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Survival models are used to analyze time-to-event data in a variety of disciplines. Proportional hazard models provide interpretable parameter estimates, but proportional hazard assumptions are not always appropriate. Non-parametric models are more flexible but often lack a clear inferential framework. We propose a Bayesian treed hazards partition model that is both flexible and inferential. Inference is obtained through the posterior tree structure and flexibility is preserved by modeling the log-hazard function in each partition using a latent Gaussian process. An efficient reversible jump Markov chain Monte Carlo algorithm is accomplished by marginalizing the parameters in each partition element via a Laplace approximation. Consistency properties for the estimator are established. The method can be used to help determine subgroups as well as prognostic and/or predictive biomarkers in time-to-event data. The method is compared with some existing methods on simulated data and a liver cirrhosis dataset. [ABSTRACT FROM AUTHOR]

We consider a Bayesian functional data analysis for observations measured as extremely long sequences. Splitting the sequence into several small windows with manageable lengths, the windows may not be independent especially when they are neighboring each other. We propose to utilize Bayesian smoothing splines to estimate individual functional patterns within each window and to establish transition models for parameters involved in each window to address the dependence structure between windows. The functional difference of groups of individuals at each window can be evaluated by the Bayes factor based on Markov Chain Monte Carlo samples in the analysis. In this paper, we examine the proposed method through simulation studies and apply it to identify differentially methylated genetic regions in TCGA lung adenocarcinoma data. [ABSTRACT FROM AUTHOR]

Genetic interactions play an important role in the progression of complex diseases, providing explanation of variations in disease phenotype missed by main genetic effects. Comparatively, there are fewer studies on survival time, given its challenging characteristics such as censoring. In recent biomedical research, two‐level analysis of both genes and their involved pathways has received much attention and been demonstrated as more effective than single‐level analysis. However, such analysis is usually limited to main effects. Pathways are not isolated, and their interactions have also been suggested to have important contributions to the prognosis of complex diseases. In this paper, we develop a novel two‐level Bayesian interaction analysis approach for survival data. This approach is the first to conduct the analysis of lower‐level gene–gene interactions and higher‐level pathway–pathway interactions simultaneously. Significantly advancing from the existing Bayesian studies based on the Markov Chain Monte Carlo (MCMC) technique, we propose a variational inference framework based on the accelerated failure time model with effective priors to accommodate two‐level selection as well as censoring. Its computational efficiency is much desirable for high‐dimensional interaction analysis. We examine performance of the proposed approach using extensive simulation. The application to TCGA melanoma and lung adenocarcinoma data leads to biologically sensible findings with satisfactory prediction accuracy and selection stability. [ABSTRACT FROM AUTHOR]

Performing causal inference in observational studies requires we assume confounding variables are correctly adjusted for. In settings with few discrete‐valued confounders, standard models can be employed. However, as the number of confounders increases these models become less feasible as there are fewer observations available for each unique combination of confounding variables. In this paper, we propose a new model for estimating treatment effects in observational studies that incorporates both parametric and nonparametric outcome models. By conceptually splitting the data, we can combine these models while maintaining a conjugate framework, allowing us to avoid the use of Markov chain Monte Carlo (MCMC) methods. Approximations using the central limit theorem and random sampling allow our method to be scaled to high‐dimensional confounders. Through simulation studies we show our method can be competitive with benchmark models while maintaining efficient computation, and illustrate the method on a large epidemiological health survey. [ABSTRACT FROM AUTHOR]

This paper introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture complex dependencies and interactions between covariates and the power spectrum, which are often observed in studies of biomedical time series. Local power spectra corresponding to terminal nodes within trees are estimated nonparametrically using Bayesian penalized linear splines. The trees are considered to be random and fit using a Bayesian backfitting Markov chain Monte Carlo (MCMC) algorithm that sequentially considers tree modifications via reversible‐jump MCMC techniques. For high‐dimensional covariates, a sparsity‐inducing Dirichlet hyperprior on tree splitting proportions is considered, which provides sparse estimation of covariate effects and efficient variable selection. By averaging over the posterior distribution of trees, the proposed method can recover both smooth and abrupt changes in the power spectrum across multiple covariates. Empirical performance is evaluated via simulations to demonstrate the proposed method's ability to accurately recover complex relationships and interactions. The proposed methodology is used to study gait maturation in young children by evaluating age‐related changes in power spectra of stride interval time series in the presence of other covariates. [ABSTRACT FROM AUTHOR]

