According to NIEHS, “It is imperative to develop methods to assess the health effects associated with complex exposures in order to minimize their impact on the development of disease.” NIEHS has held several meetings on mixtures, including the 2015 workshop on Statistical Approaches for Assessing Health Effects of Environmental Chemical Mixtures in Epidemiology Studies. Conclusions include the following. 1) An interdisciplinary perspective is needed, including insights from environmental epidemiology, statistics/mathematics, toxicology and exposure science. 2) Mixtures epidemiology has three key goals: a) identify components of a mixture contributing to the outcome; b) examine interactions between the components; c) construct summary measures of exposure where possible. 3) Different methods have different strengths and weaknesses that may be complementary. We propose to build upon three methods that performed well at the 2015 workshop: Bayesian kernel machine regression (BKMR), exposure space smoothing (ESS) and weighted quantile sum regression (WQS). We will develop two complementary methods: 1) BKMR/ESS. We will expand and combine aspects of BKMR and ESS into one method that primarily addresses the first two goals: variable selection and interactions. Crucial aspects of our proposal are i) extension to binary health outcomes, the most common type of outcome data in epidemiology (the 2015 NIEHS workshop examined continuous outcomes); ii) variable selection using the hierarchical structures observed for correlations between exposures; iii) incorporation of toxicological information. 2) Single index model: We will evaluate a generalization of WQS, the single index model (SIM). SIM non-parametrically estimates a one-dimensional smooth function of a weighted sum of exposures. The weighted sum represents a summary measure of exposure (one based on toxicological principles), a third goal of mixtures epidemiology. Following method development, we will test the methods using both synthetic and real world data sets, including the Environment And Reproductive Health (EARTH) cohort study. We will incorporate causal inference tools such as directed acyclic graphs (DAGs). For example, correlated exposures (co-exposures) are confounders under some DAGs and colliders or intermediate variables under others. This must be taken into account in both generation of synthetic data and proper interpretation of results. The specific aims of this project are as follows: Specific Aim 1: Combine features of BKMR and ESS to produce a method for analyzing epidemiologic data that incorporates toxicological information; can handle continuous, binary and repeated measures outcome data; select important exposure variables; flexibly model and examine interactions; adjust for confounders; is robust to influential points; Specific Aim 2: Evaluate the single index model (SIM) as a method for analyzing epidemiologic mixtures data and generating exposure summary measures; Specific Aim 3: Make benchmark synthetic data and method computer code publicly available. ! 1!

NARRATIVE Epidemiologists typically study links between human health and chemical exposure one chemical at a time, but people are exposed to mixtures. Examining the human health effects of chemical mixtures is a crucial and difficult challenge. This project will develop, test and apply advanced methods for this task. !