IDENTIFYING MAIN EFFECTS AND INTERACTIONS AMONG EXPOSURES USING GAUSSIAN PROCESSES

Power Analysis of Exposure Mixture Studies via Monte Carlo Simulations

Estimating sample size and statistical power is an essential part of a good epidemiological study design. Closed-form formulas exist for simple hypothesis tests but not for advanced statistical methods designed for exposure mixture studies. Estimating power with Monte Carlo simulations is flexible and applicable to these methods. However, it is not straightforward to code a simulation for non-experienced programmers and is often hard for a researcher to manually specify multivariate associations among exposure mixtures to set up a simulation. To simplify this process, we present the R package mpower for power analysis of observational studies of environmental exposure mixtures involving recently-developed mixtures analysis methods. The components within mpower are also versatile enough to accommodate any mixtures methods that will developed in the future. The package allows users to simulate realistic exposure data and mixed-typed covariates based on public data set such as the National Health and Nutrition Examination Survey or other existing data set from prior studies. Users can generate power curves to assess the trade-offs between sample size, effect size, and power of a design. This paper presents tutorials and examples of power analysis using mpower.

The single and mixed impacts of cadmium, cobalt, lead, and PAHs on systemic immunity inflammation index in male and female

Background

Studies on the association between mixed exposure to common pollutants such as cadmium (Cd), cobalt (Co), lead (Pb), and polycyclic aromatic hydrocarbons (PAHs) with Systemic Immune Inflammatory Index (SII), a novel hemocyte-based inflammatory marker, have not been reported. This study explored the relationship between co-exposure to Cd, Co, Pb, PAHs, and SII.

Methods

In this study, we used data from the National Health and Nutrition Examination Survey and enrolled adults with complete information on Cd, Co, Pb, PAHs, and SII. The linear regression was used to analyze the association of single pollutants with SII. Furthermore, a Bayesian Kernel Machine Regression analysis and a generalized weighted quantile sum regression analysis were used to analyze the association between mixed exposure to Cd, Co, Pb, and six PAHs and SII. We also separated males and females and analyzed the different effects of pollutants on SII, respectively.

Results

5,176 participants were included in the study. After adjusting for age, gender, race, education, smoking, drinking, physical activity, and sedentary, Cd, Co, 1-OHN, 2-OHN and 2-OHF were positive with SII in the total population. Compared with the 50th percentile, the joint effect of pollutants on SII was positive. In the total population, males, and females, the top contaminant with the highest effect weights on SII were Co, Cd, and 1-OHN, respectively. The result of interaction analysis showed that the low concentrations of Cd had an elevation effect on SII in males.

Conclusion

This study found a positive association of mixed exposure to Cd, Co, Pb, and six PAHs with SII, which occurred mainly in females.

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 analysing 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.

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.

Spike-and-slab least absolute shrinkage and selection operator generalized additive models and scalable algorithms for high-dimensional data analysis

There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ( p ≫ n $$ p\gg n $$ ) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating smooth functions, damaging predictive performance. Moreover, most of these GAMs consider an "all-in-all-out" approach for functional selection, rendering them difficult to answer if nonlinear effects are necessary. While some Bayesian models can address these shortcomings, using Markov chain Monte Carlo algorithms for model fitting creates a new challenge, scalability. Hence, we propose Bayesian hierarchical generalized additive models as a solution: we consider the smoothing penalty for proper shrinkage of curve interpolation via reparameterization. A novel two-part spike-and-slab LASSO prior for smooth functions is developed to address the sparsity of signals while providing extra flexibility to select the linear or nonlinear components of smooth functions. A scalable and deterministic algorithm, EM-Coordinate Descent, is implemented in an open-source R package BHAM. Simulation studies and metabolomics data analyses demonstrate improved predictive and computational performance against state-of-the-art models. Functional selection performance suggests trade-offs exist regarding the effect hierarchy assumption.

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.