Function-on-function regression for the identification of epigenetic regions exhibiting windows of susceptibility to environmental exposures

The ability to identify time periods when individuals are most suscepti-ble to exposures as well as the biological mechanisms through which these exposures act is of great public health interest. Growing evidence supports an association between prenatal exposure to air pollution and epigenetic marks, such as DNA methylation, but the timing and gene-specific effects of these epigenetic changes are not well understood. Here, we present the first study that aims to identify prenatal windows of susceptibility to air pollution exposures in cord blood DNA methylation. In particular, we propose a function-on-function regression model that leverages data from nearby DNA methyla-tion probes to identify epigenetic regions that exhibit windows of susceptibility to ambient particulate matter less than 2.5 microns (PM_2.5). By incorpo-rating the covariance structure among both the multivariate DNA methylation outcome and the time-varying exposure under study, this framework yields greater power to detect windows of susceptibility and greater control of false discoveries than methods that model probes independently. We compare our method to a distributed lag model approach that models DNA methylation in a probe-by-probe manner, both in simulation and by application to motivating data from the Project Viva birth cohort. We identify a window of susceptibility to PM_2.5 exposure in the middle of the third trimester of pregnancy in an epigenetic region selected based on prior studies of air pollution effects on epigenome-wide methylation.