A Bayesian Semiparametric Approach to Conditional Survival Estimation for Heavy-Tailed Data Under Right-Censoring

Music City Center 

This study explores the estimation of conditional survival function in heavy-tailed distributions under right-censoring, a prevalent issue in fields such as medical science. We introduce a novel Bayesian Semiparametric approach by combining a Dirichlet Process Mixture (DPM) model with the Generalized Pareto Distribution (GPD), enabling robust estimation of conditional survival functions using a unified model. The DPM model efficiently models the central portions of the distribution below a specified threshold, while the GPD addresses the tail behavior beyond this threshold. Our approach uniquely accommodates random right censoring and incorporates covariate information, enhancing the estimation of conditional survival and hazard functions tailored to specific covariates. This paper presents an inaugural development of Bayesian models in this area, along with simulation studies and real-data applications, demonstrating significant enhancements in the accuracy and reliability of conditional survival function estimations over traditional methods.

Bayesian Nonparametric

Dirichlet Process Mixture Model

Generalized Pareto Distribution

Right Censoring

Survival Curve Estimation

Extreme Quantile Estimation 

Section on Bayesian Statistical Science