed nsslasso stacking method can efficiently handle redundant sub-models and identify important sub-models. CONCLUSIONS: The proposed nsslasso method demonstrated favorable predictive accuracy, stability, and biological interpretability. Additionally, the proposed method can also be used to detect new biomarkers and key group structures.

Bayesian varying-effects vector autoregressive models for inference of brain connectivity networks and covariate effects in pediatric traumatic brain injury.

In this article, we develop an analytical approach for estimating brain connectivity networks that accounts for subject heterogeneity. More specifically, we consider a novel extension of a multi-subject Bayesian vector autoregressive model that estimates group-specific directed brain connectivity networks and accounts for the effects of covariates on the network edges. We adopt a flexible approach, allowing for (possibly) nonlinear effects of the covariates on edge strength via a novel Bayesian nonparametric prior that employs a weighted mixture of Gaussian processes. For posterior inference, we achieve computational scalability by implementing a variational Bayes scheme. Our approach enables simultaneous estimation of group-specific networks and selection of relevant covariate effects. We show improved performance over competing two-stage approaches on simulated data. We apply our method on resting-state functional magnetic resonance imaging data from children with a history of traumatic brain injury (TBI) and healthy controls to estimate the effects of age and sex on the group-level connectivities. Our results highlight differences in the distribution of parent nodes. They also suggest alteration in the relation of age, with peak edge strength in children with TBI, and differences in effective connectivity strength between males and females.

REDOMA: Bayesian random-effects dose-optimization meta-analysis using spike-and-slab priors.

The rise of cutting-edge precision cancer treatments has led to a growing significance of the optimal biological dose (OBD) in modern oncology trials. These trials now prioritize the consideration of both toxicity and efficacy simultaneously when determining the most desirable dosage for treatment. Traditional approaches in early-phase oncology trials have conventionally relied on the assumption of a monotone relationship between treatment efficacy and dosage. However, this assumption may not hold valid for novel oncology therapies. In reality, the dose-efficacy curve of such treatments may reach a plateau at a specific dose, posing challenges for conventional methods in accurately identifying the OBD. Furthermore, achieving reliable identification of the OBD is typically not possible based on a single small-sample trial. With data from multiple phase I and phase I/II trials, we propose a novel Bayesian random-effects dose-optimization meta-analysis (REDOMA) approach to identify the OBD by synthesizing toxicity and efficacy data from each trial. The REDOMA method can address trials with heterogeneous characteristics. We adopt a curve-free approach based on a Gamma process prior to model the average dose-toxicity relationship. In addition, we utilize a Bayesian model selection framework that uses the spike-and-slab prior as an automatic variable selection technique to eliminate monotonic constraints on the dose-efficacy curve. The good performance of the REDOMA method is confirmed by extensive simulation studies.

BHAFT: Bayesian heredity-constrained accelerated failure time models for detecting gene-environment interactions in survival analysis.

In addition to considering the main effects, understanding gene-environment (G × E) interactions is imperative for determining the etiology of diseases and the factors that affect their prognosis. In the existing statistical framework for censored survival outcomes, there are several challenges in detecting G × E interactions, such as handling high-dimensional omics data, diverse environmental factors, and algorithmic complications in survival analysis. The effect heredity principle has widely been used in studies involving interaction identification because it incorporates the dependence of the main and interaction effects. However, Bayesian survival models that incorporate the assumption of this principle have not been developed. Therefore, we propose Bayesian heredity-constrained accelerated failure time (BHAFT) models for identifying main and interaction (M-I) effects with novel spike-and-slab or regularized horseshoe priors to incorporate the assumption of effect heredity principle. The R package rstan was used to fit the proposed models. Extensive simulations demonstrated that BHAFT models had outperformed other existing models in terms of signal identification, coefficient estimation, and prognosis prediction. Biologically plausible G × E interactions associated with the prognosis of lung adenocarcinoma were identified using our proposed model. Notably, BHAFT models incorporating the effect heredity principle could identify both main and interaction effects, which are highly useful in exploring G × E interactions in high-dimensional survival analysis. The code and data used in our paper are available at https://github.com/SunNa-bayesian/BHAFT.

Integrating sample similarities into latent class analysis: a tree-structured shrinkage approach.

