Modern Bayesian hierarchical methodologies allow us to leverage spatio-temporal dependencies between observations, enhancing both health effect estimation and map visualization in efficient and flexible ways. However, the necessary levels of statistical software are often unavailable or difficult to access. We have recently examined Bayesian spatio-temporal models to estimate the association between COVID-19 death counts and various social and environmental risk factors, including ambient air pollution exposure. Typically, it is very common that in an infection disease mapping problem with count data, we have excessive zeros, and it is usually for over-dispersed count outcome variables. Furthermore, the theory suggests that the excess zeros are generated by a separate process from the count values and that the excess zeros need to be modeled independently. Our proposed models are specially designed to handle the zero-inflation and over-dispersion in count data through Zero-Inflated Negative Binomial regression with random effects that vary across time and space within a Markov Chain Monte Carlo framework. Drawing on our knowledge and experience, we aim to provide a simple, unified, and publicly available software that can be applied in various disease mapping studies under the contemporary Bayesian framework.

Understanding differences in microbial community structure is critical for uncovering risk factors and mechanisms underlying diseases such as colorectal cancer and preterm birth. Microbiome data present unique statistical challenges because they are compositional in nature, violating assumptions of many classical inference procedures. We propose an empirical bootstrap framework that enables robust hypothesis testing for equality of microbial community means across groups, including two-sample, paired, and multi-sample settings. The method accounts for the simplex structure of microbiome data and provides valid inference even in high-dimensional regimes. Through applications to two large-scale studies, fecal microbiota in colorectal adenoma and cancer patients, and vaginal microbiota in pregnancy with preterm birth outcomes-we demonstrate that our approach identifies clinically meaningful differences that conventional methods fail to detect, such as age-related differences in adenoma prevalence and race-associated disparities in vaginal microbiome composition. These results highlight the potential of resampling-based inference for advancing microbiome research, improving reproducibility, and uncovering clinically relevant microbial signatures.

MOTIVATION:The gut microbiome shapes cancer therapy response through its influence on host metabolism. While prior studies examine pairwise associations between individual genera and metabolites, there is limited methodology for identifying microbial genera that systematically regulate the overall metabolome. Scalable statistical tools are needed to uncover such system-level "master predictors" in high-dimensional microbiome-metabolome data. RESULTS:We introduce B-MASTER, a scalable Bayesian multivariate regression framework combining ℓ1 sparsity and ℓ2 group shrinkage to identify essential cross-metabolite regulators. A Gibbs sampler enables near-linear computational scaling, supporting models with millions of parameters. The method is supported by theoretical guarantees, including posterior contraction and selection consistency. Analysis of colorectal cancer microbiome-metabolome data reveals key microbial genera that govern global and cancer-associated metabolite patterns, highlighting system-level regulatory structure. AVAILABILITY AND IMPLEMENTATION:The B-MASTER code, including demonstration scripts, is available at https://github.com/priyamdas2/B-MASTER. An archived snapshot of the code corresponding to this manuscript is available on Zenodo with DOI: 10.5281/zenodo.20484958.

This paper introduces two novel, communication-efficient Bayesian frameworks, FLamb and OSCLamb, for clustering high-dimensional data in federated learning (FL) settings. Traditional clustering methods often struggle with the non-IID data and privacy constraints inherent in distributed environments. Our proposed methods extend the Latent Mixture for Bayesian (Lamb) model to address these challenges, enabling robust dimension reduction and variable selection without sharing raw data. FLamb is an iterative FL algorithm where a central server aggregates sufficient statistics from distributed sites to build a global consensus model. While generally more accurate, its performance can be sensitive to the number of participating sites and communication overhead. In contrast, OSCLamb is a communication-efficient, single-round decentralized framework that uses peer-to-peer consensus averaging, significantly reducing latency and proving more robust in settings with extreme data heterogeneity. Our simulation studies demonstrate the trade-offs between the methods, with FLamb achieving higher accuracy in less heterogeneous environments and OSCLamb offering superior speed and stability under challenging conditions. We validate our approaches on two real-world high-dimensional datasets, a single-cell RNA sequencing dataset and an EEG dataset, where both methods demonstrate compelling clustering performance. A key advantage of our Bayesian approach, particularly FLamb, is the ability to provide comprehensive posterior uncertainty quantification for the cluster structure, offering more interpretable and reliable results in decentralized analyses.

