arXiv subjects

Brent A. Coull

Publications and source records attributed to Brent A. Coull.

At least 19 recordsLinked to original sources

arXiv2026

Spatially Adaptive Ensemble Learning with Calibrated Predictive Uncertainty

Air pollution exposure assessment often uses ensembles of spatio-temporal models, but a critical limitation is that conventional methods use deterministic weights and fail to quantify the uncertainty of their predictions. This yields suboptimal results and prevents the assessment of prediction reliability in health effects studies. We developed a new $\textbf{Bayesian nonparametric ensemble framework}$ that addresses these issues. Our method employs a dependent random measure to adaptively combine models based on their performance in specific feature sub-regions. It also nonparametrically models the ensemble's predictive cumulative density function (CDF), providing a data-consistent measure of uncertainty. We show that our method is asymptotically consistent and improves predictive accuracy for complex data distributions. The framework is demonstrated on simulated data and applied to generate a spatial prediction model for fine particle ($PM_{2.5}$) levels in Eastern New England, USA.

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arXiv2026

Evaluating the effects of policy interventions subject to early adoption: A case study of prescription drug monitoring programs and opioid dispensing

Policies that require organizations to use new systems, such as prescription drug monitoring programs (PDMPs), are often implemented in phases, with an initial period of voluntary access followed by mandated compliance. This allows the policy intervention to be adopted before compliance is required (early adoption), causing outcomes to change before the mandate takes effect. When early adoption is present, the no-anticipation assumption underlying synthetic control methods (SCM) is violated, leading to biased policy effect estimates. We formalize early adoption in a potential outcomes framework for staggered policy implementation and decompose the total policy effect into early adoption and mandate components. We then propose a two-stage, early adoption-aware SCM procedure that first estimates early adoption effects using an interactive fixed effects model fit to pre-mandate data and then residualizes outcomes before applying SCM variants to estimate mandate and total policy effects. Simulations, including settings with correlation between early adoption and latent factors, show reduced bias and improved uncertainty quantification relative to conventional SCM estimators. We apply the framework to state-level PDMP policies and per-capita opioid dispensing. After accounting for early adoption, estimates suggest reductions in opioid dispensing following PDMP availability and mandates; however, the estimates are imprecise and not statistically significant.

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arXiv2026

Scalable Gaussian Process Regression Via Median Posterior Inference for Estimating Multi-Pollutant Mixture Health Effects

Humans are exposed to complex mixtures of environmental pollutants rather than single chemicals, necessitating methods to quantify the health effects of such mixtures. Research on environmental mixtures provides insights into realistic exposure scenarios, informing regulatory policies that better protect public health. However, statistical challenges, including complex correlations among pollutants and nonlinear multivariate exposure-response relationships, complicate such analyses. A popular Bayesian semi-parametric Gaussian process regression framework (Coull et al., 2015) addresses these challenges by modeling exposure-response functions with Gaussian processes and performing feature selection to manage high-dimensional exposures while accounting for confounders. Originally designed for small to moderate-sized cohort studies, this framework does not scale well to massive datasets. To address this, we propose a divide-and-conquer strategy, partitioning data, computing posterior distributions in parallel, and combining results using the generalized median. While we focus on Gaussian process models for environmental mixtures, the proposed distributed computing strategy is broadly applicable to other Bayesian models with computationally prohibitive full-sample Markov Chain Monte Carlo fitting. We provide theoretical guarantees for the convergence of the proposed posterior distributions to those derived from the full sample. We apply this method to estimate associations between a mixture of ambient air pollutants and ~650,000 birthweights recorded in Massachusetts during 2001-2012. Our results reveal negative associations between birthweight and traffic pollution markers, including elemental and organic carbon and PM2.5, and positive associations with ozone and vegetation greenness.

