Bayesian parametric survival models

Abstract

Survival models are useful statistical tool to predict the duration for a certain event to occur. Nowadays, survival analysis is used in several research areas to model duration of device failure or duration of relapse to drug, smoking and alcohol addiction; evaluate product reliability; estimate survival durations and life expectancy; measure viability of medical therapies, instruments and techniques; assess drug safety; estimate the duration till failure of mechanical/electrical devices and human organs, among other applications. There are two approaches to parameter estimation, which is a central component of statistical inference. In the frequentist approach, the parameters are treated as fixed and are estimated using a likelihood-based method. The Bayesian approach treats the parameters as random variables and incorporates prior information combined with observed data for parameter estimation. This paper describes the Bayesian paradigm and discusses sampling methods from the posterior distribution using the Metropolis-Hasting algorithm within the Gibbs sampler. Moreover, survival models are fitted to a data set related to aortic valve replacement to relate survival duration of patients to eleven health-related explanatory variables in pre-operative and the post-operative periods. The models are fitted using the facilities of STATA assuming an Exponential and a Weibull survival distribution.