In studies of maternal exposure to air pollution a children's health outcome is regressed on exposures observed during pregnancy. The distributed lag nonlinear model (DLNM) is a statistical method commonly implemented to estimate an exposure-time-response function when it is postulated the exposure effect is nonlinear. Previous implementations of the DLNM estimate an exposure-time-response surface parameterized with a bivariate basis expansion. However, basis functions such as splines assume smoothness across the entire exposure-time-response surface, which may be unrealistic in settings where the exposure is associated with the outcome only in a specific time window. We propose a framework for estimating the DLNM based on Bayesian additive regression trees. Our method operates using a set of regression trees that each assume piecewise constant relationships across the exposure-time space. In a simulation, we show that our model outperforms spline-based models when the exposure-time surface is not smooth, while both methods perform similarly in settings where the true surface is smooth. Importantly, the proposed approach is lower variance and more precisely identifies critical windows during which exposure is associated with a future health outcome. We apply our method to estimate the association between maternal exposure to PM$_{2.5}$ and birth weight in a Colorado USA birth cohort.
Distributed lag non-linear models with Laplacian-P-splines for analysis of spatially structured time series
Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute (DSI), Hasselt University, Hasselt, Belgium（哈瑟尔特大学）；Department of Mathematics and Statistics, College of Science and Mathematics, Mindanao State University - Iligan Institute of Technology, Iligan City, Philippines（棉兰老州立大学-伊洛伊洛理工学院）；L-BioStat, Department of Public Health and Primary Care, KU Leuven, Leuven, Belgium（荷语鲁汶大学）；Centre for Health Economic Research and Modelling Infectious Diseases (CHERMID), Vaccine & Infectious Disease Institute, Antwerp University, Antwerp, Belgium（安特卫普大学）
Spatially varying distributed lag non-linear models using Laplacian P-splines
Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute (DSI), Hasselt University, Hasselt, Belgium（哈瑟尔特大学）；L-BioStat, Department of Public Health and Primary Care, KU Leuven, Leuven, Belgium（荷语鲁汶大学）；Environment & Health Modelling (EHM) Lab, Department of Public Health Environments and Society, London School of Hygiene & Tropical Medicine, London, United Kingdom（伦敦卫生与热带医学院）
