Bayesian variable selection for understanding mixtures in environmental exposures

Combined Exposures and Mixtures Research: An Enduring NIEHS Priority

BACKGROUND

The National Institute of Environmental Health Sciences (NIEHS) continues to prioritize research to better understand the health effects resulting from exposure to mixtures of chemical and nonchemical stressors. Mixtures research activities over the last decade were informed by expert input during the development and deliberations of the 2011 NIEHS Workshop "Advancing Research on Mixtures: New Perspectives and Approaches for Predicting Adverse Human Health Effects." NIEHS mixtures research efforts since then have focused on key themes including a) prioritizing mixtures for study, b) translating mixtures data from in vitro and in vivo studies, c) developing cross-disciplinary collaborations, d) informing component-based and whole-mixture assessment approaches, e) developing sufficient similarity methods to compare across complex mixtures, f) using systems-based approaches to evaluate mixtures, and g) focusing on management and integration of mixtures-related data.

OBJECTIVES

We aimed to describe NIEHS driven research on mixtures and combined exposures over the last decade and present areas for future attention.

RESULTS

Intramural and extramural mixtures research projects have incorporated a diverse array of chemicals (e.g., polycyclic aromatic hydrocarbons, botanicals, personal care products, wildfire emissions) and nonchemical stressors (e.g., socioeconomic factors, social adversity) and have focused on many diseases (e.g., breast cancer, atherosclerosis, immune disruption). We have made significant progress in certain areas, such as developing statistical methods for evaluating multiple chemical associations in epidemiology and building translational mixtures projects that include both in vitro and in vivo models.

DISCUSSION

Moving forward, additional work is needed to improve mixtures data integration, elucidate interactions between chemical and nonchemical stressors, and resolve the geospatial and temporal nature of mixture exposures. Continued mixtures research will be critical to informing cumulative impact assessments and addressing complex challenges, such as environmental justice and climate change. https://doi.org/10.1289/EHP14340.

Regression with race-modifiers: towards equity and interpretability

The pervasive effects of structural racism and racial discrimination are well-established and offer strong evidence that the effects of many important variables on health and life outcomes vary by race. Alarmingly, standard practices for statistical regression analysis introduce racial biases into the estimation and presentation of these race-modified effects. We introduce abundance-based constraints (ABCs) to eliminate these racial biases. ABCs offer a remarkable invariance property: estimates and inference for main effects are nearly unchanged by the inclusion of race-modifiers. Thus, quantitative researchers can estimate race-specific effects "for free"-without sacrificing parameter interpretability, equitability, or statistical efficiency. The benefits extend to prominent statistical learning techniques, especially regularization and selection. We leverage these tools to estimate the joint effects of environmental, social, and other factors on 4th end-of-grade readings scores for students in North Carolina (n = 27, 638) and identify race-modified effects for racial (residential) isolation, PM2.5 exposure, and mother's age at birth.

Regression with race-modifiers: towards equity and interpretability

The pervasive effects of structural racism and racial discrimination are well-established and offer strong evidence that the effects of many important variables on health and life outcomes vary by race. Alarmingly, standard practices for statistical regression analysis introduce racial biases into the estimation and presentation of these race-modified effects. We introduce abundance-based constraints (ABCs) to eliminate these racial biases. ABCs offer a remarkable invariance property: estimates and inference for main effects are nearly unchanged by the inclusion of race-modifiers. Thus, quantitative researchers can estimate race-specific effects "for free"-without sacrificing parameter interpretability, equitability, or statistical efficiency. The benefits extend to prominent statistical learning techniques, especially regularization and selection. We leverage these tools to estimate the joint effects of environmental, social, and other factors on 4th end-of-grade readings scores for students in North Carolina (n = 27, 638) and identify race-modified effects for racial (residential) isolation, PM2.5 exposure, and mother's age at birth.

