Survival Analysis Using Dirichlet Process Mixture Model with three-parameter Burr XII distribution as kernel Bahram Haji Joudaki a , Reza Hashemi a and Soleiman Khazaei a a Department of Statistics, Razi University, Kermanshah, Iran Corresponding Author: r.hashemi@razi.ac.ir June 21, 2022 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 paper. The Monte Carlo Markov Chain algorithms, like Gibbs sampling, are developed to ft 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 diferent kernels like Weibull, Lognormal, and two-parameter Burr XII distributions. The fexibility 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 DPMM with three parameters BurXII distribution might be a suitable kernel. Key Words: Nonparametric Bayesian, Dirichlet process mixture model, Three-parameter burr XII distribution, Survival data analysis, Right censored data. 1 Introduction The Dirichlet Process(DP) is the starting point for using advanced Bayesian nonparametric methods in statistics was in- troduced by Ferguson [10]. A Bayesian formulating for nonparametric issues is not trivial because, in parametric Bayesian models, prior and consequently posterior distributions are considered for a fxed parameter space, however in the nonpara- metric issues, the dimension of parameter space changes with the sample size. Hence the Bayesian nonparametric method is a Bayesian model on infnite-dimensional parameter space, containing all probability measures. Bayesian nonparametric ap- proaches are valuable assets for analyzing survival data since they enable researchers to use more fexible models for unknown shapes of hazard and survival functions. Especially this kind of model prepares the necessary characteristics to investigate with the truncated and censored data. This kind of data is inevitable in the survival analysis, which is not simply tackled in the restricted parameter space. Susarla and Van yzin[36] frstly considered the DP prior for the survival distribution and introduced a Bayesian nonparametric estimator for the survival function in right-censored data. Their estimator is the same as the Kaplan-Meier estimator under certain conditions. Tsai[37] presented a consistent Bayesian nonparametric estimator for the survival distribution function. An excellent review for the usage of Bayesian nonparametric methods in diferent branches of statistics, including survival analysis, is prepared in Ferguson et al.[15]. 1