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arXiv2026

A varying-coefficient model for characterizing duration-driven heterogeneity in flood-related health impacts

Previous work revealed associations between flood exposure and adverse health outcomes during and in the aftermath of flood events. Floods are highly heterogeneous events, largely owing to vast differences in flood durations, i.e., flash-floods versus slow-moving floods. However, little to no work has incorporated exposure duration into the modeling of flood-related health impacts or has investigated duration-driven effect heterogeneity. To address this gap, we propose an exposure duration varying coefficient modeling (EDVCM) framework for estimating exposure day-specific health effects of consecutive-day environmental exposures that vary in duration. We develop the EDVCM within an area-level self-matched study design to eliminate time-invariant confounding followed by conditional Poisson regression modeling for exposure effect estimation and adjustment of time-varying confounders. Using a Bayesian framework, we introduce duration- and exposure day-specific exposure coefficients within the conditional Poisson model and assign them a two-dimensional Gaussian process prior to allow for sharing of information across both duration and exposure day. This approach enables highly-resolved insights into duration-driven effect heterogeneity while ensuring model stability through information sharing. Through simulations, we demonstrate that the EDVCM out-performs conventional approaches in terms of both effect estimation and uncertainty quantification. We apply the EDVCM to nationwide, multi-decade Medicare claims data linked with high-resolution flood exposure measures to investigate duration-driven heterogeneity in flood effects on musculoskeletal system disease hospitalizations.

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arXiv2025

The Traceplot Thickens: Developing All-Purpose Convergence Diagnostics for any Markov Chain Monte Carlo Algorithm

Markov Chain Monte Carlo (MCMC) algorithms are frequently used to perform inference under a Bayesian modeling framework. Convergence diagnostics, such as traceplots, the Gelman-Rubin potential scale reduction factor, and effective sample size, are used to visualize and monitor how well the sampler has explored the parameter space and the mixing of multiple chains. However, these classic diagnostics can be undefined or ineffective when the sample space of the algorithm varies in dimension or has a large number of discrete parameters. In this article, we develop a novel approach to produce convergence diagnostics in these difficult scenarios by mapping the original sample space to the real-line and then evaluating the convergence diagnostics on the mapped values. The effectiveness of our method is demonstrated on a MCMC algorithm sampling from a Dirichlet process mixture model. The proposed diagnostics are also used to evaluate the performance of a Bayesian kernel machine regression model for estimating the health effect of multi-pollutant mixtures in the Study of Environment, Lifestyle, and Fibroids. Based on diagnostics for the latter dataset, we then explain how we modify the MCMC sampler to improve convergence.

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arXiv2025

A Bayesian Multivariate Spatial Point Pattern Model: Application to Oral Microbiome FISH Image Data

Advances in cellular imaging technologies, especially those based on fluorescence in situ hybridization (FISH) now allow detailed visualization of the spatial organization of human or bacterial cells. Quantifying this spatial organization is crucial for understanding the function of multicellular tissues or biofilms, with implications for human health and disease. To address the need for better methods to achieve such quantification, we propose a flexible multivariate point process model that characterizes and estimates complex spatial interactions among multiple cell types. The proposed Bayesian framework is appealing due to its unified estimation process and the ability to directly quantify uncertainty in key estimates of interest, such as those of inter-type correlation and the proportion of variance due to inter-type relationships. To ensure stable and interpretable estimation, we consider shrinkage priors for coefficients associated with latent processes. Model selection and comparison are conducted by using a deviance information criterion designed for models with latent variables, effectively balancing the risk of overfitting with that of oversimplifying key quantities. Furthermore, we develop a hierarchical modeling approach to integrate multiple image-specific estimates from a given subject, allowing inference at both the global and subject-specific levels. We apply the proposed method to microbial biofilm image data from the human tongue dorsum and find that specific taxon pairs, such as Streptococcus mitis-Streptococcus salivarius and Streptococcus mitis-Veillonella, exhibit strong positive spatial correlations, while others, such as Actinomyces-Rothia, show slight negative correlations. For most of the taxa, a substantial portion of spatial variance can be attributed to inter-taxon relationships.

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arXiv2025

SkipTrack: A Bayesian Hierarchical Model for Self-tracked Menstrual Cycle Length and Regularity in Large Mobile Health Cohorts

Menstrual cycle length and regularity are important vital signs with implications for a variety of acute and chronic health conditions. Large datasets derived from cycle-tracking mobile health apps are being used to investigate the effects of various covariates on menstrual cycle length and regularity. One limitation on these analyses is that recorded cycle lengths can be incorrectly inflated if users skip tracking any cycle related bleeding days in the app. Here we present SkipTrack, a novel Bayesian hierarchical framework for examining baseline and time-varying effects on menstrual cycle length and regularity while accounting for the uncertainty of possible skips in cycle tracking. In simulations we demonstrate the superiority of the SkipTrack model by showing that competing methods which specify cycle skips a priori are more susceptible to issues of estimation bias and overconfidence than the SkipTrack model. Finally, we apply the SkipTrack framework to data from the Apple Women's Healthy Study, a US-based digital cohort (consent provided at study enrollment) to examine patterns of association between age, BMI and race/ethnicity, and menstrual cycle length and regularity.

