Survival Analysis with Parametric Proportional Hazards Model of Random Censorship

SYNOPTIC ABSTRACT

This article presents the survival analysis in a proportional hazards model of random censorship using Weibull distribution. It is well known for Weibull distribution that the conjugate prior of the scale and shape parameters does not exist while considering the Bayesian analysis. It is assumed here that the scale and shape parameters have gamma prior distributions. In the case of no suitable prior information about the parameters, non-informative gamma priors for the scale and shape parameters are proposed. It is seen that the closed-form expressions for the Bayes estimates cannot be obtained; we suggest Lindley's method to approximate the Bayes estimates. Unfortunately, it is not possible to construct the Bayesian credible intervals while using this method. We propose an importance sampling procedure to obtain the Bayes estimates and to also construct the Bayesian credible intervals. The method of maximum likelihood estimation is presented in a novel way. A simulation study is carried out to observe the behavior of the maximum likelihood estimators and the Bayes estimators for different combinations of sample sizes, priors, parameters, and censoring rates. One real data analysis is performed to illustrate the proposed methodology.

KEYWORDS AND PHRASES:

• Random censorship
• maximum likelihood
• Bayes estimate
• importance sampling
• Lindley's approximation