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Maternal exposure to air pollution during pregnancy has a substantial publichealth impact. Epidemiological evidence supports an association betweenmaternal exposure to air pollution and low birth weight. A popular method toestimate this association while identifying windows of susceptibility is adistributed lag model (DLM), which regresses an outcome onto exposure historyobserved at multiple time points. However, the standard DLM framework does notallow for modification of the association between repeated measures of exposureand the outcome. We propose a distributed lag interaction model that allowsmodification of the exposure-time-response associations across individuals byincluding an interaction between a continuous modifying variable and theexposure history. Our model framework is an extension of a standard DLM thatuses a cross-basis, or bi-dimensional function space, to simultaneouslydescribe both the modification of the exposure-response relationship and thetemporal structure of the exposure data. Through simulations, we showed thatour model with penalization out-performs a standard DLM when the trueexposure-time-response associations vary by a continuous variable. Using aColorado, USA birth cohort, we estimated the association between birth weightand ambient fine particulate matter air pollution modified by an area-levelmetric of health and social adversities from Colorado EnviroScreen.

Penalized Distributed Lag Interaction Model: Air Pollution, Birth Weight and Neighborhood Vulnerability