arXiv subjects

Brent A. Coull

Publications and source records attributed to Brent A. Coull.

29 records · Page 2Linked to original sources

arXiv2019

Function-on-Function Regression for the Identification of Epigenetic Regions Exhibiting Windows of Susceptibility to Environmental Exposures

The ability to identify time periods when individuals are most susceptible to exposures, as well as the biological mechanisms through which these exposures act, is of great public health interest. Growing evidence supports an association between prenatal exposure to air pollution and epigenetic marks, such as DNA methylation, but the timing and gene-specific effects of these epigenetic changes are not well understood. Here, we present the first study that aims to identify prenatal windows of susceptibility to air pollution exposures in cord blood DNA methylation. In particular, we propose a function-on-function regression model that leverages data from nearby DNA methylation probes to identify epigenetic regions that exhibit windows of susceptibility to ambient particulate matter less than 2.5 microns (PM$_{2.5}$). By incorporating the covariance structure among both the multivariate DNA methylation outcome and the time-varying exposure under study, this framework yields greater power to detect windows of susceptibility and greater control of false discoveries than methods that model probes independently. We compare our method to a distributed lag model approach that models DNA methylation in a probe-by-probe manner, both in simulation and by application to motivating data from the Project Viva birth cohort. In two epigenetic regions selected based on prior studies of air pollution effects on epigenome-wide methylation, we identify windows of susceptibility to PM$_{2.5}$ exposure near the beginning and middle of the third trimester of pregnancy.

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arXiv2019

Estimating the health effects of environmental mixtures using Bayesian semiparametric regression and sparsity inducing priors

Humans are routinely exposed to mixtures of chemical and other environmental factors, making the quantification of health effects associated with environmental mixtures a critical goal for establishing environmental policy sufficiently protective of human health. The quantification of the effects of exposure to an environmental mixture poses several statistical challenges. It is often the case that exposure to multiple pollutants interact with each other to affect an outcome. Further, the exposure-response relationship between an outcome and some exposures, such as some metals, can exhibit complex, nonlinear forms, since some exposures can be beneficial and detrimental at different ranges of exposure. To estimate the health effects of complex mixtures we propose a flexible Bayesian approach that allows exposures to interact with each other and have nonlinear relationships with the outcome. We induce sparsity using multivariate spike and slab priors to determine which exposures are associated with the outcome, and which exposures interact with each other. The proposed approach is interpretable, as we can use the posterior probabilities of inclusion into the model to identify pollutants that interact with each other. We illustrate our approach's ability to estimate complex functions using simulated data, and apply our method to two studies to determine which environmental pollutants adversely affect health.

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arXiv2019

On the Interplay Between Exposure Misclassification and Informative Cluster Size

In this paper we study the impact of exposure misclassification when cluster size is potentially informative (i.e., related to outcomes) and when misclassification is differential by cluster size. First, we show that misclassification in an exposure related to cluster size can induce informativeness when cluster size would otherwise be non-informative. Second, we show that misclassification that is differential by informative cluster size can not only attenuate estimates of exposure effects but even inflate or reverse the sign of estimates. To correct for bias in estimating marginal parameters, we propose two frameworks: (i) an observed likelihood approach for joint marginalized models of cluster size and outcomes and (ii) an expected estimating equations approach. Although we focus on estimating marginal parameters, a corollary is that the observed likelihood approach permits valid inference for conditional parameters as well. Using data from the Nurses Health Study II, we compare the results of the proposed correction methods when applied to motivating data on the multigenerational effect of in-utero diethylstilbestrol exposure on attention-deficit/hyperactivity disorder in 106,198 children of 47,450 nurses.

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arXiv2019

Bayesian Wavelet-packet Historical Functional Linear Models

Historical Functional Linear Models (HFLM) quantify associations between a functional predictor and functional outcome where the predictor is an exposure variable that occurs before, or at least concurrently with, the outcome. Current work on the HFLM is largely limited to frequentist estimation techniques that employ spline-based basis representations. In this work, we propose a novel use of the discrete wavelet-packet transformation, which has not previously been used in functional models, to estimate historical relationships in a fully Bayesian model. Since inference has not been an emphasis of the existing work on HFLMs, we also employ two established Bayesian inference procedures in this historical functional setting. We investigate the operating characteristics of our wavelet-packet HFLM, as well as the two inference procedures, in simulation and use the model to analyze data on the impact of lagged exposure to particulate matter finer than 2.5$μ$g on heart rate variability in a cohort of journeyman boilermakers over the course of a day's shift.

