Bayesian Factor Analysis for Inference on Interactions

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.

Dietary patterns associated with the incidence of hypertension among adult Japanese males: application of machine learning to a cohort study

PURPOSE

The previous studies that examined the effectiveness of unsupervised machine learning methods versus traditional methods in assessing dietary patterns and their association with incident hypertension showed contradictory results. Consequently, our aim is to explore the correlation between the incidence of hypertension and overall dietary patterns that were extracted using unsupervised machine learning techniques.

METHODS

Data were obtained from Japanese male participants enrolled in a prospective cohort study between August 2008 and August 2010. A final dataset of 447 male participants was used for analysis. Dimension reduction using uniform manifold approximation and projection (UMAP) and subsequent K-means clustering was used to derive dietary patterns. In addition, multivariable logistic regression was used to evaluate the association between dietary patterns and the incidence of hypertension.

RESULTS

We identified four dietary patterns: 'Low-protein/fiber High-sugar,' 'Dairy/vegetable-based,' 'Meat-based,' and 'Seafood and Alcohol.' Compared with 'Seafood and Alcohol' as a reference, the protective dietary patterns for hypertension were 'Dairy/vegetable-based' (OR 0.39, 95% CI 0.19-0.80, P = 0.013) and the 'Meat-based' (OR 0.37, 95% CI 0.16-0.86, P = 0.022) after adjusting for potential confounding factors, including age, body mass index, smoking, education, physical activity, dyslipidemia, and diabetes. An age-matched sensitivity analysis confirmed this finding.

CONCLUSION

This study finds that relative to the 'Seafood and Alcohol' pattern, the 'Dairy/vegetable-based' and 'Meat-based' dietary patterns are associated with a lower risk of hypertension among men.

A review of common statistical methods for dealing with multiple pollutant mixtures and multiple exposures

Traditional environmental epidemiology has consistently focused on studying the impact of single exposures on specific health outcomes, considering concurrent exposures as variables to be controlled. However, with the continuous changes in environment, humans are increasingly facing more complex exposures to multi-pollutant mixtures. In this context, accurately assessing the impact of multi-pollutant mixtures on health has become a central concern in current environmental research. Simultaneously, the continuous development and optimization of statistical methods offer robust support for handling large datasets, strengthening the capability to conduct in-depth research on the effects of multiple exposures on health. In order to examine complicated exposure mixtures, we introduce commonly used statistical methods and their developments, such as weighted quantile sum, bayesian kernel machine regression, toxic equivalency analysis, and others. Delineating their applications, advantages, weaknesses, and interpretability of results. It also provides guidance for researchers involved in studying multi-pollutant mixtures, aiding them in selecting appropriate statistical methods and utilizing R software for more accurate and comprehensive assessments of the impact of multi-pollutant mixtures on human health.

Statistical methods for chemical mixtures: a roadmap for practitioners

Quantitative characterization of the health impacts associated with exposure to chemical mixtures has received considerable attention in current environmental and epidemiological studies. With many existing statistical methods and emerging approaches, it is important for practitioners to understand when each method is best suited for their inferential goals. In this study, we conduct a review and comparison of 11 analytical methods available for use in mixtures research, through extensive simulation studies for continuous and binary outcomes. These methods fall in three different classes: identifying important components of a mixture, identifying interactions and creating a summary score for risk stratification and prediction. We carry out an illustrative data analysis in the PROTECT birth cohort from Puerto Rico. Most importantly we develop an integrated package "CompMix" that provides a platform for mixtures analysis where the practitioner can implement a pipeline for several types of mixtures analysis. Our simulation results suggest that the choice of methods depends on the goal of analysis and there is no clear winner across the board. For selection of important toxicants in the mixture and for identifying interactions, Elastic net by Zou et al. (Enet), Lasso for Hierarchical Interactions by Bien et al (HierNet), Selection of nonlinear interactions by a forward stepwise algorithm by Narisetty et al. (SNIF) have the most stable performance across simulation settings. Additionally, the predictive performance of the Super Learner ensembling method by Van de Laan et al. and HierNet are found to be superior to the rest of the methods. For overall summary or a cumulative measure, we find that using the Super Learner to combine multiple Environmental Risk Scores can lead to improved risk stratification properties. We have developed an R package "CompMix: A comprehensive toolkit for environmental mixtures analysis", allowing users to implement a variety of tasks under different settings and compare the findings. In summary, our study offers guidelines for selecting appropriate statistical methods for addressing specific scientific questions related to mixtures research. We identify critical gaps where new and better methods are needed.