Tensor regression analysis is finding vast emerging applications in a variety of clinical settings, including neuroimaging, genomics, and dental medicine. The motivation for this paper is a study of periodontal disease (PD) with an order‐3 tensor response: multiple biomarkers measured at prespecified tooth–sites within each tooth, for each participant. A careful investigation would reveal considerable skewness in the responses, in addition to response missingness. To mitigate the shortcomings of existing analysis tools, we propose a new Bayesian tensor response regression method that facilitates interpretation of covariate effects on both marginal and joint distributions of highly skewed tensor responses, and accommodates missing‐at‐random responses under a closure property of our tensor model. Furthermore, we present a prudent evaluation of the overall covariate effects while identifying their possible variations on only a sparse subset of the tensor components. Our method promises Markov chain Monte Carlo (MCMC) tools that are readily implementable. We illustrate substantial advantages of our proposal over existing methods via simulation studies and application to a real data set derived from a clinical study of PD. The R package BSTN available in GitHub implements our model. [ABSTRACT FROM AUTHOR]

Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates for uncertainty in the resulting integrative models are however unreliable unless inference accounts for the selection of these associations with accuracy. In this paper, we develop selection‐aware Bayesian methods, which (1) counteract the impact of model selection bias through a "selection‐aware posterior" in a flexible class of integrative Bayesian models post a selection of promising variables via ℓ1‐regularized algorithms; (2) strike an inevitable trade‐off between the quality of model selection and inferential power when the same data set is used for both selection and uncertainty estimation. Central to our methodological development, a carefully constructed conditional likelihood function deployed with a reparameterization mapping provides tractable updates when gradient‐based Markov chain Monte Carlo (MCMC) sampling is used for estimating uncertainties from the selection‐aware posterior. Applying our methods to a radiogenomic analysis, we successfully recover several important gene pathways and estimate uncertainties for their associations with patient survival times. [ABSTRACT FROM AUTHOR]

Correlated binary response data with covariates are ubiquitous in longitudinal or spatial studies. Among the existing statistical models, the most well‐known one for this type of data is the multivariate probit model, which uses a Gaussian link to model dependence at the latent level. However, a symmetric link may not be appropriate if the data are highly imbalanced. Here, we propose a multivariate skew‐elliptical link model for correlated binary responses, which includes the multivariate probit model as a special case. Furthermore, we perform Bayesian inference for this new model and prove that the regression coefficients have a closed‐form unified skew‐elliptical posterior with an elliptical prior. The new methodology is illustrated by an application to COVID‐19 data from three different counties of the state of California, USA. By jointly modeling extreme spikes in weekly new cases, our results show that the spatial dependence cannot be neglected. Furthermore, the results also show that the skewed latent structure of our proposed model improves the flexibility of the multivariate probit model and provides a better fit to our highly imbalanced dataset. [ABSTRACT FROM AUTHOR]

Gene–environment (G× E) interactions have important implications to elucidate the etiology of complex diseases beyond the main genetic and environmental effects. Outliers and data contamination in disease phenotypes of G× E studies have been commonly encountered, leading to the development of a broad spectrum of robust regularization methods. Nevertheless, within the Bayesian framework, the issue has not been taken care of in existing studies. We develop a fully Bayesian robust variable selection method for G× E interaction studies. The proposed Bayesian method can effectively accommodate heavy‐tailed errors and outliers in the response variable while conducting variable selection by accounting for structural sparsity. In particular, for the robust sparse group selection, the spike‐and‐slab priors have been imposed on both individual and group levels to identify important main and interaction effects robustly. An efficient Gibbs sampler has been developed to facilitate fast computation. Extensive simulation studies, analysis of diabetes data with single‐nucleotide polymorphism measurements from the Nurses' Health Study, and The Cancer Genome Atlas melanoma data with gene expression measurements demonstrate the superior performance of the proposed method over multiple competing alternatives. [ABSTRACT FROM AUTHOR]

We propose a model‐based approach that combines Bayesian variable selection tools, a novel spatial kernel convolution structure, and autoregressive processes for detecting a subject's brain activation at the voxel level in complex‐valued functional magnetic resonance imaging (CV‐fMRI) data. A computationally efficient Markov chain Monte Carlo algorithm for posterior inference is developed by taking advantage of the dimension reduction of the kernel‐based structure. The proposed spatiotemporal model leads to more accurate posterior probability activation maps and less false positives than alternative spatial approaches based on Gaussian process models, and other complex‐valued models that do not incorporate spatial and/or temporal structure. This is illustrated in the analysis of simulated data and human task‐related CV‐fMRI data. In addition, we show that complex‐valued approaches dominate magnitude‐only approaches and that the kernel structure in our proposed model considerably improves sensitivity rates when detecting activation at the voxel level. [ABSTRACT FROM AUTHOR]

