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.

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.

Bayesian Inference for an Unknown Number of Attributes in Restricted Latent Class Models

The specification of the [Formula: see text] matrix in cognitive diagnosis models is important for correct classification of attribute profiles. Researchers have proposed many methods for estimation and validation of the data-driven [Formula: see text] matrices. However, inference of the number of attributes in the general restricted latent class model remains an open question. We propose a Bayesian framework for general restricted latent class models and use the spike-and-slab prior to avoid the computation issues caused by the varying dimensions of model parameters associated with the number of attributes, K. We develop an efficient Metropolis-within-Gibbs algorithm to estimate K and the corresponding [Formula: see text] matrix simultaneously. The proposed algorithm uses the stick-breaking construction to mimic an Indian buffet process and employs a novel Metropolis-Hastings transition step to encourage exploring the sample space associated with different values of K. We evaluate the performance of the proposed method through a simulation study under different model specifications and apply the method to a real data set related to a fluid intelligence matrix reasoning test.

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.

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.

Powerful three-sample genome-wide design and robust statistical inference in summary-data Mendelian randomization

BACKGROUND

Summary-data Mendelian randomization (MR) has become a popular research design to estimate the causal effect of risk exposures. With the sample size of GWAS continuing to increase, it is now possible to use genetic instruments that are only weakly associated with the exposure.

DEVELOPMENT

We propose a three-sample genome-wide design where typically 1000 independent genetic instruments across the whole genome are used. We develop an empirical partially Bayes statistical analysis approach where instruments are weighted according to their strength; thus weak instruments bring less variation to the estimator. The estimator is highly efficient with many weak genetic instruments and is robust to balanced and/or sparse pleiotropy.

APPLICATION

We apply our method to estimate the causal effect of body mass index (BMI) and major blood lipids on cardiovascular disease outcomes, and obtain substantially shorter confidence intervals (CIs). In particular, the estimated causal odds ratio of BMI on ischaemic stroke is 1.19 (95% CI: 1.07-1.32, P-value <0.001); the estimated causal odds ratio of high-density lipoprotein cholesterol (HDL-C) on coronary artery disease (CAD) is 0.78 (95% CI: 0.73-0.84, P-value <0.001). However, the estimated effect of HDL-C attenuates and become statistically non-significant when we only use strong instruments.

CONCLUSIONS

A genome-wide design can greatly improve the statistical power of MR studies. Robust statistical methods may alleviate but not solve the problem of horizontal pleiotropy. Our empirical results suggest that the relationship between HDL-C and CAD is heterogeneous, and it may be too soon to completely dismiss the HDL hypothesis.

An Expectation Conditional Maximization approach for Gaussian graphical models

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes enormous, rendering even state-of-the-art Bayesian stochastic search computationally infeasible. We propose a deterministic alternative to estimate Gaussian and Gaussian copula graphical models using an Expectation Conditional Maximization (ECM) algorithm, extending the EM approach from Bayesian variable selection to graphical model estimation. We show that the ECM approach enables fast posterior exploration under a sequence of mixture priors, and can incorporate multiple sources of information.