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In this paper, we propose Varying Effects Regression with Graph Estimation (VERGE), a novel Bayesian method for feature selection in regression. Our model has key aspects that allow it to leverage the complex structure of data sets arising from genomics or imaging studies. We distinguish between the predictors, which are the features utilized in the outcome prediction model, and the subject-level covariates, which modulate the effects of the predictors on the outcome. We construct a varying coefficients modeling framework where we infer a network among the predictor variables and utilize this network information to encourage the selection of related predictors. We employ variable selection spike-and-slab priors that enable the selection of both network-linked predictor variables and covariates that modify the predictor effects. We demonstrate through simulation studies that our method outperforms existing alternative methods in terms of both feature selection and predictive accuracy. We illustrate VERGE with an application to characterizing the influence of gut microbiome features on obesity, where we identify a set of microbial taxa and their ecological dependence relations. We allow subject-level covariates including sex and dietary intake variables to modify the coefficients of the microbiome predictors, providing additional insight into the interplay between these factors.

Ongoing advances in microbiome profiling have allowed unprecedented insights into the molecular activities of microbial communities. This has fueled a strong scientific interest in understanding the critical role the microbiome plays in governing human health, by identifying microbial features associated with clinical outcomes of interest. Several aspects of microbiome data limit the applicability of existing variable selection approaches. In particular, microbiome data are high-dimensional, extremely sparse, and compositional. Importantly, many of the observed features, although categorized as different taxa, may play related functional roles. To address these challenges, we propose a novel compositional regression approach that leverages the data-adaptive clustering and variable selection properties of the spiked Dirichlet process to identify taxa that exhibit similar functional roles. Our proposed method, Bayesian Regression with Agglomerated Compositional Effects using a dirichLET process (BRACElet), enables the identification of a sparse set of features with shared impacts on the outcome, facilitating dimension reduction and model interpretation. We demonstrate that BRACElet outperforms existing approaches for microbiome variable selection through simulation studies and an application elucidating the impact of oral microbiome composition on insulin resistance.

In this paper, 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) non-linear 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 fMRI data from children with a history of traumatic brain injury 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 traumatic brain injury (TBI), and differences in effective connectivity strength between males and females.

In microbiome analysis, researchers often seek to identify taxonomic features associated with an outcome of interest. However, microbiome features are intercorrelated and linked by phylogenetic relationships, making it challenging to assess the association between an individual feature and an outcome. Researchers have developed global tests for the association of microbiome profiles with outcomes using beta diversity metrics which offer robustness to extreme values and can incorporate information on the phylogenetic tree structure. Despite the popularity of global association testing, most existing methods for follow-up testing of individual features only consider the marginal effect and do not provide relevant information for the design of microbiome interventions. This paper proposes a novel conditional association test, CAT, which can account for other features and phylogenetic relatedness when testing the association between a feature and an outcome. CAT adopts a leave-out method, measuring the importance of a feature in predicting the outcome by removing that feature from the data and quantifying how much the association with the outcome is weakened through the change in the coefficient of determination. By leveraging global tests including PERMANOVA and MiRKAT-based methods, CAT allows association testing for continuous, binary, categorical, count, survival, and correlated outcomes. Our simulation and real data application results illustrate the potential of CAT to inform the design of microbiome interventions aimed at improving clinical outcomes.

Advances in survival analysis have facilitated unprecedented flexibility in data modeling, yet there remains a lack of tools for graphically illustrating the influence of continuous covariates on predicted survival outcomes. We propose the utilization of a colored contour plot to depict the predicted survival probabilities over time, and provide a Shiny app and R package as implementations of this tool. Our approach is capable of supporting conventional models, including the Cox and Fine-Gray models. However, its capability shines when coupled with cutting-edge machine learning models such as random survival forests and deep neural networks.