This paper is concerned with using multivariate binary observations to estimate the probabilities of unobserved classes with scientific meanings. We focus on the setting where additional information about sample similarities is available and represented by a rooted weighted tree. Every leaf in the given tree contains multiple samples. Shorter distances over the tree between the leaves indicate a priori higher similarity in class probability vectors. We propose a novel data integrative extension to classical latent class models with tree-structured shrinkage. The proposed approach enables (1) borrowing of information across leaves, (2) estimating data-driven leaf groups with distinct vectors of class probabilities, and (3) individual-level probabilistic class assignment given the observed multivariate binary measurements. We derive and implement a scalable posterior inference algorithm in a variational Bayes framework. Extensive simulations show more accurate estimation of class probabilities than alternatives that suboptimally use the additional sample similarity information. A zoonotic infectious disease application is used to illustrate the proposed approach. The paper concludes by a brief discussion on model limitations and extensions.

Genome-wide search algorithms for identifying dynamic gene co-expression via Bayesian variable selection.

A wealth of gene expression data generated by high-throughput techniques provides exciting opportunities for studying gene-gene interactions systematically. Gene-gene interactions in a biological system are tightly regulated and are often highly dynamic. The interactions can change flexibly under various internal cellular signals or external stimuli. Previous studies have developed statistical methods to examine these dynamic changes in gene-gene interactions. However, due to the massive number of possible gene combinations that need to be considered in a typical genomic dataset, intensive computation is a common challenge for exploring gene-gene interactions. On the other hand, oftentimes only a small proportion of gene combinations exhibit dynamic co-expression changes. To solve this problem, we propose Bayesian variable selection approaches based on spike-and-slab priors. The proposed algorithms reduce the computational intensity by focusing on identifying subsets of promising gene combinations in the search space. We also adopt a Bayesian multiple hypothesis testing procedure to identify strong dynamic gene co-expression changes. Simulation studies are performed to compare the proposed approaches with existing exhaustive search heuristics. We demonstrate the implementation of our proposed approach to study the association between gene co-expression patterns and overall survival using the RNA-sequencing dataset from The Cancer Genome Atlas breast cancer BRCA-US project.

A Bayesian method for estimating gene-level polygenicity under the framework of transcriptome-wide association study.

Polygenicity refers to the phenomenon that multiple genetic variants have a nonzero effect on a complex trait. It is defined as the proportion of genetic variants with a nonzero effect on the trait. Evaluation of polygenicity can provide valuable insights into the genetic architecture of the trait. Several recent works have attempted to estimate polygenicity at the single nucleotide polymorphism level. However, evaluating polygenicity at the gene level can be biologically more meaningful. We propose the notion of gene-level polygenicity, defined as the proportion of genes having a nonzero effect on the trait under the framework of a transcriptome-wide association study. We introduce a Bayesian approach genepoly to estimate this quantity for a trait. The method is based on spike and slab prior and simultaneously estimates the subset of non-null genes. Our simulation study shows that genepoly efficiently estimates gene-level polygenicity. The method produces a downward bias for small choices of trait heritability due to a non-null gene, which diminishes rapidly with an increase in the genome-wide association study (GWAS) sample size. While identifying the subset of non-null genes, genepoly offers a high level of specificity and an overall good level of sensitivity-the sensitivity increases as the sample size of the reference panel expression and GWAS data increase. We applied the method to seven phenotypes in the UK Biobank, integrating expression data. We find height to be the most polygenic and asthma to be the least polygenic.

Fully and partially exploratory factor analysis with bi-level Bayesian regularization.

This research introduces the fully and partially exploratory factor analysis (EFA) with bi-level Bayesian regularization. The proposed models enable factor selection with a sparse model by conceptualizing the factor and loading as the group and individual levels, respectively. They offer a series of benefits such as factor extraction and parameter estimation in one step, simultaneous estimation of the model and tuning parameters, and the availability of interval estimates. Moreover, partial knowledge can be incorporated together with unknown number of factors in the partially EFA. Simulation studies and real-data analyses demonstrated that both models performed satisfactorily under reasonable conditions and were robust to interference of local dependence, while the partially EFA with appropriate information can outperform the fully version and work well under more extreme conditions. The proposed models have been implemented in the R package LAWBL.

Subgroup-specific dose finding for phase I-II trials using Bayesian clustering.