We introduce B-MASTER (Bayesian Multivariate regression Analysis for Selecting Targeted Essential Regressors), a fully Bayesian framework for scalable multivariate regression in high dimensions. B-MASTER is designed to identify master predictors, i.e., covariates exerting widespread influence across many outcomes, via a hybrid penalty: an L1 penalty induces elementwise sparsity, while an L2 penalty enforces groupwise shrinkage across rows of the coefficient matrix. This structure selects a parsimonious set of key covariates, enhancing interpretability. A tailored Gibbs sampler achieves scalability, with runtime growing linearly in parameter dimension and remaining stable across sample sizes; full posterior inference is feasible for models with up to four million parameters. We establish posterior consistency and contraction rate results, showing that B-MASTER concentrates around the truth at the minimax-optimal rate under sparsity. These theoretical guarantees are supported by strong empirical performance; in simulations, B-MASTER outperforms competing methods in estimation and signal recovery. Applied to microbiome-metabolomics data from colorectal cancer patients, B-MASTER reveals microbial genera that shape broad metabolite profiles, uncovering relationships missed by other methods. The proposed approach is principled, interpretable, and scalable for discovering systemic patterns in ultra-high-dimensional biomedical data.

Selecting the appropriate set of variables is a crucial challenge in predicting outcomes in clinical research. Effective variable selection improves model prediction accuracy and helps clarify the underlying prediction process. This paper categorizes four different types of variable selection methods based on their underlying models: p value‐based methods, penalty methods, tree‐based methods, and Bayesian methods. We introduce commonly used models for each category, summarize the existing software and packages available, and provide an overview of how these models function within a statistical framework. We also demonstrate the application of each method in clinical research, discussing their advantages and disadvantages in terms of model complexity, robustness, and accessibility. Additionally, we explore how these methods relate to others and how researchers can interpret them. In the final section, we discuss how appropriate variable selection can improve model prediction accuracy in different aspects of clinical research. We also summarize the data sizes most suitable for each variable selection method, propose general guidelines for using various methods with other data types, and comment on recent developments in variable selection methodologies. Lastly, we address considerations for new challenges, such as high‐dimensional data.

With the growing availability of multi-platform biomedical data-such as epigenomics, gene expression, and clinical features-there is an increasing need for methods that jointly analyze these datasets. We present BayesMultiomics, an R package for integrating and analyzing gene expression, DNA methylation, gene function annotations, and clinical variables using a two-stage hierarchical Bayesian model. Built with user-friendliness in mind, the package caters to multidisciplinary researchers without extensive programming expertise in Bayesian hierarchical models. Its application is demonstrated using an illustrative Glioblastoma (GBM) dataset.

Information borrowing has been a general tool for improving estimation, testing, and prediction while learning from data distributed over several siloes (devices, trial groups, architecture, or sites), with or without preserving the privacy of the data, depending on the objectives. Federated learning is a more recent tool in this regard, which focuses on privacy preservation: this follows the concept of sharing the model parameters for a learning task rather than sharing the data, running algorithm constituents locally, and then globally optimizing parameters. There are other versions of privacy preserving information borrowing, such as personalized federated learning; the interest in such tasks can be evinced by the recent formation of a UN group to study computation measures enabling information borrowing under privacy guarantees. Heterogeneity is a bottleneck that significantly reduces the utility of information borrowing. In this paper, we identify the progress and gaps in current research regarding heterogeneity in information borrowing for federated learning. In addition to that, we also show using carefully constructed examples the limits of the federated learning paradigm when heterogeneity may be “washed out” when enough data are present. We show the limitations of current research in statistical learning and inference when heterogeneity is present. This article is categorized under:Statistical Learning and Exploratory Methods of the Data Sciences > Modeling MethodsStatistical Learning and Exploratory Methods of the Data Sciences > Deep LearningStatistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical Learning and Exploratory Methods of the Data Sciences > Deep Learning Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms

In this study, we employed a novel approach of combining Gaussian processes (GPs) with boosting techniques to model the spatial variability inherent in End-Stage Kidney Disease (ESKD) data. Our use of the Gaussian processes boosting, or GPBoost, methodology underscores the efficacy of this hybrid method in capturing intricate spatial dynamics and enhancing predictive accuracy. Specifically, our analysis demonstrates a notable improvement in out-of-sample prediction accuracy regarding the percentage of the population remaining on the wait list within geographic regions. Furthermore, our investigation unveils race and gender-based factors that significantly influence patient wait-listing. By leveraging the GPBoost approach, we identify these pertinent factors, shedding light on the complex interplay between demographic variables and access to kidney transplantation services. Our findings underscore the imperative for a multifaceted strategy aimed at reducing spatial disparities in kidney transplant wait-listing. Key components of such an approach include mitigating gender disparities, bolstering access to healthcare services, fostering greater awareness of transplantation options, and dismantling structural barriers to care. By addressing these multifactorial challenges, we can strive towards a more equitable and inclusive landscape in kidney transplantation.