Purpose: This study aimed to use deep learning-based dose prediction to assess head and neck (HN) plan quality and identify suboptimal plans. Methods: A total of 245 VMAT HN plans were created using RapidPlan knowledge-based planning (KBP). A subset of 112 high-quality plans was selected under the supervision of an HN radiation oncologist. We trained a 3D Dense Dilated U-Net architecture to predict 3-dimensional dose distributions using 3-fold cross-validation on 90 plans. Model inputs included CT images, target prescriptions, and contours for targets and organs at risk (OARs). The model's performance was assessed on the remaining 22 test plans. We then tested the application of the dose prediction model for automated review of plan quality. Dose distributions were predicted on 14 clinical plans. The predicted versus clinical OAR dose metrics were compared to flag OARs with suboptimal normal tissue sparing using a 2 Gy dose difference or 3% dose-volume threshold. OAR flags were compared to manual flags by 3 HN radiation oncologists. Results: The predicted dose distributions were of comparable quality to the KBP plans. The differences between the predicted and KBP-planned D1%, D95%, and D99% across the targets were within -2.53%(SD=1.34%), -0.42%(SD=1.27%), and -0.12%(SD=1.97%), respectively, and the OAR mean and maximum doses were within -0.33Gy(SD=1.40Gy) and -0.96Gy(SD=2.08Gy). For the plan quality assessment study, radiation oncologists flagged 47 OARs for possible plan improvement. There was high interphysician variability; 83% of physician-flagged OARs were flagged by only one of 3 physicians. The comparative dose prediction model flagged 63 OARs, including 30 of 47 physician-flagged OARs. Conclusion: Deep learning can predict high-quality dose distributions, which can be used as comparative dose distributions for automated, individualized assessment of HN plan quality., Comment: updated to reflect the published peer-reviewed article

Meta-analysis is a powerful tool for assessing drug safety by combining treatment-related toxicological findings across multiple studies, as clinical trials are typically underpowered for detecting adverse drug effects. However, incomplete reporting of adverse events (AEs) in published clinical studies is a frequent issue, especially if the observed number of AEs is below a pre-specified study-dependent threshold. Ignoring the censored AE information, often found in lower frequency, can significantly bias the estimated incidence rate of AEs. Despite its importance, this common meta-analysis problem has received little statistical or analytic attention in the literature. To address this challenge, we propose a Bayesian approach to accommodating the censored and possibly rare AEs for meta-analysis of safety data. Through simulation studies, we demonstrate that the proposed method can improves accuracy in point and interval estimation of incidence probabilities, particularly in the presence of censored data. Overall, the proposed method provides a practical solution that can facilitate better-informed decisions regarding drug safety.

Network estimation and variable selection have been extensively studied in the statistical literature, but only recently have those two challenges been addressed simultaneously. In this paper, we seek to develop a novel method to simultaneously estimate network interactions and associations to relevant covariates for count data, and specifically for compositional data, which have a fixed sum constraint. We use a hierarchical Bayesian model with latent layers and employ spike-and-slab priors for both edge and covariate selection. For posterior inference, we develop a novel variational inference scheme with an expectation maximization step, to enable efficient estimation. Through simulation studies, we demonstrate that the proposed model outperforms existing methods in its accuracy of network recovery. We show the practical utility of our model via an application to microbiome data. The human microbiome has been shown to contribute to many of the functions of the human body, and also to be linked with a number of diseases. In our application, we seek to better understand the interaction between microbes and relevant covariates, as well as the interaction of microbes with each other. We provide a Python implementation of our algorithm, called SINC (Simultaneous Inference for Networks and Covariates), available online.

There is a keen interest in characterizing variation in the microbiome across cancer patients, given increasing evidence of its important role in determining treatment outcomes. Here our goal is to discover subgroups of patients with similar microbiome profiles. We propose a novel unsupervised clustering approach in the Bayesian framework that innovates over existing model-based clustering approaches, such as the Dirichlet multinomial mixture model, in three key respects: we incorporate feature selection, learn the appropriate number of clusters from the data, and integrate information on the tree structure relating the observed features. We compare the performance of our proposed method to existing methods on simulated data designed to mimic real microbiome data. We then illustrate results obtained for our motivating data set, a clinical study aimed at characterizing the tumor microbiome of pancreatic cancer patients.

Identification of features is a critical task in microbiome studies that is complicated by the fact that microbial data are high dimensional and heterogeneous. Masked by the complexity of the data, the problem of separating signals from noise becomes challenging and troublesome. For instance, when performing differential abundance tests, multiple testing adjustments tend to be overconservative, as the probability of a type I error (false positive) increases dramatically with the large numbers of hypotheses. Moreover, the grouping effect of interest can be obscured by heterogeneity. These factors can incorrectly lead to the conclusion that there are no differences in the microbiome compositions. We translate and represent the problem of identifying differential features as a dynamic layout of separating the signal from its random background. We propose progressive permutation as a method to achieve this process and show converging patterns. More specifically, we progressively permute the grouping factor labels of the microbiome samples and perform multiple differential abundance tests in each scenario. We then compare the signal strength of the top features from the original data with their performance in permutations, and observe an apparent decreasing trend if these top features are true positives identified from the data. We have developed this into a user-friendly RShiny tool and R package, which consist of functions that can convey the overall association between the microbiome and the grouping factor, rank the robustness of the discovered microbes, and list the discoveries, their effect sizes, and individual abundances., Comment: 8 pages, 6 figures