In most models and algorithms for dose-finding clinical trials, it is assumed that the trial participants are homogeneous-the optimal dose is the same for all those who qualify for the trial. However, if there are heterogeneous populations who may benefit from the same treatment, it is inefficient to conduct dose-finding separately for each group, and assuming homogeneity across all subpopulations may lead to identification of the incorrect dose for some (or all) subgroups. To accommodate heterogeneity in dose-finding trials when both efficacy and toxicity outcomes must be used to identify the optimal dose (as in immunotherapeutic oncology treatments), we utilize an adaptive Bayesian clustering method which borrows strength among similar subgroups and clusters truly homogeneous subgroups. Unlike methodology already described in the literature, our proposed methodology does not require the assumption of exchangeability between subgroups or a priori ordering of subgroups, but does allow for specification of different subgroup-specific priors if prior information is available. We provide a comparison of operating characteristics between our method and Bayesian hierarchical models for subgroups in a variety of relevant scenarios. After simulation studies with four a priori subgroups, we observed that our method and the hierarchical models both outperform separate subgroup-specific models when all subgroups have the same dose-efficacy and dose-toxicity curves. However, our method outperforms hierarchical models when one subgroup has a different dose-efficacy or dose-toxicity curve from the other three subgroups.

Bayesian inference of networks across multiple sample groups and data types.

In this article, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to differing disease stage or subtype, is profiled across multiple platforms, such as metabolomics, proteomics, or transcriptomics data. Our proposed Bayesian hierarchical model first links the network structures within each platform using a Markov random field prior to relate edge selection across sample groups, and then links the network similarity parameters across platforms. This enables joint estimation in a flexible manner, as we make no assumptions on the directionality of influence across the data types or the extent of network similarity across the sample groups and platforms. In addition, our model formulation allows the number of variables and number of subjects to differ across the data types, and only requires that we have data for the same set of groups. We illustrate the proposed approach through both simulation studies and an application to gene expression levels and metabolite abundances on subjects with varying severity levels of chronic obstructive pulmonary disease. Bayesian inference; Chronic obstructive pulmonary disease (COPD); Data integration; Gaussian graphical model; Markov random field prior; Spike and slab prior.

Bayesian group selection in logistic regression with application to MRI data analysis.

We consider Bayesian logistic regression models with group-structured covariates. In high-dimensional settings, it is often assumed that only a small portion of groups are significant, and thus, consistent group selection is of significant importance. While consistent frequentist group selection methods have been proposed, theoretical properties of Bayesian group selection methods for logistic regression models have not been investigated yet. In this paper, we consider a hierarchical group spike and slab prior for logistic regression models in high-dimensional settings. Under mild conditions, we establish strong group selection consistency of the induced posterior, which is the first theoretical result in the Bayesian literature. Through simulation studies, we demonstrate that the proposed method outperforms existing state-of-the-art methods in various settings. We further apply our method to a magnetic resonance imaging data set for predicting Parkinson's disease and show its benefits over other contenders.

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.

Gsslasso Cox: a Bayesian hierarchical model for predicting survival and detecting associated genes by incorporating pathway information.

BACKGROUND: Group structures among genes encoded in functional relationships or biological pathways are valuable and unique features in large-scale molecular data for survival analysis. However, most of previous approaches for molecular data analysis ignore such group structures. It is desirable to develop powerful analytic methods for incorporating valuable pathway information for predicting disease survival outcomes and detecting associated genes. RESULTS: We here propose a Bayesian hierarchical Cox survival model, called the group spike-and-slab lasso Cox (gsslasso Cox), for predicting disease survival outcomes and detecting associated genes by incorporating group structures of biological pathways. Our hierarchical model employs a novel prior on the coefficients of genes, i.e., the group spike-and-slab double-exponential distribution, to integrate group structures and to adaptively shrink the effects of genes. We have developed a fast and stable deterministic algorithm to fit the proposed models. We performed extensive simulation studies to assess the model fitting properties and the prognostic performance of the proposed method, and also applied our method to analyze three cancer data sets. CONCLUSIONS: Both the theoretical and empirical studies show that the proposed method can induce weaker shrinkage on predictors in an active pathway, thereby incorporating the biological similarity of genes within a same pathway into the hierarchical modeling. Compared with several existing methods, the proposed method can more accurately estimate gene effects and can better predict survival outcomes. For the three cancer data sets, the results show that the proposed method generates more powerful models for survival prediction and detecting associated genes. The method has been implemented in a freely available R package BhGLM at https://github.com/nyiuab/BhGLM .

Multivariate Bayesian variable selection exploiting dependence structure among outcomes: Application to air pollution effects on DNA methylation.