Spatial partitioning methods correct for nonstationarity in spatially related data by partitioning the space into regions of local stationarity. Existing spatial partitioning methods can only estimate linear partitioning boundaries. This is inadequate for detecting an arbitrarily shaped anomalous spatial region within a larger area. We propose a novel Bayesian functional spatial partitioning (BFSP) algorithm, which estimates closed curves that act as partitioning boundaries around anomalous regions of data with a distinct distribution or spatial process. Our method utilizes transitions between a fixed Cartesian and moving polar coordinate system to model the smooth boundary curves using functional estimation tools. Using adaptive Metropolis‐Hastings, the BFSP algorithm simultaneously estimates the partitioning boundary and the parameters of the spatial distributions within each region. Through simulation we show that our method is robust to shape of the target zone and region‐specific spatial processes. We illustrate our method through the detection of prostate cancer lesions using magnetic resonance imaging. [ABSTRACT FROM AUTHOR]

As pointed out by DWA HT ht is not strongly spatially correlated. Both remove from the mean of the distribution of HT ht the common spatial component that B Y b and B X b share. Next I focus on the joint distribution HT ht . [Extracted from the article]

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject‐level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation‐based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large‐population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation‐based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS‐CoV‐2 dynamics, and apply our method to national surveillance counts from the 2013–2015 West Africa Ebola outbreak. [ABSTRACT FROM AUTHOR]

We develop an envelope model for joint mean and covariance regression in the large p, small n setting. In contrast to existing envelope methods, which improve mean estimates by incorporating estimates of the covariance structure, we focus on identifying covariance heterogeneity by incorporating information about mean‐level differences. We use a Monte Carlo EM algorithm to identify a low‐dimensional subspace that explains differences in both means and covariances as a function of covariates, and then use MCMC to estimate the posterior uncertainty conditional on the inferred low‐dimensional subspace. We demonstrate the utility of our model on a motivating application on the metabolomics of aging. We also provide R code that can be used to develop and test other generalizations of the response envelope model. [ABSTRACT FROM AUTHOR]

In causal inference problems, one is often tasked with estimating causal effects which are analytically intractable functionals of the data‐generating mechanism. Relevant settings include estimating intention‐to‐treat effects in longitudinal problems with missing data or computing direct and indirect effects in mediation analysis. One approach to computing these effects is to use the g‐formula implemented via Monte Carlo integration; when simulation‐based methods such as the nonparametric bootstrap or Markov chain Monte Carlo are used for inference, Monte Carlo integration must be nested within an already computationally intensive algorithm. We develop a widely‐applicable approach to accelerating this Monte Carlo integration step which greatly reduces the computational burden of existing g‐computation algorithms. We refer to our method as accelerated g‐computation (AGC). The algorithms we present are similar in spirit to multiple imputation, but require removing within‐imputation variance from the standard error rather than adding it. We illustrate the use of AGC on a mediation analysis problem using a beta regression model and in a longitudinal clinical trial subject to nonignorable missingness using a Bayesian additive regression trees model. [ABSTRACT FROM AUTHOR]

The presence of protein aggregates in cells is a known feature of many human age‐related diseases, such as Huntington's disease. Simulations using fixed parameter values in a model of the dynamic evolution of expanded polyglutaime (PolyQ) proteins in cells have been used to gain a better understanding of the biological system. However, there is considerable uncertainty about the values of some of the parameters governing the system. Currently, appropriate values are chosen by ad hoc attempts to tune the parameters so that the model output matches experimental data. The problem is further complicated by the fact that the data only offer a partial insight into the underlying biological process: the data consist only of the proportions of cell death and of cells with inclusion bodies at a few time points, corrupted by measurement error. Developing inference procedures to estimate the model parameters in this scenario is a significant task. The model probabilities corresponding to the observed proportions cannot be evaluated exactly, and so they are estimated within the inference algorithm by repeatedly simulating realizations from the model. In general such an approach is computationally very expensive, and we therefore construct Gaussian process emulators for the key quantities and reformulate our algorithm around these fast stochastic approximations. We conclude by highlighting appropriate values of the model parameters leading to new insights into the underlying biological processes. [ABSTRACT FROM AUTHOR]

Cell migration, the process by which cells move from one location to another, plays crucial roles in many biological events. While much research has been devoted to understand the process, most statistical cell migration models rely on using time‐lapse microscopy data from cell trajectories alone. However, the cell and its associated nucleus work together to orchestrate cell movement, which motivates a joint analysis of coupled cell–nucleus trajectories. In this paper, we propose a Bayesian hierarchical model for analyzing cell migration. We incorporate a bivariate angular distribution to handle the coupled cell–nucleus trajectories and introduce latent motility status indicators to model a cell's motility as a time‐dependent characteristic. A Markov chain Monte Carlo algorithm is provided for practical implementation of our model, which is used on real experimental data from MDA‐MB‐231 and NIH 3T3 cells. Through the fitted models, deeper insights into the migratory patterns of these experimental cell populations are gained and their differences are quantified. [ABSTRACT FROM AUTHOR]

