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This article introduces BART with Targeted Smoothing, or tsBART, a newBayesian tree-based model for nonparametric regression. The goal of tsBART isto introduce smoothness over a single target covariate t, while not necessarilyrequiring smoothness over other covariates x. TsBART is based on the BayesianAdditive Regression Trees (BART) model, an ensemble of regression trees. TsBARTextends BART by parameterizing each tree's terminal nodes with smooth functionsof t, rather than independent scalars. Like BART, tsBART captures complexnonlinear relationships and interactions among the predictors. But unlike BART,tsBART guarantees that the response surface will be smooth in the targetcovariate. This improves interpretability and helps regularize the estimate.  After introducing and benchmarking the tsBART model, we apply it to ourmotivating example: pregnancy outcomes data from the National Center for HealthStatistics. Our aim is to provide patient-specific estimates of stillbirth riskacross gestational age (t), based on maternal and fetal risk factors (x).Obstetricians expect stillbirth risk to vary smoothly over gestational age, butnot necessarily over other covariates, and tsBART has been designed preciselyto reflect this structural knowledge. The results of our analysis show theclear superiority of the tsBART model for quantifying stillbirth risk, therebyproviding patients and doctors with better information for managing the risk ofperinatal mortality. All methods described here are implemented in the Rpackage tsbart.

BART with Targeted Smoothing: An analysis of patient-specific stillbirth risk