Nonparametric Failure Time: Time-to-event Machine Learning with Heteroskedastic Bayesian Additive Regression Trees and Low Information Omnibus Dirichlet Process Mixtures

The Spring 2022 SDS Seminar Series begins on Friday, April 22 from 2:00 p.m. to 3:00 p.m. with Dr. Robert McCulloch (Professor of Statistics at Arizona State University). This event is in-person, but a virtual option will be available as well. 

Title: Nonparametric Failure Time: Time-to-event Machine Learning with Heteroskedastic Bayesian Additive Regression Trees and Low Information Omnibus Dirichlet Process Mixtures (with R.A. Sparapani, B.R. Logan, P.W. Laud)

Abstract: Many popular survival models rely on restrictive parametric or semiparametric assumptions that may lead to incorrect inference or survival predictions when the effects of covariates are complex. Modern advances in computational hardware has led to increasing interest in flexible Bayesian nonparametric methods for time-to-event data such as that provided by Bayesian additive regression trees (BART). We propose a novel approach, called nonparametric failure time (NFT) BART, that incorporates flexibility in Accelerated Failure Time (AFT) models in three ways: 1) a BART component for the mean function of the natural logarithm with time’s distribution; 2) a heteroskedastic BART component to handle a covariate dependent variance function; and 3) a flexible nonparametric error distribution using Dirichlet Process Mixtures (DPM). Our proposed approach can be scaled up to large sample sizes, and can be seamlessly employed for variable selection. We provide convenient, user-friendly, computer software that is freely available as a reference implementation. Simulations demonstrate that NFT BART maintains excellent performance even when AFT assumptions are violated. We illustrate the proposed model on a real data example of hematopoietic stem cell transplantation as a treatment for blood-borne cancers.