Parametric Survival Analysis Assuming the Proportional Hazard Functions of Survival and Censoring Times Distributions

Abstract

The article deals with frequentist and Bayesian Survival analysis in Proportional Hazards model of random censorship using Burr type XII distribution. The Joint Conjugate Prior distribution of the model parameters does not exists while computing the Bayes estimates; we suggest pairwise independent gamma priors for the shape and scale parameters. The closed-form expressions for the Bayes estimates are not possible; we consider two different methods of Bayesian computation, namely, importance sampling and Lindley’s approximation to obtain the Bayes estimates. The Maximum Likelihood estimation is presented in a novel way. Monte Carlo simulation study is carried out to observe the behavior of the Maximum Likelihood estimators and Bayes estimators for different combinations of the quantities involved. One real data analysis is performed for illustration.