Type I Tobit Bayesian Additive Regression Trees for Censored Outcome Regression

TL;DR

This paper introduces TOBART-1, a Bayesian regression tree model designed for censored outcomes, providing accurate predictions and flexible error modeling, addressing biases from traditional methods that ignore censoring.

Contribution

The paper presents a novel Bayesian additive regression tree model specifically for censored data, incorporating flexible error distribution modeling with Dirichlet process mixtures.

Findings

TOBART-1 yields accurate censored outcome predictions.

The model provides reliable posterior intervals.

Flexible error modeling improves expectation estimates.

Abstract

Censoring occurs when an outcome is unobserved beyond some threshold value. Methods that do not account for censoring produce biased predictions of the unobserved outcome. This paper introduces Type I Tobit Bayesian Additive Regression Tree (TOBART-1) models for censored outcomes. Simulation results and real data applications demonstrate that TOBART-1 produces accurate predictions of censored outcomes. TOBART-1 provides posterior intervals for the conditional expectation and other quantities of interest. The error term distribution can have a large impact on the expectation of the censored outcome. Therefore the error is flexibly modeled as a Dirichlet process mixture of normal distributions.