Prior distributions, which represent one's belief in the distributions of unknown parameters before observing the data, impact Bayesian inference in a critical and fundamental way. With the ability to incorporate external information from expert opinions or historical datasets, the priors, if specified appropriately, can improve the statistical efficiency of Bayesian inference. In survival analysis, based on the concept of unit information (UI) under parametric models, we propose the unit information Dirichlet process (UIDP) as a new class of nonparametric priors for the underlying distribution of time-to-event data. By deriving the Fisher information in terms of the differential of the cumulative hazard function, the UIDP prior is formulated to match its prior UI with the weighted average of UI in historical datasets and thus can utilize both parametric and nonparametric information provided by historical datasets. With a Markov chain Monte Carlo algorithm, simulations and real data analysis demonstrate that the UIDP prior can adaptively borrow historical information and improve statistical efficiency in survival analysis., (© The Author(s) 2024. Published by Oxford University Press on behalf of The International Biometric Society.)

The article discusses a book titled "Bayesian Nonparametric for Causal Inference and Missing Data," which explores the use of Bayesian methods in causal inference and handling missing data. The book is divided into three topics, covering an overview of causal inference, missing value problems, Bayesian methods, and identifiability issues. It also delves into nonparametric estimation using Bayesian approaches, including generalized additive models, Dirichlet process mixtures, and Gaussian process priors. The book concludes with case studies that apply these methods to various settings. Overall, the book provides valuable insights and strategies for researchers interested in causal inference and missing value problems. [Extracted from the article]

In this work, we propose a new Bayesian spatial homogeneity pursuit method for survival data under the proportional hazards model to detect spatially clustered patterns in baseline hazard and regression coefficients. Specially, regression coefficients and baseline hazard are assumed to have spatial homogeneity pattern over space. To capture such homogeneity, we develop a geographically weighted Chinese restaurant process prior to simultaneously estimating coefficients and baseline hazards and their uncertainty measures. An efficient Markov chain Monte Carlo (MCMC) algorithm is designed for our proposed methods. Performance is evaluated using simulated data, and further applied to a real data analysis of respiratory cancer in the state of Louisiana. [ABSTRACT FROM AUTHOR]

We introduce a framework for estimating causal effects of binary and continuous treatments in high dimensions. We show how posterior distributions of treatment and outcome models can be used together with doubly robust estimators. We propose an approach to uncertainty quantification for the doubly robust estimator, which utilizes posterior distributions of model parameters and (1) results in good frequentist properties in small samples, (2) is based on a single run of a Markov chain Monte Carlo (MCMC) algorithm, and (3) improves over frequentist measures of uncertainty which rely on asymptotic properties. We consider a flexible framework for modeling the treatment and outcome processes within the Bayesian paradigm that reduces model dependence, accommodates nonlinearity, and achieves dimension reduction of the covariate space. We illustrate the ability of the proposed approach to flexibly estimate causal effects in high dimensions and appropriately quantify uncertainty. We show that our proposed variance estimation strategy is consistent when both models are correctly specified, and we see empirically that it performs well in finite samples and under model misspecification. Finally, we estimate the effect of continuous environmental exposures on cholesterol and triglyceride levels. [ABSTRACT FROM AUTHOR]

This article presents a new method for modelling collective movement in continuous time with behavioural switching, motivated by simultaneous tracking of wild or semi‐domesticated animals. Each individual in the group is at times attracted to a unobserved leading point. However, the behavioural state of each individual can switch between 'following' and 'independent'. The 'following' movement is modelled through a linear stochastic differential equation, while the 'independent' movement is modelled as Brownian motion. The movement of the leading point is modelled either as an Ornstein‐Uhlenbeck (OU) process or as Brownian motion (BM), which makes the whole system a higher‐dimensional Ornstein‐Uhlenbeck process, possibly an intrinsic non‐stationary version. An inhomogeneous Kalman filter Markov chain Monte Carlo algorithm is developed to estimate the diffusion and switching parameters and the behaviour states of each individual at a given time point. The method successfully recovers the true behavioural states in simulated data sets , and is also applied to model a group of simultaneously tracked reindeer (Rangifer tarandus). [ABSTRACT FROM AUTHOR]

This paper presents a model‐based method for clustering multivariate binary observations that incorporates constraints consistent with the scientific context. The approach is motivated by the precision medicine problem of identifying autoimmune disease patient subsets or classes who may require different treatments. We start with a family of restricted latent class models or RLCMs. However, in the motivating example and many others like it, the unknown number of classes and the definition of classes using binary states are among the targets of inference. We use a Bayesian approach to RLCMs in order to use informative prior assumptions on the number and definitions of latent classes to be consistent with scientific knowledge so that the posterior distribution tends to concentrate on smaller numbers of clusters and sparser binary patterns. The paper derives a posterior sampling algorithm based on Markov chain Monte Carlo with split‐merge updates to efficiently explore the space of clustering allocations. Through simulations under the assumed model and realistic deviations from it, we demonstrate greater interpretability of results and superior finite‐sample clustering performance for our method compared to common alternatives. The methods are illustrated with an analysis of protein data to detect clusters representing autoantibody classes among scleroderma patients. [ABSTRACT FROM AUTHOR]