In fields such as ecology, microbiology, and genomics, non-Euclidean distances are widely applied to describe pairwise dissimilarity between samples. Given these pairwise distances, principal coordinates analysis (PCoA) is commonly used to construct a visualization of the data. However, confounding covariates can make patterns related to the scientific question of interest difficult to observe. We provide aPCoA as an easy-to-use tool, available as both an R package and a Shiny app, to improve data visualization in this context, enabling enhanced presentation of the effects of interest.

In the context of a binary classification problem, the optimal linear combination of continuous predictors can be estimated by maximizing an empirical estimate of the area under the receiver operating characteristic (ROC) curve (AUC). For multi-category responses, the optimal predictor combination can similarly be obtained by maximization of the empirical hypervolume under the manifold (HUM). This problem is particularly relevant to medical research, where it may be of interest to diagnose a disease with various subtypes or predict a multi-category outcome. Since the empirical HUM is discontinuous, non-differentiable, and possibly multi-modal, solving this maximization problem requires a global optimization technique. Estimation of the optimal coefficient vector using existing global optimization techniques is computationally expensive, becoming prohibitive as the number of predictors and the number of outcome categories increases. We propose an efficient derivative-free black-box optimization technique based on pattern search to solve this problem. Through extensive simulation studies, we demonstrate that the proposed method achieves better performance compared to existing methods including the step-down algorithm. Finally, we illustrate the proposed method to predict swallowing difficulty after radiation therapy for oropharyngeal cancer based on radiation dose to various structures in the head and neck.

In this paper, 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 (COPD).

Alzheimer's disease is the most common neurodegenerative disease. The aim of this study is to infer structural changes in brain connectivity resulting from disease progression using cortical thickness measurements from a cohort of participants who were either healthy control, or with mild cognitive impairment, or Alzheimer's disease patients. For this purpose, we develop a novel approach for inference of multiple networks with related edge values across groups. Specifically, we infer a Gaussian graphical model for each group within a joint framework, where we rely on Bayesian hierarchical priors to link the precision matrix entries across groups. Our proposal differs from existing approaches in that it flexibly learns which groups have the most similar edge values, and accounts for the strength of connection (rather than only edge presence or absence) when sharing information across groups. Our results identify key alterations in structural connectivity which may reflect disruptions to the healthy brain, such as decreased connectivity within the occipital lobe with increasing disease severity. We also illustrate the proposed method through simulations, where we demonstrate its performance in structure learning and precision matrix estimation with respect to alternative approaches., Comment: Accepted to Biometrics January 2020

Network-based analyses of high-throughput genomics data provide a holistic, systems-level understanding of various biological mechanisms for a common population. However, when estimating multiple networks across heterogeneous sub-populations, varying sample sizes pose a challenge in the estimation and inference, as network differences may be driven by differences in power. We are particularly interested in addressing this challenge in the context of proteomic networks for related cancers, as the number of subjects available for rare cancer (sub-)types is often limited. We develop NExUS (Network Estimation across Unequal Sample sizes), a Bayesian method that enables joint learning of multiple networks while avoiding artefactual relationship between sample size and network sparsity. We demonstrate through simulations that NExUS outperforms existing network estimation methods in this context, and apply it to learn network similarity and shared pathway activity for groups of cancers with related origins represented in The Cancer Genome Atlas (TCGA) proteomic data., Comment: 8 pages, 8 figues

We introduce a multiple testing procedure (TreeBH) which addresses the challenge of controlling error rates at multiple levels of resolution. Conceptually, we frame this problem as the selection of hypotheses which are organized hierarchically in a tree structure. We describe a fast algorithm for the proposed sequential procedure, and prove that it controls relevant error rates given certain assumptions on the dependence among the p-values. Through simulations, we demonstrate that TreeBH offers the desired guarantees under a range of dependency structures (including one similar to that encountered in genome-wide association studies) and that it has the potential of gaining power over alternative methods. We also introduce a modified version of TreeBH which we prove to control the relevant error rates under any dependency structure. We conclude with two case studies: we first analyze data collected as part of the Genotype-Tissue Expression (GTEx) project, which aims to characterize the genetic regulation of gene expression across multiple tissues in the human body, and secondly, data examining the relationship between the gut microbiome and colorectal cancer.