A Semiparametric Bayesian Regression Framework with Bernstein Polynomial Model for Analyzing Dependent Current Status Data and Applications to Primary Biliary Cirrhosis and Melanoma Data

Abstract

This paper proposes a semiparametric Bayesian estimation framework for survival regression models applied to dependent current status data. In many situations, ignoring the dependence between survival and censoring times can lead to biased estimates. To address this issue, we employ various copula models to capture dependence. We consider both proportional hazards and proportional odds regression approaches to model the effects of covariates. We use the Bernstein polynomial model for nonparametric approximation of the baseline hazard function. Since the joint posterior distribution of the regression parameters and Bernstein polynomial coefficients lacks a closed-form expression, we use a robust adaptive Metropolis–Hastings algorithm to perform sample-based Bayesian inferences. Simulation studies are performed to discriminate models and estimate the probability of correct selection for identifying the true underlying copula model. The proposed Bayesian framework is illustrated through two real-life datasets pertaining to primary biliary cirrhosis and melanoma. We determine the best-fitting model using the deviance information criterion. The Bernstein and I-spline polynomial models are also evaluated in terms of their fit to empirical datasets.