Changepoint detection methods are used in many areas of science and engineering, for example, in the analysis of copy number variation data to detect abnormalities in copy numbers along the genome. Despite the broad array of available tools, methodology for quantifying our uncertainty in the strength (or the presence) of given changepoints post‐selection are lacking. Post‐selection inference offers a framework to fill this gap, but the most straightforward application of these methods results in low‐powered hypothesis tests and leaves open several important questions about practical usability. In this work, we carefully tailor post‐selection inference methods toward changepoint detection, focusing on copy number variation data. To accomplish this, we study commonly used changepoint algorithms: binary segmentation, as well as two of its most popular variants, wild and circular, and the fused lasso. We implement some of the latest developments in post‐selection inference theory, mainly auxiliary randomization. This improves the power, which requires implementations of Markov chain Monte Carlo algorithms (importance sampling and hit‐and‐run sampling) to carry out our tests. We also provide recommendations for improving practical useability, detailed simulations, and example analyses on array comparative genomic hybridization as well as sequencing data. [ABSTRACT FROM AUTHOR]

We propose a new highly flexible and tractable Bayesian approach to undertake variable selection in non‐Gaussian regression models. It uses a copula decomposition for the joint distribution of observations on the dependent variable. This allows the marginal distribution of the dependent variable to be calibrated accurately using a nonparametric or other estimator. The family of copulas employed are "implicit copulas" that are constructed from existing hierarchical Bayesian models widely used for variable selection, and we establish some of their properties. Even though the copulas are high dimensional, they can be estimated efficiently and quickly using Markov chain Monte Carlo. A simulation study shows that when the responses are non‐Gaussian, the approach selects variables more accurately than contemporary benchmarks. A real data example in the Web Appendix illustrates that accounting for even mild deviations from normality can lead to a substantial increase in accuracy. To illustrate the full potential of our approach, we extend it to spatial variable selection for fMRI. Using real data, we show our method allows for voxel‐specific marginal calibration of the magnetic resonance signal at over 6000 voxels, leading to an increase in the quality of the activation maps. [ABSTRACT FROM AUTHOR]

The simultaneous testing of multiple hypotheses is common to the analysis of high‐dimensional data sets. The two‐group model, first proposed by Efron, identifies significant comparisons by allocating observations to a mixture of an empirical null and an alternative distribution. In the Bayesian nonparametrics literature, many approaches have suggested using mixtures of Dirichlet Processes in the two‐group model framework. Here, we investigate employing mixtures of two‐parameter Poisson‐Dirichlet Processes instead, and show how they provide a more flexible and effective tool for large‐scale hypothesis testing. Our model further employs nonlocal prior densities to allow separation between the two mixture components. We obtain a closed‐form expression for the exchangeable partition probability function of the two‐group model, which leads to a straightforward Markov Chain Monte Carlo implementation. We compare the performance of our method for large‐scale inference in a simulation study and illustrate its use on both a prostate cancer data set and a case‐control microbiome study of the gastrointestinal tracts in children from underdeveloped countries who have been recently diagnosed with moderate‐to‐severe diarrhea. [ABSTRACT FROM AUTHOR]

It is given as HT ht , where I z i is the true value, I y i is the measured value, and HT ht is the measurement error. It should really be written as HT ht , as "measured value = truth + error.". [Extracted from the article]

We develop a Bayesian nonparametric mixture modeling framework for quantal bioassay settings. The approach is built upon modeling dose-dependent response distributions. We adopt a structured nonparametric prior mixture model, which induces a monotonicity restriction for the dose-response curve. Particular emphasis is placed on the key risk assessment goal of calibration for the dose level that corresponds to a specified response. The proposed methodology yields flexible inference for the dose-response relationship as well as for other inferential objectives, as illustrated with two data sets from the literature.