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arXiv2024

Multivariate cluster point process to quantify and explore multi-entity configurations: Application to biofilm image data

Clusters of similar or dissimilar objects are encountered in many fields. Frequently used approaches treat the central object of each cluster as latent. Yet, often objects of one or more types cluster around objects of another type. Such arrangements are common in biomedical images of cells, in which nearby cell types likely interact. Quantifying spatial relationships may elucidate biological mechanisms. Parent-offspring statistical frameworks can be usefully applied even when central objects (parents) differ from peripheral ones (offspring). We propose the novel multivariate cluster point process (MCPP) to quantify multi-object (e.g., multi-cellular) arrangements. Unlike commonly used approaches, the MCPP exploits locations of the central parent object in clusters. It accounts for possibly multilayered, multivariate clustering. The model formulation requires specification of which object types function as cluster centers and which reside peripherally. If such information is unknown, the relative roles of object types may be explored by comparing fit of different models via the deviance information criterion (DIC). In simulated data, we compared DIC of a series of models; the MCPP correctly identified simulated relationships. It also produced more accurate and precise parameter estimates than the classical univariate Neyman-Scott process model. We also used the MCPP to quantify proposed configurations and explore new ones in human dental plaque biofilm image data. MCPP models quantified simultaneous clustering of Streptococcus and Porphyromonas around Corynebacterium and of Pasteurellaceae around Streptococcus and successfully captured hypothesized structures for all taxa. Further exploration suggested the presence of clustering between Fusobacterium and Leptotrichia, a previously unreported relationship.

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arXiv2024

Collapsible Kernel Machine Regression for Exposomic Analyses

An important goal of environmental epidemiology is to quantify the complex health risks posed by a wide array of environmental exposures. In analyses focusing on a smaller number of exposures within a mixture, flexible models like Bayesian kernel machine regression (BKMR) are appealing because they allow for non-linear and non-additive associations among mixture components. However, this flexibility comes at the cost of low power and difficult interpretation, particularly in exposomic analyses when the number of exposures is large. We propose a flexible framework that allows for separate selection of additive and non-additive effects, unifying additive models and kernel machine regression. The proposed approach yields increased power and simpler interpretation when there is little evidence of interaction. Further, it allows users to specify separate priors for additive and non-additive effects, and allows for tests of non-additive interaction. We extend the approach to the class of multiple index models, in which the special case of kernel machine-distributed lag models are nested. We apply the method to motivating data from a subcohort of the Human Early Life Exposome (HELIX) study containing 65 mixture components grouped into 13 distinct exposure classes.

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arXiv2023

A Bayesian Spatial Berkson error approach to estimate small area opioid mortality rates accounting for population-at-risk uncertainty

Monitoring small-area geographical population trends in opioid mortality has large scale implications to informing preventative resource allocation. A common approach to obtain small area estimates of opioid mortality is to use a standard disease mapping approach in which population-at-risk estimates are treated as fixed and known. Assuming fixed populations ignores the uncertainty surrounding small area population estimates, which may bias risk estimates and under-estimate their associated uncertainties. We present a Bayesian Spatial Berkson Error (BSBE) model to incorporate population-at-risk uncertainty within a disease mapping model. We compare the BSBE approach to the naive (treating denominators as fixed) using simulation studies to illustrate potential bias resulting from this assumption. We show the application of the BSBE model to obtain 2020 opioid mortality risk estimates for 159 counties in GA accounting for population-at-risk uncertainty. Utilizing our proposed approach will help to inform interventions in opioid related public health responses, policies, and resource allocation. Additionally, we provide a general framework to improve in the estimation and mapping of health indicators.

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arXiv2023

Impacts of Census Differential Privacy for Small-Area Disease Mapping to Monitor Health Inequities

The US Census Bureau will implement a new privacy-preserving disclosure avoidance system (DAS), which includes application of differential privacy, on the public-release 2020 census data. There are concerns that the DAS may bias small-area and demographically-stratified population counts, which play a critical role in public health research and policy, serving as denominators in estimation of disease/mortality rates. Employing three DAS demonstration products, we quantify errors attributable to reliance on DAS-protected denominators in standard small-area disease mapping models for characterizing health inequities. We conduct simulation studies and real data analyses of inequities in premature mortality at the census tract level in Massachusetts. Results show that overall patterns of inequity by racialized group and economic deprivation level are not compromised by the DAS. While early versions of DAS induce errors in mortality rate estimation that are larger for Black than for non-Hispanic white populations, this issue is ameliorated in newer DAS versions.