The analysis of multiple outcomes is becoming increasingly common in modern biomedical studies. It is well-known that joint statistical models for multiple outcomes are more flexible and more powerful than fitting a separate model for each outcome; they yield more powerful tests of exposure or treatment effects by taking into account the dependence among outcomes and pooling evidence across outcomes. It is, however, unlikely that all outcomes are related to the same subset of covariates. Therefore, there is interest in identifying exposures or treatments associated with particular outcomes, which we term outcome-specific variable selection. In this work, we propose a variable selection approach for multivariate normal responses that incorporates not only information on the mean model, but also information on the variance-covariance structure of the outcomes. The approach effectively leverages evidence from all correlated outcomes to estimate the effect of a particular covariate on a given outcome. To implement this strategy, we develop a Bayesian method that builds a multivariate prior for the variable selection indicators based on the variance-covariance of the outcomes. We show via simulation that the proposed variable selection strategy can boost power to detect subtle effects without increasing the probability of false discoveries. We apply the approach to the Normative Aging Study (NAS) epigenetic data and identify a subset of five genes in the asthma pathway for which gene-specific DNA methylations are associated with exposures to either black carbon, a marker of traffic pollution, or sulfate, a marker of particles generated by power plants.

Bayesian variable selection for post-analytic interrogation of susceptibility loci.

Understanding the complex interplay among protein coding genes and regulatory elements requires rigorous interrogation with analytic tools designed for discerning the relative contributions of overlapping genomic regions. To this aim, we offer a novel application of Bayesian variable selection (BVS) for classifying genomic class level associations using existing large meta-analysis summary level resources. This approach is applied using the expectation maximization variable selection (EMVS) algorithm to typed and imputed SNPs across 502 protein coding genes (PCGs) and 220 long intergenic non-coding RNAs (lncRNAs) that overlap 45 known loci for coronary artery disease (CAD) using publicly available Global Lipids Gentics Consortium (GLGC) (Teslovich et al., 2010; Willer et al., 2013) meta-analysis summary statistics for low-density lipoprotein cholesterol (LDL-C). The analysis reveals 33 PCGs and three lncRNAs across 11 loci with >50% posterior probabilities for inclusion in an additive model of association. The findings are consistent with previous reports, while providing some new insight into the architecture of LDL-cholesterol to be investigated further. As genomic taxonomies continue to evolve, additional classes such as enhancer elements and splicing regions, can easily be layered into the proposed analysis framework. Moreover, application of this approach to alternative publicly available meta-analysis resources, or more generally as a post-analytic strategy to further interrogate regions that are identified through single point analysis, is straightforward. All coding examples are implemented in R version 3.2.1 and provided as supplemental material.

Meta-analysis of incomplete microarray studies.

Meta-analysis of microarray studies to produce an overall gene list is relatively straightforward when complete data are available. When some studies lack information-providing only a ranked list of genes, for example-it is common to reduce all studies to ranked lists prior to combining them. Since this entails a loss of information, we consider a hierarchical Bayes approach to meta-analysis using different types of information from different studies: the full data matrix, summary statistics, or ranks. The model uses an informative prior for the parameter of interest to aid the detection of differentially expressed genes. Simulations show that the new approach can give substantial power gains compared with classical meta-analysis and list aggregation methods. A meta-analysis of 11 published studies with different data types identifies genes known to be involved in ovarian cancer and shows significant enrichment.

A variational Bayes spatiotemporal model for electromagnetic brain mapping.

In this article, we present a new variational Bayes approach for solving the neuroelectromagnetic inverse problem arising in studies involving electroencephalography (EEG) and magnetoencephalography (MEG). This high-dimensional spatiotemporal estimation problem involves the recovery of time-varying neural activity at a large number of locations within the brain, from electromagnetic signals recorded at a relatively small number of external locations on or near the scalp. Framing this problem within the context of spatial variable selection for an underdetermined functional linear model, we propose a spatial mixture formulation where the profile of electrical activity within the brain is represented through location-specific spike-and-slab priors based on a spatial logistic specification. The prior specification accommodates spatial clustering in brain activation, while also allowing for the inclusion of auxiliary information derived from alternative imaging modalities, such as functional magnetic resonance imaging (fMRI). We develop a variational Bayes approach for computing estimates of neural source activity, and incorporate a nonparametric bootstrap for interval estimation. The proposed methodology is compared with several alternative approaches through simulation studies, and is applied to the analysis of a multimodal neuroimaging study examining the neural response to face perception using EEG, MEG, and fMRI.

Variable selection for quantile autoregressive model: Bayesian methods versus classical methods.

In this article, we introduce three Bayesian variable selection methods for the quantile autoregressive model with explanatory variables. The Gibbs sampling algorithms are developed for each method by setting different priors. The numerical simulations suggest that the Gibbs sampling algorithms converge fast and Bayesian variable selection methods are reliable. A real example is given to analysis the relationship between the count of total rental bikes and five explanatory variables. Both simulations and data example indicate that the proposed methods are feasible, reliable, and appropriate for analyzing the Bike Sharing data set.