Type I Tobit Bayesian Additive Regression Trees for censored outcome regression

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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. An R package is available at https://github.com/EoghanONeill/TobitBART.