Survival analysis using Dirichlet process mixture model with three-parameter Burr XII distribution as kernel

Abstract

Modeling multimodal survival data using parametric distributions is yet a challenging task. Mixture distributions in a nonparametric Bayesian framework can be applied as a sophisticated tool. Dirichlet process mixture model (DPMM) is a suitable asset in this approach. Choosing a kernel for the mixture model is an essential issue in this context. Survival data analysis using the DPMM with a three-parameter Burr XII kernel is the objective of this article. The Monte Carlo Markov Chain algorithms, like Gibbs sampling, are developed to fit the three-parameter Burr XII mixture model. A Simulation study based on right-censored data illustrates the performance of this kind of mixture model. We compare the proposed model results with other DPMM with different kernels like Weibull, Lognormal, and two-parameter Burr XII distributions. The flexibility of the proposed mixture model is demonstrated using three real datasets. In some instances, DPMM with Weibull or lognormal kernels perform well; meanwhile, these kernels may not outperform in the clustering or hazard rate estimation context. In these cases, a three parameters BurXII distribution might be a suitable kernel for Dirichlet process mixture model.