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The ability to identify time periods when individuals are most susceptible toexposures, as well as the biological mechanisms through which these exposuresact, is of great public health interest. Growing evidence supports anassociation between prenatal exposure to air pollution and epigenetic marks,such as DNA methylation, but the timing and gene-specific effects of theseepigenetic changes are not well understood. Here, we present the first studythat aims to identify prenatal windows of susceptibility to air pollutionexposures in cord blood DNA methylation. In particular, we propose afunction-on-function regression model that leverages data from nearby DNAmethylation probes to identify epigenetic regions that exhibit windows ofsusceptibility to ambient particulate matter less than 2.5 microns(PM$_{2.5}$). By incorporating the covariance structure among both themultivariate DNA methylation outcome and the time-varying exposure under study,this framework yields greater power to detect windows of susceptibility andgreater control of false discoveries than methods that model probesindependently. We compare our method to a distributed lag model approach thatmodels DNA methylation in a probe-by-probe manner, both in simulation and byapplication to motivating data from the Project Viva birth cohort. In twoepigenetic regions selected based on prior studies of air pollution effects onepigenome-wide methylation, we identify windows of susceptibility to PM$_{2.5}$exposure near the beginning and middle of the third trimester of pregnancy.

Function-on-Function Regression for the Identification of Epigenetic Regions Exhibiting Windows of Susceptibility to Environmental Exposures