Summary 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 exposures to PM$_{2.5}$ and birth weight in a Colorado, USA birth cohort.

Maternal exposure to environmental chemicals during pregnancy can alter birth and children's health outcomes. Research seeks to identify critical windows, time periods when exposures can change future health outcomes, and estimate the exposure-response relationship. Existing statistical approaches focus on estimation of the association between maternal exposure to a single environmental chemical observed at high temporal resolution (e.g., weekly throughout pregnancy) and children's health outcomes. Extending to multiple chemicals observed at high temporal resolution poses a dimensionality problem and statistical methods are lacking. We propose a regression tree-based model for mixtures of exposures observed at high temporal resolution. The proposed approach uses an additive ensemble of tree pairs that defines structured main effects and interactions between time-resolved predictors and performs variable selection to select out of the model predictors not correlated with the outcome. In simulation, we show that the tree-based approach performs better than existing methods for a single exposure and can accurately estimate critical windows in the exposureresponse relation for mixtures. We apply our method to estimate the relationship between five exposures measured weekly throughout pregnancy and birth weight in a Denver, Colorado, birth cohort. We identified critical windows during which fine particulate matter, sulfur dioxide, and temperature are negatively associated with birth weight and an interaction between fine particulate matter and temperature. Software is made available in the R package dlmtree.

BackgroundSubchondral lucencies (SCLs) in the distal aspect of the medial femoral condyle (MFC) of young Thoroughbred horses are a source of controversy on presale radiographs. There is limited scientific evidence regarding the risk of progression and impact on future racing performance.ObjectivesTo (1) identify the prevalence of MFC SCLs on sales repository radiographs in yearling and 2‐year‐old Thoroughbreds; (2) identify any association between grade of MFC SCL and future racing performance and (3) monitor changes in MFC SCL grades between yearling and 2‐year‐old sales.Study designProspective cohort study.MethodsRadiographs were obtained with consignor permission from a 2016 yearling sale and five 2017 2‐year‐old sales. Stifle radiographs were evaluated and MFC SCLs graded on a scale of 0–3. Axial MFC lucencies were recorded separately. Maximum MFC grades per horse were analysed for associations with racing performance outcomes, adjusted for sex, to the end of the horses' 4‐year‐old racing year. Analysis was via logistic, negative binomial or linear regression as appropriate, with the threshold for significance set at α = 0.05.ResultsRadiographs from 2508 yearlings (5016 stifles) and 436 2‐year‐olds (872 stifles) were included in the study. MFC SCLs of grades 1–3 were observed in 242 (9.65%) yearlings and 49 (11.2%) 2‐year‐olds. Bilateral MFC SCLs of grades 1–3 were observed in 54 (2.2%) yearlings and 12 (2.8%) 2‐year‐olds. Grade 1 MFC SCLs in yearlings either remained unchanged (14/31), progressed to a grade 2 (6/31) or resolved (11/31) by the 2‐year‐old sale. Grade 2 MFC SCLs in yearlings remained unchanged (6/10), progressed to a grade 3 (2/10) or improved to a grade 1 (2/10). Yearlings with a grade 3 MFC SCL had a 78% probability of starting a race (95% confidence interval [CI] 58.2–89.6%), compared with an 84% probability of racing for grade 0 yearlings (95% CI 82.7–85.8%). Six of the seven yearlings with axial MFC lucencies raced.Main limitationsThis study may underestimate the prevalence of severe lesions in the general yearling population of U.S. Thoroughbreds. However, the convenience sample used is representative of the population of interest at sales. The study design could not address exclusions prior to sale.ConclusionsGrade 1 MFC SCLs are the most common type seen in yearling and 2‐year‐old sales horses. The majority of yearling grade 1 MFC SCLs resolved or remained static by 2‐year‐old sales. It was also possible for grade 2 and 3 MFC SCLs to improve one grade between sales. Fewer sales yearlings with a grade 3 MFC SCL raced, but in those that did race there was no evidence of worse performance compared to unaffected peers. Axial MFC lucencies did not affect racing performance.

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