Selection of nonlinear interactions by a forward stepwise algorithm: Application to identifying environmental chemical mixtures affecting health outcomes

Abstract

In this paper, we propose a stepwise forward selection algorithm for detecting the effects of a set of correlated exposures and their interactions on a health outcome of interest when the underlying relationship could potentially be nonlinear. Though the proposed method is very general, our application in this paper remains to be on analysis of multiple pollutants and their interactions. Simultaneous exposure to multiple environmental pollutants could affect human health in a multitude of complex ways. For understanding the health effects of multiple environmental exposures, it is often important to identify and estimate complex interactions among exposures. However, this issue becomes analytically challenging in the presence of potential nonlinearity in the outcome‐exposure response surface and a set of correlated exposures. Through simulation studies and analyses of test datasets that were simulated as a part of a data challenge in multipollutant modeling organized by the National Institute of Environmental Health Sciences (http://www.niehs.nih.gov/about/events/pastmtg/2015/statistical/), we illustrate the advantages of our proposed method in comparison with existing alternative approaches. A particular strength of our method is that it demonstrates very low false positives across empirical studies. Our method is also used to analyze a dataset that was released from the Health Outcomes and Measurement of the Environment Study as a benchmark beta‐tester dataset as a part of the same workshop.

A hierarchical integrative group least absolute shrinkage and selection operator for analyzing environmental mixtures

“…In addition to penalization-based methods, forward selection methods (Boos et al, 2009;Luo & Ghosal, 2015;Wasserman & Roeder, 2009) are also commonly used for variable selection in practice. Several forward selection methods which incorporate heredity constraints with linear and nonlinear interactions have been proposed (Crews et al, 2011;Hao & Zhang, 2014;Narisetty et al, 2018;Wu et al, 2010).…”

A latent functional approach for modeling the effects of multidimensional exposures on disease risk

“…where D * = (y, Z, U, g, 𝝃, 𝝀) is the complete data. Using the complete data likelihood in (7), an efficient MCMC algorithm can be developed. We will explain the efficient Gibbs sampling algorithm in Section A.…”

“…where L(𝜷 * , 𝜶 * , 𝜽|D * ) is defined in (7). Employing the MCMC techniques, we can generate a sample from the joint posterior distribution in ( 9) and make appropriate inference of the various model parameters using this sample.…”

“…Herring 6 proposed nonparametric Bayes shrinkage priors for model selection to investigations of complex mixtures by developing a formal hierarchical modeling framework to allow different degrees of shrinkage for main effects and interactions and to handle censoring of exposures at a limit of detection. More recently, Narisetty et al 7 proposed a penalized likelihood approach for model selection for chemical mixtures and their interactions. Luo et al 8 proposed a two‐step approach that uses random forests regression followed by adaptive LASSO.…”

Estimation and false discovery control for the analysis of environmental mixtures

“…Most of these approaches are fully Bayesian, but recent proposals have used penalized likelihood estimators to identify interactions. A forward stepwise algorithm is developed in Narisetty et al (2019) that identifies important main effects and interactions as well as whether linear or nonlinear terms are required to model these effects. Group lasso was adapted for environmental mixtures in a way that enforces strong heredity of interactions and allows for nonlinear relationships in Boss et al (2020).…”