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arXiv2019

A Cross-validated Ensemble Approach to Robust Hypothesis Testing of Continuous Nonlinear Interactions: Application to Nutrition-Environment Studies

Gene-environment and nutrition-environment studies often involve testing of high-dimensional interactions between two sets of variables, each having potentially complex nonlinear main effects on an outcome. Construction of a valid and powerful hypothesis test for such an interaction is challenging, due to the difficulty in constructing an efficient and unbiased estimator for the complex, nonlinear main effects. In this work we address this problem by proposing a Cross-validated Ensemble of Kernels (CVEK) that learns the space of appropriate functions for the main effects using a cross-validated ensemble approach. With a carefully chosen library of base kernels, CVEK flexibly estimates the form of the main-effect functions from the data, and encourages test power by guarding against over-fitting under the alternative. The method is motivated by a study on the interaction between metal exposures in utero and maternal nutrition on children's neurodevelopment in rural Bangladesh. The proposed tests identified evidence of an interaction between minerals and vitamins intake and arsenic and manganese exposures. Results suggest that the detrimental effects of these metals are most pronounced at low intake levels of the nutrients, suggesting nutritional interventions in pregnant women could mitigate the adverse impacts of in utero metal exposures on children's neurodevelopment.

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arXiv2019

Bayesian data fusion for unmeasured confounding

Bayesian causal inference offers a principled approach to policy evaluation of proposed interventions on mediators or time-varying exposures. We outline a general approach to the estimation of causal quantities for settings with time-varying confounding, such as exposure-induced mediator-outcome confounders. We further extend this approach to propose two Bayesian data fusion (BDF) methods for unmeasured confounding. Using informative priors on quantities relating to the confounding bias parameters, our methods incorporate data from an external source where the confounder is measured in order to make inferences about causal estimands in the main study population. We present results from a simulation study comparing our data fusion methods to two common frequentist correction methods for unmeasured confounding bias in the mediation setting. We also demonstrate our method with an investigation of the role of stage at cancer diagnosis in contributing to Black-White colorectal cancer survival disparities.

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arXiv2018

Adaptive and Calibrated Ensemble Learning with Dependent Tail-free Process

Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assigns to base models a set of deterministic, constant model weights that (1) do not fully account for variations in base model accuracy across subgroups, nor (2) provide uncertainty estimates for the ensemble prediction, which could result in mis-calibrated (i.e. precise but biased) predictions that could in turn negatively impact the algorithm performance in real-word applications. In this work, we present an adaptive, probabilistic approach to ensemble learning using dependent tail-free process as ensemble weight prior. Given input feature $\mathbf{x}$, our method optimally combines base models based on their predictive accuracy in the feature space $\mathbf{x} \in \mathcal{X}$, and provides interpretable uncertainty estimates both in model selection and in ensemble prediction. To encourage scalable and calibrated inference, we derive a structured variational inference algorithm that jointly minimize KL objective and the model's calibration score (i.e. Continuous Ranked Probability Score (CRPS)). We illustrate the utility of our method on both a synthetic nonlinear function regression task, and on the real-world application of spatio-temporal integration of particle pollution prediction models in New England.

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arXiv2018

The Role of Body Mass Index at Diagnosis on Black-White Disparities in Colorectal Cancer Survival: A Density Regression Mediation Approach

The study of racial/ethnic inequalities in health is important to reduce the uneven burden of disease. In the case of colorectal cancer (CRC), disparities in survival among non-Hispanic Whites and Blacks are well documented, and mechanisms leading to these disparities need to be studied formally. It has also been established that body mass index (BMI) is a risk factor for developing CRC, and recent literature shows BMI at diagnosis of CRC is associated with survival. Since BMI varies by racial/ethnic group, a question that arises is whether disparities in BMI is partially responsible for observed racial/ethnic disparities in CRC survival. This paper presents new methodology to quantify the impact of the hypothetical intervention that matches the BMI distribution in the Black population to a potentially complex distributional form observed in the White population on racial/ethnic disparities in survival. We perform a simulation that shows our proposed Bayesian density regression approach performs as well as or better than current methodology allowing for a shift in the mean of the distribution only, and that standard practice of categorizing BMI leads to large biases. When applied to motivating data from the Cancer Care Outcomes Research and Surveillance (CanCORS) Consortium, our approach suggests the proposed intervention is potentially beneficial for elderly and low income Black patients, yet harmful for young and high income Black populations.

