{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T02:55:06Z","timestamp":1789268106702,"version":"build-2803163510"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,2,2]],"date-time":"2021-02-02T00:00:00Z","timestamp":1612224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["ES028811"],"award-info":[{"award-number":["ES028811"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007590","name":"Colorado Department of Public Health and Environment","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007590","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ACI-1532235"],"award-info":[{"award-number":["ACI-1532235"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ACI-1532236"],"award-info":[{"award-number":["ACI-1532236"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"University of Colorado Boulder, and Colorado State University"},{"name":"University of Colorado Boulder and Colorado State University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,18]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In studies of maternal exposure to air pollution, a children\u2019s 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\u2013time\u2013response function when it is postulated the exposure effect is nonlinear. Previous implementations of the DLNM estimate an exposure\u2013time\u2013response surface parameterized with a bivariate basis expansion. However, basis functions such as splines assume smoothness across the entire exposure\u2013time\u2013response 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\u2013time space. In a simulation, we show that our model outperforms spline-based models when the exposure\u2013time 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 exposures to PM$_{2.5}$ and birth weight in a Colorado, USA birth cohort.<\/jats:p>","DOI":"10.1093\/biostatistics\/kxaa051","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T15:12:15Z","timestamp":1604329935000},"page":"754-771","source":"Crossref","is-referenced-by-count":41,"title":["Treed distributed lag nonlinear models"],"prefix":"10.1093","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7924-0706","authenticated-orcid":false,"given":"Daniel","family":"Mork","sequence":"first","affiliation":[{"name":"Statistics Department, Colorado State University , 1877 Campus Delivery, Fort Collins, CO, USA 80523"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4774-3883","authenticated-orcid":false,"given":"Ander","family":"Wilson","sequence":"additional","affiliation":[{"name":"Statistics Department, Colorado State University , 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