Lagged WQS regression for mixtures with many components

The developmental timing of exposures to toxic chemicals or combinations of chemicals may be as important as the dosage itself. This concept is called "critical windows of exposure." The time boundaries of such windows can be detected if exposure data are collected repeatedly in short time intervals. The development of tooth-matrix biomarkers which provide prenatal and postnatal exposure measures in repeated intervals can provide such data. Using teeth, we use reverse distributed lagged models (DLMs) to incorporate weekly prenatal and postnatal measures of exposures to estimate time-varying associations with developmental effects. The analysis of such data using lagged weighted quantile sum (WQS) regression as an extension to reverse DLMs for complex mixtures was first proposed by Bello et al. This prior algorithm was not operationally generalizable to large numbers of components (say, more than five or six). We propose a revised algorithm that may be useful for larger mixtures by combining time-specific WQS(t) indices in a reverse DLM. We demonstrate the new algorithm using tooth data in association with a neurodevelopmental score and in simulated data from 3 cases wherein different components of a mixture have time varying associations and in the case where none have associations. The new algorithm correctly detects the simulated associations when the number of samples within the time-specific analyses is moderate to large.