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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. [ABSTRACT FROM AUTHOR]