Bayesian and likelihood inference for cure rates based on defective inverse Gaussian regression models

Abstract

Failure time models are considered when there is a subpopulation of individuals that is immune, or not susceptible, to an event of interest. Such models are of considerable interest in biostatistics. The most common approach is to postulate a proportion p of immunes or long-term survivors and to use a mixture model [5]. This paper introduces the defective inverse Gaussian model as a cure model and examines the use of the Gibbs sampler together with a data augmentation algorithm to study Bayesian inferences both for the cured fraction and the regression parameters. The results of the Bayesian and likelihood approaches are illustrated on two real data sets.

Keywords:

• cure rates
• defective inverse Gaussian
• Gibbs sampler
• survival analysis

Acknowledgements

We are grateful to two anonymous referees for a number of constructive criticisms which helped to improve this manuscript.

This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Specifically, in the form of a scholarship to the first author and respective Discovery Grants to the second and third authors.