Large amounts of longitudinal health records are now available for dynamic monitoring of the underlying processes governing the observations. However, the health status progression across time is not typically observed directly: records are observed only when a subject interacts with the system, yielding irregular and often sparse observations. This suggests that the observed trajectories should be modeled via a latent continuous‐time process potentially as a function of time‐varying covariates. We develop a continuous‐time hidden Markov model to analyze longitudinal data accounting for irregular visits and different types of observations. By employing a specific missing data likelihood formulation, we can construct an efficient computational algorithm. We focus on Bayesian inference for the model: this is facilitated by an expectation‐maximization algorithm and Markov chain Monte Carlo methods. Simulation studies demonstrate that these approaches can be implemented efficiently for large data sets in a fully Bayesian setting. We apply this model to a real cohort where patients suffer from chronic obstructive pulmonary disease with the outcome being the number of drugs taken, using health care utilization indicators and patient characteristics as covariates. [ABSTRACT FROM AUTHOR]

Inferring the cancer-type specificities of ultra-rare, genome-wide somatic mutations is an open problem. Traditional statistical methods cannot handle such data due to their ultra-high dimensionality and extreme data sparsity. To harness information in rare mutations, we have recently proposed a formal multilevel multilogistic "hidden genome" model. Through its hierarchical layers, the model condenses information in ultra-rare mutations through meta-features embodying mutation contexts to characterize cancer types. Consistent, scalable point estimation of the model can incorporate 10s of millions of variants across thousands of tumors and permit impressive prediction and attribution. However, principled statistical inference is infeasible due to the volume, correlation, and noninterpretability of mutation contexts. In this paper, we propose a novel framework that leverages topic models from computational linguistics to effectuate dimension reduction of mutation contexts producing interpretable, decorrelated meta-feature topics. We propose an efficient MCMC algorithm for implementation that permits rigorous full Bayesian inference at a scale that is orders of magnitude beyond the capability of existing out-of-the-box inferential high-dimensional multi-class regression methods and software. Applying our model to the Pan Cancer Analysis of Whole Genomes dataset reveals interesting biological insights including somatic mutational topics associated with UV exposure in skin cancer, aging in colorectal cancer, and strong influence of epigenome organization in liver cancer. Under cross-validation, our model demonstrates highly competitive predictive performance against blackbox methods of random forest and deep learning., (© The Author(s) 2024. Published by Oxford University Press on behalf of The International Biometric Society.)

Semi‐competing risks data include the time to a nonterminating event and the time to a terminating event, while competing risks data include the time to more than one terminating event. Our work is motivated by a prostate cancer study, which has one nonterminating event and two terminating events with both semi‐competing risks and competing risks present as well as two censoring times. In this paper, we propose a new multi‐risks survival (MRS) model for this type of data. In addition, the proposed MRS model can accommodate noninformative right‐censoring times for nonterminating and terminating events. Properties of the proposed MRS model are examined in detail. Theoretical and empirical results show that the estimates of the cumulative incidence function for a nonterminating event may be biased if the information on a terminating event is ignored. A Markov chain Monte Carlo sampling algorithm is also developed. Our methodology is further assessed using simulations and also an analysis of the real data from a prostate cancer study. As a result, a prostate‐specific antigen velocity greater than 2.0 ng/mL per year and higher biopsy Gleason scores are positively associated with a shorter time to death due to prostate cancer. [ABSTRACT FROM AUTHOR]

Bayesian model–based clustering provides a powerful and flexible tool that can be incorporated into regression models to better understand the grouping of observations. Using data from the Seychelles Child Development Study, we explore the effect of prenatal methylmercury exposure on 20 neurodevelopmental outcomes measured in 9‐year‐old children. Rather than cluster individual subjects, we cluster the outcomes within a multiple outcomes model. By using information in the data to nest the outcomes into groups called domains, the model more accurately reflects the shared characteristics of neurodevelopmental domains and improves estimation of the overall and outcome‐specific exposure effects by shrinking effects within and between domains selected by the data. The Bayesian paradigm allows for sampling from the posterior distribution of the grouping parameters; thus, inference can be made about group membership and their defining characteristics. We avoid the often difficult and highly subjective requirement of a priori identification of the total number of groups by incorporating a Dirichlet process prior to form a fully Bayesian multiple outcomes model. [ABSTRACT FROM AUTHOR]

Habitat selection models are used in ecology to link the spatial distribution of animals to environmental covariates and identify preferred habitats. The most widely used models of this type, resource selection functions, aim to capture the steady‐state distribution of space use of the animal, but they assume independence between the observed locations of an animal. This is unrealistic when location data display temporal autocorrelation. The alternative approach of step selection functions embed habitat selection in a model of animal movement, to account for the autocorrelation. However, inferences from step selection functions depend on the underlying movement model, and they do not readily predict steady‐state space use. We suggest an analogy between parameter updates and target distributions in Markov chain Monte Carlo (MCMC) algorithms, and step selection and steady‐state distributions in movement ecology, leading to a step selection model with an explicit steady‐state distribution. In this framework, we explain how maximum likelihood estimation can be used for simultaneous inference about movement and habitat selection. We describe the local Gibbs sampler, a novel rejection‐free MCMC scheme, use it as the basis of a flexible class of animal movement models, and derive its likelihood function for several important special cases. In a simulation study, we verify that maximum likelihood estimation can recover all model parameters. We illustrate the application of the method with data from a zebra. [ABSTRACT FROM AUTHOR]