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arXiv2022

Towards a Unified Framework for Uncertainty-aware Nonlinear Variable Selection with Theoretical Guarantees

We develop a simple and unified framework for nonlinear variable selection that incorporates uncertainty in the prediction function and is compatible with a wide range of machine learning models (e.g., tree ensembles, kernel methods, neural networks, etc). In particular, for a learned nonlinear model $f(\mathbf{x})$, we consider quantifying the importance of an input variable $\mathbf{x}^j$ using the integrated partial derivative $Ψ_j = \Vert \frac{\partial}{\partial \mathbf{x}^j} f(\mathbf{x})\Vert^2_{P_\mathcal{X}}$. We then (1) provide a principled approach for quantifying variable selection uncertainty by deriving its posterior distribution, and (2) show that the approach is generalizable even to non-differentiable models such as tree ensembles. Rigorous Bayesian nonparametric theorems are derived to guarantee the posterior consistency and asymptotic uncertainty of the proposed approach. Extensive simulations and experiments on healthcare benchmark datasets confirm that the proposed algorithm outperforms existing classic and recent variable selection methods.

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arXiv2021

Bayesian kernel machine regression-causal mediation analysis

Greater understanding of the pathways through which an environmental mixture operates is important to design effective interventions. We present new methodology to estimate natural direct and indirect effects and controlled direct effects of a complex mixture exposure on an outcome through a mediator variable. We implement Bayesian Kernel Machine Regression (BKMR) to allow for all possible interactions and nonlinear effects of (1) the co-exposures on the mediator, (2) the co-exposures and mediator on the outcome, and (3) selected covariates on the mediator and/or outcome. From the posterior predictive distributions of the mediator and outcome, we simulate counterfactuals to obtain posterior samples, estimates, and credible intervals of the mediation effects. Our simulation study demonstrates that when the exposure-mediator and exposure-mediator-outcome relationships are complex, BKMR--Causal Mediation Analysis performs better than current mediation methods. We applied our methodology to quantify the contribution of birth length as a mediator between in utero co-exposure to arsenic, manganese and lead, and children's neurodevelopmental scores, in a prospective birth cohort in Bangladesh. Among younger children, we found a negative (adverse) association between the metal mixture and neurodevelopment. We also found evidence that birth length mediates the effect of exposure to the metal mixture on neurodevelopment for younger children. If birth length were fixed to its $75^{th}$ percentile value, the harmful effect of the metal mixture on neurodevelopment is attenuated, suggesting nutritional interventions to help increase fetal growth, and thus birth length, could potentially block the harmful effect of the metal mixture on neurodevelopment.

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arXiv2021

Kernel Machine and Distributed Lag Models for Assessing Windows of Susceptibility to Environmental Mixtures in Children's Health Studies

Exposures to environmental chemicals during gestation can alter health status later in life. Most studies of maternal exposure to chemicals during pregnancy have focused on a single chemical exposure observed at high temporal resolution. Recent research has turned to focus on exposure to mixtures of multiple chemicals, generally observed at a single time point. We consider statistical methods for analyzing data on chemical mixtures that are observed at a high temporal resolution. As motivation, we analyze the association between exposure to four ambient air pollutants observed weekly throughout gestation and birth weight in a Boston-area prospective birth cohort. To explore patterns in the data, we first apply methods for analyzing data on (1) a single chemical observed at high temporal resolution, and (2) a mixture measured at a single point in time. We highlight the shortcomings of these approaches for temporally-resolved data on exposure to chemical mixtures. Second, we propose a novel method, a Bayesian kernel machine regression distributed lag model (BKMR-DLM), that simultaneously accounts for nonlinear associations and interactions among time-varying measures of exposure to mixtures. BKMR-DLM uses a functional weight for each exposure that parameterizes the window of susceptibility corresponding to that exposure within a kernel machine framework that captures non-linear and interaction effects of the multivariate exposure on the outcome. In a simulation study, we show that the proposed method can better estimate the exposure-response function and, in high signal settings, can identify critical windows in time during which exposure has an increased association with the outcome. Applying the proposed method to the Boston birth cohort data, we find evidence of a negative association between organic carbon and birth weight and that nitrate modifies the organic carbon, ...

