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.

Allostatic load is commonly operationalized using a sum-score of high-risk biomarkers. However, this method implies that biomarkers contribute equally to allostatic load, as each is given equal weight. Our goal in this methodological paper is to evaluate this, and complementarily, to identify biomarkers that are most informative and least informative for developing an allostatic load index. Item response theory models provide an alternate approach to calculating the allostatic load score, by treating individual biomarkers (e.g. “items”) as indicators of a latent allostatic load construct. Item response theory scores account for the data-driven discriminating power of each biomarker, and an individual’s pattern of biomarker responses. To demonstrate feasibility of this approach, we used data from the 2015–2016 National Health Examination and Nutrition Survey (NHANES; N ​= ​3751), with twelve allostatic load biomarkers representing immune response, metabolic function and cardiovascular health. Item response theory models revealed that body-mass-index and C-reactive protein were the most informative biomarkers for allostatic load. Both higher allostatic load sum-score and allostatic load item response theory score were associated with lower socio-economic status (p ​= ​0.008; p<0.001, respectively). Further, both formulations of allostatic load were positively associated with a nine-item depression screener (p<0.001 for both), but only the item response theory score was also positively associated with the impact of depressive symptoms on daily life (p ​= ​0.045). Item response theory scores may be more finely tuned to tease out effects, compared to sum-scores, and also provide more flexibility when there are missing biomarker measurements. Supplemental R code for our approach are included.