Personal exposure assessment is a challenging task that requires both measurements of the state of the environment as well as the individual's movements. In this paper, we show how location data collected by smartphone applications can be exploited to quantify the personal exposure of a large group of people to air pollution. A Bayesian approach that blends air quality monitoring data with individual location data is proposed to assess the individual exposure over time, under uncertainty of both the pollutant level and the individual location. A comparison with personal exposure obtained assuming fixed locations for the individuals is also provided. Location data collected by the Earthquake Network research project are employed to quantify the dynamic personal exposure to fine particulate matter of around 2500 people living in Santiago (Chile) over a 4‐month period. For around 30% of individuals, the personal exposure based on people movements emerges significantly different over the static exposure. On the basis of this result and thanks to a simulation study, we claim that even when the individual location is known with nonnegligible error, this helps to better assess personal exposure to air pollution. The approach is flexible and can be adopted to quantify the personal exposure based on any location‐aware smartphone application. [ABSTRACT FROM AUTHOR]

In application of diagnostic accuracy, it is possible that a priori information may exist regarding the test score distributions, either between different disease populations for a single test or between multiple correlated tests. Few have considered constrained diagnostic accuracy analysis when the true disease status is binary; almost none when the disease status is ordinal. Motivated by a study on diagnosing endometriosis, we propose an approach to estimating diagnostic accuracy measures that can incorporate different stochastic order constraints on the test scores when an ordinal true disease status is in consideration. We show that the Dirichlet process mixture provides a convenient framework to both flexibly model the test score distributions and embed the a priori ordering constraints. We also utilize the Dirichlet process mixture to model the correlation between multiple tests. In taking a Bayesian perspective to inference, we develop an efficient Markov chain Monte Carlo algorithm to sample from the posterior distribution and provide posterior estimates of the receiver operating characteristic surfaces and the associated summary measures. The proposed approach is evaluated with extensive simulation studies, and is demonstrated with an application to the endometriosis study. [ABSTRACT FROM AUTHOR]

For many real‐life studies with skewed multivariate responses, the level of skewness and association structure assumptions are essential for evaluating the covariate effects on the response and its predictive distribution. We present a novel semiparametric multivariate model and associated Bayesian analysis for multivariate skewed responses. Similar to multivariate Gaussian densities, this multivariate model is closed under marginalization, allows a wide class of multivariate associations, and has meaningful physical interpretations of skewness levels and covariate effects on the marginal density. Other desirable properties of our model include the Markov Chain Monte Carlo computation through available statistical software, and the assurance of consistent Bayesian estimates of the parameters and the nonparametric error density under a set of plausible prior assumptions. We illustrate the practical advantages of our methods over existing alternatives via simulation studies and the analysis of a clinical study on periodontal disease. [ABSTRACT FROM AUTHOR]

Summary: There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health outcome. A main focus in these studies is inference on dose levels associated with a given increase in risk relative to a baseline. In addressing this goal, popular methods either dichotomize the continuous response or focus on modeling changes with the dose in the expectation of the outcome. Such choices may lead to information loss and provide inaccurate inference on dose‐response relationships. We instead propose a Bayesian convex mixture regression model that allows the entire distribution of the health outcome to be unknown and changing with the dose. To balance flexibility and parsimony, we rely on a mixture model for the density at the extreme doses, and express the conditional density at each intermediate dose via a convex combination of these extremal densities. This representation generalizes classical dose‐response models for quantitative outcomes, and provides a more parsimonious, but still powerful, formulation compared to nonparametric methods, thereby improving interpretability and efficiency in inference on risk functions. A Markov chain Monte Carlo algorithm for posterior inference is developed, and the benefits of our methods are outlined in simulations, along with a study on the impact of dde exposure on gestational age. [ABSTRACT FROM AUTHOR]

Summary: Medical imaging data with thousands of spatially correlated data points are common in many fields. Methods that account for spatial correlation often require cumbersome matrix evaluations which are prohibitive for data of this size, and thus current work has either used low‐rank approximations or analyzed data in blocks. We propose a method that accounts for nonstationarity, functional connectivity of distant regions of interest, and local signals, and can be applied to large multi‐subject datasets using spectral methods combined with Markov Chain Monte Carlo sampling. We illustrate using simulated data that properly accounting for spatial dependence improves precision of estimates and yields valid statistical inference. We apply the new approach to study associations between cortical thickness and Alzheimer's disease, and find several regions of the cortex where patients with Alzheimer's disease are thinner on average than healthy controls. [ABSTRACT FROM AUTHOR]