The gut microbiome significantly influences responses to cancer therapies, including immunotherapies, primarily through its impact on the metabolome. Despite some studies on effects of specific microbial genera on individual metabolites, there is little prior work identifying key microbiome components at the genus level that shape the overall metabolome profile. To address this gap, we introduce B-MASTER (Bayesian Multivariate regression Analysis for Selecting Targeted Essential Regressors), a fully Bayesian framework with an L1 penalty to promote sparsity and an L2 penalty to shrink coefficients for non-major covariates, thereby isolating essential regressors. The method is paired with a scalable Gibbs sampling algorithm, whose computation grows linearly with the number of parameters and remains largely unaffected by sample size for models of fixed dimensions. Notably, B-MASTER enables full posterior inference for models with up to four million parameters within a practical time-frame. Its theoretical guarantees include posterior contraction, selection consistency, and robustness under mild misspecification. Using this approach, we identify key microbial genera shaping the metabolite profile, analyze their effects on the most abundant metabolites, and investigate metabolites differentially abundant in colorectal cancer (CRC) patients. These results provide foundational insights into microbiome-metabolite relationships relevant to cancer, a connection largely unexplored in existing literature.

With the increasing availability of biomedical data from multiple platforms of the same patients in clinical research, such as epigenomics, gene expression, and clinical features, there is a growing need for statistical methods that can jointly analyze data from different platforms to provide complementary information for clinical studies. In this paper, we propose a two-stage hierarchical Bayesian model that integrates high-dimensional biomedical data from diverse platforms to select biomarkers associated with clinical outcomes of interest. In the first stage, we use Expectation Maximization-based approach to learn the regulating mechanism between epigenomics (e.g., gene methylation) and gene expression while considering functional gene annotations. In the second stage, we group genes based on the regulating mechanism learned in the first stage. Then, we apply a group-wise penalty to select genes significantly associated with clinical outcomes while incorporating clinical features. Simulation studies suggest that our model-based data integration method shows lower false positives in selecting predictive variables compared with existing method. Moreover, real data analysis based on a glioblastoma (GBM) dataset reveals our method's potential to detect genes associated with GBM survival with higher accuracy than the existing method. Moreover, most of the selected biomarkers are crucial in GBM prognosis as confirmed by existing literature.

In contemporary times, high-dimensional datasets have become increasingly prevalent, owing to the expansion and complexity of data collection facilitated by advancements in computer science, biology, and related fields. Analyzing such high-dimensional data poses distinct challenges compared to traditional data analysis, particularly in the realm of variable selection. Structural Equation Modeling (SEM) serves as a pivotal tool for scrutinizing the relationships between observable (manifest) variables and underlying (latent) variables. Traditionally, SEM primarily focuses on elucidating these relationships among latent variables. This paper proposes an extension of semiparametric structural equation modeling, which employs natural cubic splines to approximate nonlinear functional relationships. Moreover, we introduce priors based on Fused Lasso and Elastic Net to address correlations within both covariates and spline expansions. Through comprehensive simulation studies and real-world data analyses, we validate the efficacy of our approach. Our semiparametric structural equation models, enhanced with Bayesian fused Lasso and Bayesian elastic-net priors, consistently outperform conventional Bayesian Lasso models in both simulated and real-world datasets.

Background Tuberculosis is one of the top ten causes of death globally and the leading cause of death from a single infectious agent. Eradicating the Tuberculosis epidemic by 2030 is one of the top United Nations Sustainable Development Goals. Early diagnosis is essential to achieving this goal because it improves individual prognosis and reduces transmission rates of asymptomatic infected. We aim to support this goal by developing rapid and sensitive diagnostics using machine learning algorithms to minimize the need for expert intervention. Methods and findings A single molecule fluorescence immunosorbent assay was used to detect Tuberculosis biomarker lipoarabinomannan from a set of twenty clinical patient samples and a control set of spiked human urine. Tuberculosis status was separately confirmed by GeneXpert MTB/RIF and cell culture. Two machine learning algorithms, an automatic and a semiautomatic model, were developed and trained by the calibrated lipoarabinomannan titration assay data and then tested against the ground truth patient data. The semiautomatic model differed from the automatic model by an expert review step in the former, which calibrated the lower threshold to determine single molecules from background noise. The semiautomatic model was found to provide 88.89% clinical sensitivity, while the automatic model resulted in 77.78% clinical sensitivity. Conclusions The semiautomatic model outperformed the automatic model in clinical sensitivity as a result of the expert intervention applied during calibration and both models vastly outperformed manual expert counting in terms of time-to-detection and completion of analysis. Meanwhile, the clinical sensitivity of the automatic model could be improved significantly with a larger training dataset. In short, semiautomatic, and automatic Gaussian Mixture Models have a place in supporting rapid detection of Tuberculosis in resource-limited settings without sacrificing clinical sensitivity.

