Survival Data Analysis using Additive and Multiplicative Gamma Polygonal Hazards Function

Abstract

Proportional hazards model (PHM) is commonly used in survival analysis for estimating the effects of different covariates influencing the survival data. The hazard function in proportional hazards model (PHM) is commonly defined as a product of the baseline hazard function and a non-negative function of covariates. However, the hazard function may also be presented as the sum of the baseline hazard function and a nonnegative function of covariates. We propose the new additive and multiplicative Gamma Polygonal in the hazards function using OpenBugs Statistical Packages. Both models are an alternative to the existing additive and multiplicative models but the new additive Gamma polygonal intensity model is quite complex compared to the new multiplicative Gamma polygonal intensity model. The application for right-censored data from Bayesian perspective will be discussed and the Markov Chain Monte Carlo (MCMC) method will be used to compute the Bayesian estimator using Leukemia data and DSR data. The results obtained show that the propose model is as good as the existing models in analyzing paired survival data. Keywords: Additive model; Multiplicative model; Baseline hazards function; MCMC 2010 Mathematics Subject Classification: 46N60; 92B99