Summary: The standard approach to fitting capture–recapture data collected in continuous time involves arbitrarily forcing the data into a series of distinct discrete capture sessions. We show how continuous‐time models can be fitted as easily as discrete‐time alternatives. The likelihood is factored so that efficient Markov chain Monte Carlo algorithms can be implemented for Bayesian estimation, available online in the R package ctime. We consider goodness‐of‐fit tests for behavior and heterogeneity effects as well as implementing models that allow for such effects. [ABSTRACT FROM AUTHOR]

Summary: Advanced hepatocellular carcinoma (HCC) has limited treatment options and poor survival, therefore early detection is critical to improving the survival of patients with HCC. Current guidelines for high‐risk patients include ultrasound screenings every six months, but ultrasounds are operator dependent and not sensitive for early HCC. Serum α‐Fetoprotein (AFP) is a widely used diagnostic biomarker, but it has limited sensitivity and is not elevated in all HCC cases so, we incorporate a second blood‐based biomarker, des’ γ carboxy‐prothrombin (DCP), that has shown potential as a screening marker for HCC. The data from the Hepatitis C Antiviral Long‐term Treatment against Cirrhosis (HALT‐C) Trial is a valuable source of data to study biomarker screening for HCC. We assume the trajectories of AFP and DCP follow a joint hierarchical mixture model with random changepoints that allows for distinct changepoint times and subsequent trajectories of each biomarker. The changepoint indicators are jointly modeled with a Markov Random Field distribution to help detect borderline changepoints. Markov chain Monte Carlo methods are used to calculate posterior distributions, which are used in risk calculations among future patients and determine whether a patient has a positive screen. The screening algorithm was compared to alternatives in simulations studies under a range of possible scenarios and in the HALT‐C Trial using cross‐validation. [ABSTRACT FROM AUTHOR]

Panel counts are often encountered in longitudinal, such as diary, studies where individuals are followed over time and the number of events occurring in time intervals, or panels, is recorded. This article develops methods for situations where, in addition to the counts of events, a mark, denoting a measure of severity of the events, is recorded. In many situations there is an association between the panel counts and their marks. This is the case for our motivating application that studies the effect of two hormone therapy treatments in reducing counts and severities of vasomotor symptoms in women after hysterectomy/ovariectomy. We model the event counts and their severities jointly through the use of shared random effects. We also compare, through simulation, the power of testing for the treatment effect based on such joint modeling and an alternative scoring approach, which is commonly employed. The scoring approach analyzes the compound outcome of counts times weighted severity. We discuss this approach and quantify challenges which may arise in isolating the treatment effect when such a scoring approach is used. We also show that the power of detecting a treatment effect is higher when using the joint model than analysis using the scoring approach. Inference is performed via Markov chain Monte Carlo methods. [ABSTRACT FROM AUTHOR]

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. [ABSTRACT FROM AUTHOR]

To assess the compliance of air quality regulations, the Environmental Protection Agency (EPA) must know if a site exceeds a pre-specified level. In the case of ozone, the level for compliance is fixed at 75 parts per billion, which is high, but not extreme at all locations. We present a new space-time model for threshold exceedances based on the skew- t process. Our method incorporates a random partition to permit long-distance asymptotic independence while allowing for sites that are near one another to be asymptotically dependent, and we incorporate thresholding to allow the tails of the data to speak for themselves. We also introduce a transformed AR(1) time-series to allow for temporal dependence. Finally, our model allows for high-dimensional Bayesian inference that is comparable in computation time to traditional geostatistical methods for large data sets. We apply our method to an ozone analysis for July 2005, and find that our model improves over both Gaussian and max-stable methods in terms of predicting exceedances of a high level. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Finding rare variants and gene-environment interactions (GXE) is critical in dissecting complex diseases. We consider the problem of detecting GXE where G is a rare haplotype and E is a nongenetic factor. Such methods typically assume G-E independence, which may not hold in many applications. A pertinent example is lung cancer-there is evidence that variants on Chromosome 15q25.1 interact with smoking to affect the risk. However, these variants are associated with smoking behavior rendering the assumption of G-E independence inappropriate. With the motivation of detecting GXE under G-E dependence, we extend an existing approach, logistic Bayesian LASSO, which assumes G-E independence (LBL-GXE-I) by modeling G-E dependence through a multinomial logistic regression (referred to as LBL-GXE-D). Unlike LBL-GXE-I, LBL-GXE-D controls type I error rates in all situations; however, it has reduced power when G-E independence holds. To control type I error without sacrificing power, we further propose a unified approach, LBL-GXE, to incorporate uncertainty in the G-E independence assumption by employing a reversible jump Markov chain Monte Carlo method. Our simulations show that LBL-GXE has power similar to that of LBL-GXE-I when G-E independence holds, yet has well-controlled type I errors in all situations. To illustrate the utility of LBL-GXE, we analyzed a lung cancer dataset and found several significant interactions in the 15q25.1 region, including one between a specific rare haplotype and smoking. [ABSTRACT FROM AUTHOR]