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arXiv2021

Ordinal Probit Functional Outcome Regression with Application to Computer-Use Behavior in Rhesus Monkeys

Research in functional regression has made great strides in expanding to non-Gaussian functional outcomes, but exploration of ordinal functional outcomes remains limited. Motivated by a study of computer-use behavior in rhesus macaques (Macaca mulatta), we introduce the Ordinal Probit Functional Outcome Regression model (OPFOR). OPFOR models can be fit using one of several basis functions including penalized B-splines, wavelets, and O'Sullivan splines -- the last of which typically performs best. Simulation using a variety of underlying covariance patterns shows that the model performs reasonably well in estimation under multiple basis functions with near nominal coverage for joint credible intervals. Finally, in application, we use Bayesian model selection criteria adapted to functional outcome regression to best characterize the relation between several demographic factors of interest and the monkeys' computer use over the course of a year. In comparison with a standard ordinal longitudinal analysis, OPFOR outperforms a cumulative-link mixed-effects model in simulation and provides additional and more nuanced information on the nature of the monkeys' computer-use behavior.

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arXiv2021

Bayesian Multiple Index Models for Environmental Mixtures

An important goal of environmental health research is to assess the risk posed by mixtures of environmental exposures. Two popular classes of models for mixtures analyses are response-surface methods and exposure-index methods. Response-surface methods estimate high-dimensional surfaces and are thus highly flexible but difficult to interpret. In contrast, exposure-index methods decompose coefficients from a linear model into an overall mixture effect and individual index weights; these models yield easily interpretable effect estimates and efficient inferences when model assumptions hold, but, like most parsimonious models, incur bias when these assumptions do not hold. In this paper we propose a Bayesian multiple index model framework that combines the strengths of each, allowing for non-linear and non-additive relationships between exposure indices and a health outcome, while reducing the dimensionality of the exposure vector and estimating index weights with variable selection. This framework contains response-surface and exposure-index models as special cases, thereby unifying the two analysis strategies. This unification increases the range of models possible for analyzing environmental mixtures and health, allowing one to select an appropriate analysis from a spectrum of models varying in flexibility and interpretability. In an analysis of the association between telomere length and 18 organic pollutants in the National Health and Nutrition Examination Survey (NHANES), the proposed approach fits the data as well as more complex response-surface methods and yields more interpretable results.

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arXiv2020

CVEK: Robust Estimation and Testing for Nonlinear Effects using Kernel Machine Ensemble

The R package CVEK introduces a suite of flexible machine learning models and robust hypothesis tests for learning the joint nonlinear effects of multiple covariates in limited samples. It implements the Cross-validated Ensemble of Kernels (CVEK)(Liu and Coull 2017), an ensemble-based kernel machine learning method that adaptively learns the joint nonlinear effect of multiple covariates from data, and provides powerful hypothesis tests for both main effects of features and interactions among features. The R Package CVEK provides a flexible, easy-to-use implementation of CVEK, and offers a wide range of choices for the kernel family (for instance, polynomial, radial basis functions, Matérn, neural network, and others), model selection criteria, ensembling method (averaging, exponential weighting, cross-validated stacking), and the type of hypothesis test (asymptotic or parametric bootstrap). Through extensive simulations we demonstrate the validity and robustness of this approach, and provide practical guidelines on how to design an estimation strategy for optimal performance in different data scenarios.

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arXiv2020

Reflection on modern methods: Good practices for applied statistical learning in epidemiology

Statistical learning (SL) includes methods that extract knowledge from complex data. SL methods beyond generalized linear models are being increasingly implemented in public health research and epidemiology because they can perform better in instances with complex or high-dimensional data---settings when traditional statistical methods fail. These novel methods, however, often include random sampling which may induce variability in results. Best practices in data science can help to ensure robustness. As a case study, we included four SL models that have been applied previously to analyze the relationship between environmental mixtures and health outcomes. We ran each model across 100 initializing values for random number generation, or "seeds," and assessed variability in resulting estimation and inference. All methods exhibited some seed-dependent variability in results. The degree of variability differed across methods and exposure of interest. Any SL method reliant on a random seed will exhibit some degree of seed sensitivity. We recommend that researchers repeat their analysis with various seeds as a sensitivity analysis when implementing these methods to enhance interpretability and robustness of results.

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