An integrated Bayesian framework for multi-omics prediction and classification

With the growing commonality of multi-omics datasets, there is now increasing evidence that integrated omics profiles lead to more efficient discovery of clinically actionable biomarkers that enable better disease outcome prediction and patient stratification. Several methods exist to perform host phenotype prediction from cross-sectional, single-omics data modalities but decentralized frameworks that jointly analyze multiple time-dependent omics data to highlight the integrative and dynamic impact of repeatedly measured biomarkers are currently limited. In this article, we propose a novel Bayesian ensemble method to consolidate prediction by combining information across several longitudinal and cross-sectional omics data layers. Unlike existing frequentist paradigms, our approach enables uncertainty quantification in prediction as well as interval estimation for a variety of quantities of interest based on posterior summaries. We apply our method to four published multi-omics datasets and demonstrate that it recapitulates known biology in addition to providing novel insights while also outperforming existing methods in estimation, prediction, and uncertainty quantification. Our open-source software is publicly available at https://github.com/himelmallick/IntegratedLearner.

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.

In Utero Exposure to Metals and Birth Outcomes in an Artisanal and Small-Scale Gold Mining Birth Cohort in Madre de Dios, Peru

BACKGROUND

Few birth cohorts in South America evaluate the joint effect of minerals and toxic metals on neonatal health. In Madre de Dios, Peru, mercury exposure is prevalent owing to artisanal gold mining, yet its effect on neonatal health is unknown.

OBJECTIVES

We aimed to determine whether toxic metals are associated with lower birth weight and shorter gestational age independently of antenatal care and other maternal well-being factors.

METHODS

Data are from the COhorte de NAcimiento de MAdre de Dios (CONAMAD) birth cohort, which enrolled pregnant women in Madre de Dios prior to their third trimester and obtained maternal and cord blood samples at birth. We use structural equation models (SEMs) to construct latent variables for the maternal metals environment (ME) and the fetal environment (FE) using concentrations of calcium, iron, selenium, zinc, magnesium, mercury, lead, and arsenic measured in maternal and cord blood, respectively. We then assessed the relationship between the latent variables ME and FE, toxic metals, prenatal visits, hypertension, and their effect on gestational age and birth weight.

RESULTS

Among 198 mothers successfully enrolled and followed at birth, 29% had blood mercury levels that exceeded the U.S. Centers for Disease Control and Prevention threshold of 5.8 μ g / L and 2 mothers surpassed the former 5 - μ g / dL threshold for blood lead. The current threshold value is 3.5 μ g / dL . Minerals and toxic metals loaded onto ME and FE latent variables. ME was associated with FE (β = 0.24; 95% CI: 0.05, 0.45). FE was associated with longer gestational age (β = 2.31; 95% CI: - 0.3 , 4.51) and heavier birth weight. Mercury exposure was not directly associated with health outcomes. A 1% increase in maternal blood lead shortened gestational age by 0.05 d (β = - 0.75 ; 95% CI: - 1.51 , - 0.13 ), which at the 5 - μ g / dL threshold resulted in a loss of 3.6 gestational days and 76.5 g in birth weight for newborns. Prenatal care visits were associated with improved birth outcomes, with a doubling of visits from 6 to 12 associated with 5.5 more gestational days (95% CI: 1.6, 9.4) and 319 g of birth weight (95% CI: 287.6, 350.7).

DISCUSSION

Maternal lead, even at low exposures, was associated with shorter gestation and lower birth weight. Studies that focus only on harmful exposures or nutrition may mischaracterize the dynamic maternal ME and FE. SEMs provide a framework to evaluate these complex relationships during pregnancy and reduce overcontrolling that can occur with linear regression. https://doi.org/10.1289/EHP10557.

Nutritional Modulation of Associations between Prenatal Exposure to Persistent Organic Pollutants and Childhood Obesity: A Prospective Cohort Study

BACKGROUND

Prenatal exposure to persistent organic pollutants (POPs) may contribute to the development of childhood obesity and metabolic disorders. However, little is known about whether the maternal nutritional status during pregnancy can modulate these associations.

OBJECTIVES

The main objective was to characterize the joint associations and interactions between prenatal levels of POPs and nutrients on childhood obesity.