Machine Learning Assisted Discovery of Interactions between Pesticides, Phthalates, Phenols, and Trace Elements in Child Neurodevelopment

A growing body of literature suggests that developmental exposure to individual or mixtures of environmental chemicals (ECs) is associated with autism spectrum disorder (ASD). However, investigating the effect of interactions among these ECs can be challenging. We introduced a combination of the classical exposure-mixture Weighted Quantile Sum (WQS) regression and a machine-learning method termed Signed iterative Random Forest (SiRF) to discover synergistic interactions between ECs that are (1) associated with higher odds of ASD diagnosis, (2) mimic toxicological interactions, and (3) are present only in a subset of the sample whose chemical concentrations are higher than certain thresholds. In a case-control Childhood Autism Risks from Genetics and Environment (CHARGE) study, we evaluated multiordered synergistic interactions among 62 ECs measured in the urine samples of 479 children in association with increased odds for ASD diagnosis (yes vs no). WQS-SiRF identified two synergistic two-ordered interactions between (1) trace-element cadmium (Cd) and the organophosphate pesticide metabolite diethyl-phosphate (DEP); and (2) 2,4,6-trichlorophenol (TCP-246) and DEP. Both interactions were suggestively associated with increased odds of ASD diagnosis in the subset of children with urinary concentrations of Cd, DEP, and TCP-246 above the 75th percentile. This study demonstrates a novel method that combines the inferential power of WQS and the predictive accuracy of machine-learning algorithms to discover potentially biologically relevant chemical-chemical interactions associated with ASD.

Subset selection for linear mixed models

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates-while accounting for this structured dependence-remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.

Powering Research through Innovative Methods for Mixtures in Epidemiology (PRIME) Program: Novel and Expanded Statistical Methods

Humans are exposed to a diverse mixture of chemical and non-chemical exposures across their lifetimes. Well-designed epidemiology studies as well as sophisticated exposure science and related technologies enable the investigation of the health impacts of mixtures. While existing statistical methods can address the most basic questions related to the association between environmental mixtures and health endpoints, there were gaps in our ability to learn from mixtures data in several common epidemiologic scenarios, including high correlation among health and exposure measures in space and/or time, the presence of missing observations, the violation of important modeling assumptions, and the presence of computational challenges incurred by current implementations. To address these and other challenges, NIEHS initiated the Powering Research through Innovative methods for Mixtures in Epidemiology (PRIME) program, to support work on the development and expansion of statistical methods for mixtures. Six independent projects supported by PRIME have been highly productive but their methods have not yet been described collectively in a way that would inform application. We review 37 new methods from PRIME projects and summarize the work across previously published research questions, to inform methods selection and increase awareness of these new methods. We highlight important statistical advancements considering data science strategies, exposure-response estimation, timing of exposures, epidemiological methods, the incorporation of toxicity/chemical information, spatiotemporal data, risk assessment, and model performance, efficiency, and interpretation. Importantly, we link to software to encourage application and testing on other datasets. This review can enable more informed analyses of environmental mixtures. We stress training for early career scientists as well as innovation in statistical methodology as an ongoing need. Ultimately, we direct efforts to the common goal of reducing harmful exposures to improve public health.

Bayesian subset selection and variable importance for interpretable prediction and classification

Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with post-selection inference. We address these challenges from a Bayesian perspective. Given any Bayesian predictive model ℳ , we extract a family of near-optimal subsets of variables for linear prediction or classification. This strategy deemphasizes the role of a single "best" subset and instead advances the broader perspective that often many subsets are highly competitive. The acceptable family of subsets offers a new pathway for model interpretation and is neatly summarized by key members such as the smallest acceptable subset, along with new (co-) variable importance metrics based on whether variables (co-) appear in all, some, or no acceptable subsets. More broadly, we apply Bayesian decision analysis to derive the optimal linear coefficients for any subset of variables. These coefficients inherit both regularization and predictive uncertainty quantification via ℳ . For both simulated and real data, the proposed approach exhibits better prediction, interval estimation, and variable selection than competing Bayesian and frequentist selection methods. These tools are applied to a large education dataset with highly correlated covariates. Our analysis provides unique insights into the combination of environmental, socioeconomic, and demographic factors that predict educational outcomes, and identifies over 200 distinct subsets of variables that offer near-optimal out-of-sample predictive accuracy.