A Multivariate Proportional Odds Frailty Model with Weibull Hazard under Bayesian Mechanism

Abstract

Objectives: The objective of this study is to develop a new Proportional Odds frailty model by using a Weibull hazard function in context of Bayesian mechanism. Methods: Frailty models provide a convenient way to introduce random effects, association and unobserved heterogeneity into models for survival data. Proportional Odds (PO) model is a widely pursued model in survival analysis which extends the concept of Odds ratio considered for lifetime data with covariates. Proportional Odds models can be derived under frailty approach by introducing a frailty term for each individual in the exponent of the hazard function, which acts multiplicatively on the baseline hazard function. In this paper an attempt has been made to develop a new Proportional Odds frailty model by using a Weibull hazard function in context of Bayesian mechanism. Findings: The methodologies are applied to a real life survival data set and the posterior inferences are drawn using Markov Chain Monte Carlo (MCMC) simulation methods and model comparison tools like Deviance Information Criteria (DIC) and the Log Pseudo Marginal Likelihood (LPML) are also calculated and to check the fit of the model Cox-Snell residual plot is employed. The performance of the newly developed model is compared with an existing proportional odds model without the frailty term and it is observed that the newly developed frailty model perform well as compered to the traditional non frailty model. Novelty: A new Proportional Odds frailty model using Weibull hazard function under Bayesian mechanism is developed in this paper which is an added contribution in the field of Survival Analysis.