Frailty Additive and Multiplicative Gamma Polygonal in Survival Data Analysis

Abstract

Proportional hazards model is commonly used in survival analysis for estimating the effects of different covariates influencing survival data. There are two ways to define the hazard function model: as a product of the baseline hazard function and a non-negative function of covariates or as the sum of the baseline hazard function and a non-negative function of covariates. In this paper, we propose an additive and multiplicative Gamma Polygonal with frailty in the hazard function using OpenBUGS. The family of frailty models can make the hazard modeling scheme more flexible and facilitates a variety of relationships between the baseline hazard and hazard function. The proposed models are more flexible survival models for non-informative censored data using a Bayesian approach. Multiplicative Gamma Polygonal has given a better performance compared to additive Gamma Polygonal since an additive Gamma Polygonal intensity model with frailty is a complex model. We have used the Markov Chain Monte Carlo method to compute the Bayesian estimator on Leukemia data.