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

TL;DR

This paper introduces tsBART, a Bayesian tree-based model that enforces smoothness over a specific covariate, improving interpretability and accuracy in patient-specific risk estimation, demonstrated through stillbirth risk analysis.

Contribution

The paper develops tsBART, extending BART with smooth functions over a target covariate, tailored for applications like gestational age risk modeling.

Findings

tsBART outperforms existing models in risk quantification.

The model provides smooth, interpretable estimates over gestational age.

Application to pregnancy data improves risk assessment accuracy.

Abstract

This article introduces BART with Targeted Smoothing, or tsBART, a new Bayesian tree-based model for nonparametric regression. The goal of tsBART is to introduce smoothness over a single target covariate t, while not necessarily requiring smoothness over other covariates x. TsBART is based on the Bayesian Additive Regression Trees (BART) model, an ensemble of regression trees. TsBART extends BART by parameterizing each tree's terminal nodes with smooth functions of t, rather than independent scalars. Like BART, tsBART captures complex nonlinear relationships and interactions among the predictors. But unlike BART, tsBART guarantees that the response surface will be smooth in the target covariate. This improves interpretability and helps regularize the estimate. After introducing and benchmarking the tsBART model, we apply it to our motivating example: pregnancy outcomes data from the National Center for Health Statistics. Our aim is to provide patient-specific estimates of stillbirth risk across gestational age (t), based on maternal and fetal risk factors (x). Obstetricians expect stillbirth risk to vary smoothly over gestational age, but not necessarily over other covariates, and tsBART has been designed precisely to reflect this structural knowledge. The results of our analysis show the clear superiority of the tsBART model for quantifying stillbirth risk, thereby providing patients and doctors with better information for managing the risk of perinatal mortality. All methods described here are implemented in the R package tsbart.