In this paper, we introduce a kernel-based nonlinear Bayesian model for a right-censored survival outcome data set. Our kernel-based approach provides a flexible nonparametric modeling framework to explore nonlinear relationships between predictors with right-censored survival outcome data. Our proposed kernel-based model is shown to provide excellent predictive performance via several simulation studies and real-life examples. Unplanned hospital readmissions greatly impair patients’ quality of life and have imposed a significant economic burden on American society. In this paper, we focus our application on predicting 30-day readmissions of patients. Our survival Bayesian additive regression kernel model (survival BARK or sBARK) improves the timeliness of readmission preventive intervention through a data-driven approach.

The world is experiencing a pandemic due to Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), also known as COVID-19. The USA is also suffering from a catastrophic death toll from COVID-19. Several studies are providing preliminary evidence that short- and long-term exposure to air pollution might increase the severity of COVID-19 outcomes, including a higher risk of death. In this study, we develop a spatiotemporal model to estimate the association between exposure to fine particulate matter PM2.5 and mortality accounting for several social and environmental factors. More specifically, we implement a Bayesian zero-inflated negative binomial regression model with random effects that vary in time and space. Our goal is to estimate the association between air pollution and mortality accounting for the spatiotemporal variability that remained unexplained by the measured confounders. We applied our model to four regions of the USA with weekly data available for each county within each region. We analyze the data separately for each region because each region shows a different disease spread pattern. We found a positive association between long-term exposure to PM2.5 and the mortality from the COVID-19 disease for all four regions with three of four being statistically significant. Data and code are available at our GitHub repository. Supplementary materials accompanying this paper appear on-line.

State-level policy interventions have been critical in managing the spread of the new coronavirus. Here, we study the lag time between policy interventions and change in COVID-19 outcome trajectory in the United States. We develop a stepwise drifts random walk model to account for non-stationarity and strong temporal correlation and subsequently apply a change-point detection algorithm to estimate the number and times of change points in the COVID-19 outcome data. Furthermore, we harmonize data on the estimated change points with non-pharmaceutical interventions adopted by each state of the United States, which provides us insights regarding the lag time between the enactment of a policy and its effect on COVID-19 outcomes. We present the estimated change points for each state and the District of Columbia and find five different emerging trajectory patterns. We also provide insight into the lag time between the enactment of a policy and its effect on COVID-19 outcomes.

Understanding deficits in motor control through the analysis of pedaling biomechanics plays a key role in the treatment of stroke patients. A thorough study of the impact of different exercise patterns and workloads on the change between pre- and post-treatment movement patterns in the patients is therefore of utmost importance to the clinicians. The objective of this study was to analyze the difference between pre- and post-treatment pedaling torques when the patients are subject to different exercise groups with varying workloads. The effects of affected vs unaffected side along with the covariates age and BMI have also been accounted for in this work. Two different three-way ANOVA-based approaches have been implemented here. In the first approach, a random projection-based ANOVA technique has been performed treating the pedaling torques as functional response, whereas the second approach utilizes distance measures to summarize the difference between pre- and post-treatment torques and perform nonparametric tests on it. Bayesian bootstrap has been used here to perform tests on the median distance. A group of stroke patients have been studied in the Cleveland Clinic categorizing them into different exercise groups and workload patterns. The data obtained have been analyzed with the aforementioned techniques, and the results have been reported here. These techniques turn out to be promising and will help clinicians recommend personalized treatment to stroke patients for optimal results.

Survival (time-to-event) analysis is commonly used in clinical research. Key features of performing a survival analysis include checking proportional hazards assumptions, reporting CIs for hazards ratios and relative risks, graphically displaying the findings, and analyzing with consideration of competing risks. This article provides a brief overview of important statistical considerations for survival analysis. Censoring schemes, different methods of survival function estimation, and ways to compare survival curves are described. We also explain competing risk and how to model survival data in the presence of it. Different kinds of bias that influence survival estimation and avenues to model the data under these circumstances are also described. Several analysis techniques are accompanied by graphical representations illustrating proper reporting strategies. We provide a list of guiding statements for researchers and reviewers.