METHODS

We used data from to the Spanish INfancia y Medio Ambiente-Environment and Childhood (INMA) birth cohort, on POPs and nutritional biomarkers measured in maternal blood collected at the first trimester of pregnancy and child anthropometric measurements at 7 years of age. Six organochlorine compounds (OCs) [dichlorodiphenyldichloroethylene, hexachlorobenzene (HCB), β-hexachlorocyclohexane (β-HCH) and polychlorinated biphenyls 138, 153, 180] and four per- and polyfluoroalkyl substances (PFAS) were measured. Nutrients included vitamins (D, B12, and folate), polyunsaturated fatty acids (PUFAs), and dietary carotenoids. Two POPs-nutrients mixtures data sets were established: a) OCs, PFAS, vitamins, and carotenoids (n=660), and b) OCs, PUFAs, and vitamins (n=558). Joint associations of mixtures on obesity were characterized using Bayesian kernel machine regression (BKMR). Relative importance of biomarkers and two-way interactions were identified using gradient boosting machine, hierarchical group lasso regularization, and BKMR. Interactions were further characterized using multivariate regression models in the multiplicative and additive scale.

RESULTS

Forty percent of children had overweight or obesity. We observed a positive overall joint association of both POPs-nutrients mixtures on overweight/obesity risk, with HCB and vitamin B12 the biomarkers contributing the most. Recurrent interactions were found between HCB and vitamin B12 across screening models. Relative risk for a natural log increase of HCB was 1.31 (95% CI: 1.11, 1.54, pInteraction=0.02) in the tertile 2 of vitamin B12 and in the additive scale a relative excess risk due to interaction of 0.11 (95% CI: 0.02, 0.20) was found. Interaction between perfluorooctane sulfonate and β-cryptoxanthin suggested a protective effect of the antioxidant on overweight/obesity risk.

CONCLUSION

These results support that maternal nutritional status may modulate the effect of prenatal exposure to POPs on childhood overweight/obesity. These findings may help to develop a biological hypothesis for future toxicological studies and to better interpret inconsistent findings in epidemiological studies. https://doi.org/10.1289/EHP11258.

CRITICAL WINDOW VARIABLE SELECTION FOR MIXTURES: ESTIMATING THE IMPACT OF MULTIPLE AIR POLLUTANTS ON STILLBIRTH

Understanding the role of time-varying pollution mixtures on human health is critical as people are simultaneously exposed to multiple pollutants during their lives. For vulnerable subpopulations who have well-defined exposure periods (e.g., pregnant women), questions regarding critical windows of exposure to these mixtures are important for mitigating harm. We extend critical window variable selection (CWVS) to the multipollutant setting by introducing CWVS for mixtures (CWVSmix), a hierarchical Bayesian method that combines smoothed variable selection and temporally correlated weight parameters to: (i) identify critical windows of exposure to mixtures of time-varying pollutants, (ii) estimate the time-varying relative importance of each individual pollutant and their first order interactions within the mixture, and (iii) quantify the impact of the mixtures on health. Through simulation we show that CWVSmix offers the best balance of performance in each of these categories in comparison to competing methods. Using these approaches, we investigate the impact of exposure to multiple ambient air pollutants on the risk of stillbirth in New Jersey, 2005-2014. We find consistent elevated risk in gestational weeks 2, 16-17, and 20 for non-Hispanic Black mothers, with pollution mixtures dominated by ammonium (weeks 2, 17, 20), nitrate (weeks 2, 17), nitrogen oxides (weeks 2, 16), PM2.5 (week 2), and sulfate (week 20). The method is available in the R package CWVSmix.

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.

Gene-gene interaction analysis incorporating network information via a structured Bayesian approach

Increasing evidence has shown that gene-gene interactions have important effects in biological processes of human diseases. Due to the high dimensionality of genetic measurements, interaction analysis usually suffers from a lack of sufficient information and has unsatisfactory results. Biological network information has been massively accumulated, allowing researchers to identify biomarkers while taking a system perspective, conducting network selection (of functionally related biomarkers), and accommodating network structures. In main-effect-only analysis, network information has been incorporated. However, effort has been limited in interaction analysis. Recently, link networks that describe the relationships between genetic interactions have been demonstrated as effective for revealing multiscale hierarchical organizations in networks and providing interesting findings beyond node networks. In this study, we develop a novel structured Bayesian interaction analysis approach to effectively incorporate network information. This study is among the first to identify gene-gene interactions with the assistance of network selection, while simultaneously accommodating the underlying network structures of both main effects and interactions. It innovatively respects multiple hierarchies among main effects, interactions, and networks. The Bayesian technique is adopted, which may be more informative for estimation and prediction over some other techniques. An efficient variational Bayesian expectation-maximization algorithm is developed to explore the posterior distribution. Extensive simulation studies demonstrate the practical superiority of the proposed approach. The analysis of TCGA data on melanoma and lung cancer leads to biologically sensible findings with satisfactory prediction accuracy and selection stability.

