A Comparison of Cure Fraction Estimation Methods in Promotion Time Cure Model based on Burr Type XII Distribution

Abstract

Survival data from clinical trials often show the proportion of patients with long-term survivors and the standard models like Cox and accelerated failure time model are inappropriate for fitting such data. The two-component mixture cure model is often used for this purpose. However, for the failure time data with proportional hazards structure, the promotion time cure model can be more adaptable than the mixture cure model. The present paper compares semiparametric method with parametric Bayesian and maximum likelihood methods for estimating the proportion of insusceptible patients using log link function and for modeling the failure times of susceptible subjects using Burr-XII distribution. For Bayesian estimation, we use improper uniform prior distributions for regression parameters and vague gamma prior distributions for baseline distribution parameters. Numerical experiments are considered to examine the performance of different methods. It is observed that for small sample sizes, the Bayes method perform better than the parametric and semiparametric methods in terms of biases, mean square errors and empirical variances and for large sample sizes, the performance of the Bayes and maximum likelihood methods is approximately equal. The proposed methods are applied to real data for illustration and motivation.