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March 2020 BART with targeted smoothing: An analysis of patient-specific stillbirth risk
Jennifer E. Starling, Jared S. Murray, Carlos M. Carvalho, Radek K. Bukowski, James G. Scott
Ann. Appl. Stat. 14(1): 28-50 (March 2020). DOI: 10.1214/19-AOAS1268

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 to 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 $(t)$ and 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 fetal mortality. All methods described here are implemented in the R package tsbart.

Citation

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Jennifer E. Starling. Jared S. Murray. Carlos M. Carvalho. Radek K. Bukowski. James G. Scott. "BART with targeted smoothing: An analysis of patient-specific stillbirth risk." Ann. Appl. Stat. 14 (1) 28 - 50, March 2020. https://doi.org/10.1214/19-AOAS1268

Information

Received: 1 January 2019; Revised: 1 May 2019; Published: March 2020
First available in Project Euclid: 16 April 2020

zbMATH: 07200160
MathSciNet: MR4085082
Digital Object Identifier: 10.1214/19-AOAS1268

Keywords: Bayesian additive regression tree , ensemble method , Gaussian process , regression tree , regularization

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.14 • No. 1 • March 2020
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