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arXiv2018

A Variational Inference Algorithm for BKMR in the Cross-Sectional Setting

The identification of pollutant effects is an important task in environmental health. Bayesian kernel machine regression (BKMR) is a standard tool for inference of individual-level pollutant health-effects, and we present a mean field Variational Inference (VI) algorithm for quick inference when only a single response per individual is recorded. Using simulation studies in the case of informative priors, we show that VI, although fast, produces anti-conservative credible intervals of covariate effects and conservative credible intervals for pollutant effects. To correct the coverage probabilities of covariate effects, we propose a simple Generalized Least Squares (GLS) approach that induces conservative credible intervals. We also explore using BKMR with flat priors and find that, while slower than the case with informative priors, this approach yields uncorrected credible intervals for covariate effects with coverage probabilities that are much closer to the nominal 95% level. We further note that fitting BKMR by VI provides a remarkable improvement in speed over existing MCMC methods.

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arXiv2018

Bayesian Variable Selection for Multivariate Zero-Inflated Models: Application to Microbiome Count Data

Microorganisms play critical roles in human health and disease. It is well known that microbes live in diverse communities in which they interact synergistically or antagonistically. Thus for estimating microbial associations with clinical covariates, multivariate statistical models are preferred. Multivariate models allow one to estimate and exploit complex interdependencies among multiple taxa, yielding more powerful tests of exposure or treatment effects than application of taxon-specific univariate analyses. In addition, the analysis of microbial count data requires special attention because data commonly exhibit zero inflation. To meet these needs, we developed a Bayesian variable selection model for multivariate count data with excess zeros that incorporates information on the covariance structure of the outcomes (counts for multiple taxa), while estimating associations with the mean levels of these outcomes. Although there has been a great deal of effort in zero-inflated models for longitudinal data, little attention has been given to high-dimensional multivariate zero-inflated data modeled via a general correlation structure. Through simulation, we compared performance of the proposed method to that of existing univariate approaches, for both the binary and count parts of the model. When outcomes were correlated the proposed variable selection method maintained type I error while boosting the ability to identify true associations in the binary component of the model. For the count part of the model, in some scenarios the the univariate method had higher power than the multivariate approach. This higher power was at a cost of a highly inflated false discovery rate not observed with the proposed multivariate method. We applied the approach to oral microbiome data from the Pediatric HIV/AIDS Cohort Oral Health Study and identified five species (of 44) associated with HIV infection.

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arXiv2016

Bayesian Distributed Lag Interaction Models to Identify Perinatal Windows of Vulnerability in Children's Health

Epidemiological research supports an association between maternal exposure to air pollution during pregnancy and adverse children's health outcomes. Advances in exposure assessment and statistics allow for estimation of both critical windows of vulnerability and exposure effect heterogeneity. Simultaneous estimation of windows of vulnerability and effect heterogeneity can be accomplished by fitting a distributed lag model (DLM) stratified by subgroup. However, this can provide an incomplete picture of how effects vary across subgroups because it does not allow for subgroups to have the same window but different within-window effects or to have different windows but the same within-window effect. Because the timing of some developmental processes are common across subpopulations of infants while for others the timing differs across subgroups, both scenarios are important to consider when evaluating health risks of prenatal exposures. We propose a new approach that partitions the DLM into a constrained functional predictor that estimates windows of vulnerability and a scalar effect representing the within-window effect directly. The proposed method allows for heterogeneity in only the window, only the within-window effect, or both. In a simulation study we show that a model assuming a shared component across groups results in lower bias and mean squared error for the estimated windows and effects when that component is in fact constant across groups. We apply the proposed method to estimate windows of vulnerability in the association between prenatal exposures to fine particulate matter and each of birth weight and asthma incidence, and estimate how these associations vary by sex and maternal obesity status, in a Boston-area prospective pre-birth cohort study.

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