Lagged kernel machine regression for identifying time windows of susceptibility to exposures of complex mixtures

Abstract

The impact of neurotoxic chemical mixtures on children's health is a critical public health concern. It is well known that during early life, toxic exposures may impact cognitive function during critical time intervals of increased vulnerability, known as windows of susceptibility. Knowledge on time windows of susceptibility can help inform treatment and prevention strategies, as chemical mixtures may affect a developmental process that is operating at a specific life phase. There are several statistical challenges in estimating the health effects of time-varying exposures to multi-pollutant mixtures, such as: multi-collinearity among the exposures both within time points and across time points, and complex exposure-response relationships. To address these concerns, we develop a flexible statistical method, called lagged kernel machine regression (LKMR). LKMR identifies critical exposure windows of chemical mixtures, and accounts for complex non-linear and non-additive effects of the mixture at any given exposure window. Specifically, LKMR estimates how the effects of a mixture of exposures change with the exposure time window using a Bayesian formulation of a grouped, fused lasso penalty within a kernel machine regression (KMR) framework. A simulation study demonstrates the performance of LKMR under realistic exposure-response scenarios, and demonstrates large gains over approaches that consider each time window separately, particularly when serial correlation among the time-varying exposures is high. Furthermore, LKMR demonstrates gains over another approach that inputs all time-specific chemical concentrations together into a single KMR. We apply LKMR to estimate associations between neurodevelopment and metal mixtures in Early Life Exposures in Mexico and Neurotoxicology, a prospective cohort study of child health in Mexico City.

Modeling the health effects of time‐varying complex environmental mixtures: Mean field variational Bayes for lagged kernel machine regression

“…In the recent years, there has been growing interest in the concept of the exposome, that is, the totality of human exposures over a lifetime (Buck Louis, Smarr, & Patel, ; Stigone et al, ). This interest, in turn, led to the rapid growth of research into statistical methods to address complex mixtures (Bobb et al, ; Braun, Gennings, Hauser, & Webster, ; Gennings et al, ; Herring, ; Liu, ; Liu et al, ; Park, Tao, Meeker, Harlow, & Mukherjee, ). In parallel, the growing recognition of the role of critical windows in toxicology has led to new methods to address finding critical windows (Wright, ).…”

“…Liu () and Liu et al () detailed the LKMR model, which can be represented as a hierarchical model. For brevity, we present a brief description of the hierarchical model here, with a primary focus on the MFVB approximation.…”

“…The form for modeling the interactions is specified via the kernel function. A common choice for the kernel function is the quadratic kernel used by Liu et al (), which is defined as . The quadratic kernel allows for both linear and nonlinear interactions among mixture components at every time window.…”

“…An important aim of environmental health studies is the characterization of the exposure–response surface, particularly for the prediction of health effects for unobserved exposure profiles at a given time point. Liu et al () provided details of this prediction approach; here, we summarize the approach and its adaptation to the variational Bayes context. In order to predict the exposure–response relationship for P new unobserved profiles of metal mixture exposures at time t , denoted by , where each for t =1,…, T and p =1,.., P , we first model the observed exposure data from n subjects measured at T time points.…”

“…Liu et al () showed that we can define as a reordered h vector with time t , the time point of interest, at the end of the vector such that , so that the covariance matrix of h can be easily defined. denotes the corresponding reordered covariance matrix.…”