The generalized exponential cure rate model with covariates

Abstract

In this article, we consider a parametric survival model that is appropriate when the population of interest contains long-term survivors or immunes. The model referred to as the cure rate model was introduced by Boag 1 in terms of a mixture model that included a component representing the proportion of immunes and a distribution representing the life times of the susceptible population. We propose a cure rate model based on the generalized exponential distribution that incorporates the effects of risk factors or covariates on the probability of an individual being a long-time survivor. Maximum likelihood estimators of the model parameters are obtained using the the expectation-maximisation (EM) algorithm. A graphical method is also provided for assessing the goodness-of-fit of the model. We present an example to illustrate the fit of this model to data that examines the effects of different risk factors on relapse time for drug addicts.

Keywords:

• cure rate
• long-term survivor
• generalized exponential distribution
• EM algorithm
• goodness-of-fit

Acknowledgements

The authors would like to thank the associate editor and the two referees for their valuable comments, which have improved the earlier version of the manuscript. Part of this work is supported by a grant from the Department of Science and Technology, Government of India.