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We propose Bayesian nonparametric Weibull delegate racing (WDR) for survivalanalysis with competing events and achieve both model interpretability andflexibility. Utilizing a natural mechanism of surviving competing events, weassume a race among a potentially infinite number of sub-events. In doing this,WDR accommodates nonlinear covariate effects with no need of datatransformation. Moreover, WDR is able to handle left truncation, time-varyingcovariates, different types of censoring, and missing event times or types. Wedevelop an efficient MCMC algorithm based on Gibbs sampling for Bayesianinference and provide an \texttt{R} package. Synthetic data analysis andcomparison with benchmark approaches demonstrate WDR's outstanding performanceand parsimonious nonlinear modeling capacity. In addition, we analyze two realdata sets and showcase advantages of WDR. Specifically, we study time to deathof three types of lymphoma and show the potential of WDR in modeling nonlinearcovariate effects and discovering new diseases. We also use WDR to investigatethe age at onset of mild cognitive impairment and interpret the accelerating ordecelerating effects of biomarkers on the progression of Alzheimer's disease.

Weibull Racing Survival Analysis with Competing Events, Left Truncation, and Time-varying Covariates