Mixture and Non-Mixture Cure fraction Models based on Generalized Gompertz Distribution under Bayesian approach

Abstract

The cure fraction models are generally used to model lifetime data with long term survivors. In   a cohort of cancer patients, it has been observed that due to the development of new drugs some patients are cured permanently, and some are not cured. The patients who are cured permanently are called cured or long term survivors while patients who experience the recurrence of the disease are termed as susceptibles or uncured. The proportion of cured individuals after a treatment is typically known as the cure fraction (cure rate). Thus, the population is divided into two groups: a group of cured individuals and a group of susceptible individuals. In this paper, we have introduced a three parameter Gompertz (viz. scale, shape and acceleration) or Generalized Gompertz Distribution in the presence of cure fraction, censored data and covariates for estimating the proportion of cure fraction through Bayesian Approach. Inferences are obtained using standard Markov Chain Monte Carlo technique in openBUGS software.