Generalized infinite factorization models

Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to infer the relative impact of the different components as well as the number of components. A popular idea is to include infinitely many components having impact decreasing with the component index. This article is motivated by two limitations of existing methods: (i) the lack of careful consideration of the within component sparsity structure; and (ii) no accommodation for grouped variables and other non-exchangeable structures. We propose a general class of infinite factorization models that address these limitations. Theoretical support is provided, practical gains are shown in simulation studies, and an ecology application focusing on modelling bird species occurrence is discussed.

Non-linear and non-additive associations between the pregnancy metabolome and birthweight

BACKGROUND

Birthweight is an indicator of fetal growth and environmental-related alterations of birthweight have been linked with multiple disorders and conditions progressing into adulthood. Although a few studies have assessed the association between birthweight and the totality of exogenous exposures and their downstream molecular responses in maternal urine and cord blood; no prior research has considered a) the maternal serum prenatal metabolome, which is enriched for hormones, and b) non-linear and synergistic associations among exposures.

METHODS

We measured the maternal serum metabolome during pregnancy using an untargeted metabolomics approach and birthweight for gestational age (BWGA) z-score in 410 mother-child dyads enrolled in the PRogramming of Intergenerational Stress Mechanisms (PRISM) cohort. We leveraged a Bayesian factor analysis for interaction to select the most important metabolites associated with BWGA z-score and to evaluate their linear, non-linear and non-additive associations. We also assessed the primary biological functions of the identified proteins using the MetaboAnalyst, a centralized repository of curated functional information. We compared our findings with those of a traditional metabolite-wide association study (MWAS) in which metabolites are individually associated with BWGA z-score.

RESULTS

Among 1110 metabolites, 46 showed evidence of U-shape associations with BWGA z-score. Most of the identified metabolites (85%) were lipids primarily enriched for pathways central to energy production, immune function, and androgen and estrogen metabolism, which are essential for pregnancy and parturition processes. Metabolites within the same class, i.e. steroids and phospholipids, showed synergistic relationships with each other.

CONCLUSIONS

Our results support that the aspects of the maternal metabolome during pregnancy contribute linearly, non-linearly and synergistically to variation in newborn birthweight.

IDENTIFYING MAIN EFFECTS AND INTERACTIONS AMONG EXPOSURES USING GAUSSIAN PROCESSES

This article is motivated by the problem of studying the joint effect of different chemical exposures on human health outcomes. This is essentially a nonparametric regression problem, with interest being focused not on a black box for prediction but instead on selection of main effects and interactions. For interpretability we decompose the expected health outcome into a linear main effect, pairwise interactions and a nonlinear deviation. Our interest is in model selection for these different components, accounting for uncertainty and addressing nonidentifiability between the linear and nonparametric components of the semiparametric model. We propose a Bayesian approach to inference, placing variable selection priors on the different components, and developing a Markov chain Monte Carlo (MCMC) algorithm. A key component of our approach is the incorporation of a heredity constraint to only include interactions in the presence of main effects, effectively reducing dimensionality of the model search. We adapt a projection approach developed in the spatial statistics literature to enforce identifiability in modeling the nonparametric component using a Gaussian process. We also employ a dimension reduction strategy to sample the nonlinear random effects that aids the mixing of the MCMC algorithm. The proposed MixSelect framework is evaluated using a simulation study, and is illustrated using data from the National Health and Nutrition Examination Survey (NHANES). Code is available on GitHub.

Moving beyond Ordinary Factor Analysis in Studies of Personality and Personality Disorder: A Computational Modeling Perspective

Almost all forms of psychopathology, including personality disorders, are arrived at through complex interactions among neurobiological vulnerabilities and environmental risk factors across development. Yet despite increasing recognition of etiological complexity, psychopathology research is still dominated by searches for large main effects causes. This derives in part from reliance on traditional inferential methods, including ordinary factor analysis, regression, ANCOVA, and other techniques that use statistical partialing to isolate unique effects. In principle, some of these methods can accommodate etiological complexity, yet as typically applied they are insensitive to interactive functional dependencies (modulating effects) among etiological influences. Here, we use our developmental model of antisocial and borderline traits to illustrate challenges faced when modeling complex etiological mechanisms of psychopathology. We then consider how computational models, which are rarely used in the personality disorders literature, remedy some of these challenges when combined with hierarchical Bayesian analysis.