Nonparametric failure time: Time-to-event machine learning with heteroskedastic Bayesian additive regression trees and low information omnibus Dirichlet process mixtures.

Many popular survival models rely on restrictive parametric, or semiparametric, assumptions that could provide erroneous predictions when the effects of covariates are complex. Modern advances in computational hardware have led to an increasing interest in flexible Bayesian nonparametric methods for time-to-event data such as Bayesian additive regression trees (BART). We propose a novel approach that we call nonparametric failure time (NFT) BART in order to increase the flexibility beyond accelerated failure time (AFT) and proportional hazard models. NFT BART has three key features: (1) a BART prior for the mean function of the event time logarithm; (2) a heteroskedastic BART prior to deduce a covariate-dependent variance function; and (3) a flexible nonparametric error distribution using Dirichlet process mixtures (DPM). Our proposed approach widens the scope of hazard shapes including nonproportional hazards, can be scaled up to large sample sizes, naturally provides estimates of uncertainty via the posterior 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 for survival prediction especially when AFT assumptions are violated by heteroskedasticity. We illustrate the proposed approach on a study examining predictors for mortality risk in patients undergoing hematopoietic stem cell transplant (HSCT) for blood-borne cancer, where heteroskedasticity and nonproportional hazards are likely present.

Optimal Donor Selection for Hematopoietic Cell Transplantation Using Bayesian Machine Learning.

PURPOSE: Donor selection practices for matched unrelated donor (MUD) hematopoietic cell transplantation (HCT) vary, and the impact of optimizing donor selection in a patient-specific way using modern machine learning (ML) models has not been studied. METHODS: We trained a Bayesian ML model in 10,318 patients who underwent MUD HCT from 1999 to 2014 to provide patient- and donor-specific predictions of clinically severe (grade 3 or 4) acute graft-versus-host disease or death by day 180. The model was validated in 3,501 patients from 2015 to 2016 with archived records of potential donors at search. Donor selection optimizing predicted outcomes was implemented over either an unlimited donor pool or the donors in the search archives. Posterior mean differences in outcomes from optimal donor selection versus actual practice were summarized per patient and across the population with 95% intervals. RESULTS: Event rates were 33% (training) and 37% (validation). Among donor features, only age affected outcomes, with the effect consistent regardless of patient features. The median (interquartile range) difference in age between the youngest donor at search and the selected donor was 6 (1-10) years, whereas the number of donors per patient younger than the selected donor was 6 (1-36). Fourteen percent of the validation data set had an approximate 5% absolute reduction in event rates from selecting the youngest donor at search versus the actual donor used, leading to an absolute population reduction of 1% (95% interval, 0 to 3). CONCLUSION: We confirmed the singular importance of selecting the youngest available MUD, irrespective of patient features, identified potential for improved HCT outcomes by selecting a younger MUD, and demonstrated use of novel ML models transferable to optimize other complex treatment decisions in a patient-specific way.

Nonparametric competing risks analysis using Bayesian Additive Regression Trees.

Many time-to-event studies are complicated by the presence of competing risks. Such data are often analyzed using Cox models for the cause-specific hazard function or Fine and Gray models for the subdistribution hazard. In practice, regression relationships in competing risks data are often complex and may include nonlinear functions of covariates, interactions, high-dimensional parameter spaces and nonproportional cause-specific, or subdistribution, hazards. Model misspecification can lead to poor predictive performance. To address these issues, we propose a novel approach: flexible prediction modeling of competing risks data using Bayesian Additive Regression Trees (BART). We study the simulation performance in two-sample scenarios as well as a complex regression setting, and benchmark its performance against standard regression techniques as well as random survival forests. We illustrate the use of the proposed method on a recently published study of patients undergoing hematopoietic stem cell transplantation.

Decision making and uncertainty quantification for individualized treatments using Bayesian Additive Regression Trees.

Individualized treatment rules can improve health outcomes by recognizing that patients may respond differently to treatment and assigning therapy with the most desirable predicted outcome for each individual. Flexible and efficient prediction models are desired as a basis for such individualized treatment rules to handle potentially complex interactions between patient factors and treatment. Modern Bayesian semiparametric and nonparametric regression models provide an attractive avenue in this regard as these allow natural posterior uncertainty quantification of patient specific treatment decisions as well as the population wide value of the prediction-based individualized treatment rule. In addition, via the use of such models, inference is also available for the value of the optimal individualized treatment rules. We propose such an approach and implement it using Bayesian Additive Regression Trees as this model has been shown to perform well in fitting nonparametric regression functions to continuous and binary responses, even with many covariates. It is also computationally efficient for use in practice. With Bayesian Additive Regression Trees, we investigate a treatment strategy which utilizes individualized predictions of patient outcomes from Bayesian Additive Regression Trees models. Posterior distributions of patient outcomes under each treatment are used to assign the treatment that maximizes the expected posterior utility. We also describe how to approximate such a treatment policy with a clinically interpretable individualized treatment rule, and quantify its expected outcome. The proposed method performs very well in extensive simulation studies in comparison with several existing methods. We illustrate the usage of the proposed method to identify an individualized choice of conditioning regimen for patients undergoing hematopoietic cell transplantation and quantify the value of this method of choice in relation to the optimal individualized treatment rule as well as non-individualized treatment strategies.

Nonparametric survival analysis using Bayesian Additive Regression Trees (BART).

Bayesian additive regression trees (BART) provide a framework for flexible nonparametric modeling of relationships of covariates to outcomes. Recently, BART models have been shown to provide excellent predictive performance, for both continuous and binary outcomes, and exceeding that of its competitors. Software is also readily available for such outcomes. In this article, we introduce modeling that extends the usefulness of BART in medical applications by addressing needs arising in survival analysis. Simulation studies of one-sample and two-sample scenarios, in comparison with long-standing traditional methods, establish face validity of the new approach. We then demonstrate the model's ability to accommodate data from complex regression models with a simulation study of a nonproportional hazards scenario with crossing survival functions and survival function estimation in a scenario where hazards are multiplicatively modified by a highly nonlinear function of the covariates. Using data from a recently published study of patients undergoing hematopoietic stem cell transplantation, we illustrate the use and some advantages of the proposed method in medical investigations. Copyright © 2016 John Wiley & Sons, Ltd.