Likelihood Inference for Flexible Cure Rate Models with Gamma Lifetimes

A flexible cure rate survival model was developed by Rodrigues et al. (2009a Rodrigues, J., de Castro, M., Cancho, V.G., Balakrishnan, N. (2009a). COM-Poisson cure rate survival models and an application to a cutaneous melanoma data. J. Statist. Plann. Infer. 139:3605–3611.[Crossref], [Web of Science ®] , [Google Scholar]) by assuming the competing cause variable to follow the Conway-Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models. As the data obtained from cancer clinical trials are often right censored, the EM algorithm can be efficiently used to estimate the model parameters based on right censored data. In this paper, we consider the cure rate model developed by Rodrigues et al. (2009a Rodrigues, J., de Castro, M., Cancho, V.G., Balakrishnan, N. (2009a). COM-Poisson cure rate survival models and an application to a cutaneous melanoma data. J. Statist. Plann. Infer. 139:3605–3611.[Crossref], [Web of Science ®] , [Google Scholar]) and by assuming the time-to-event to follow the gamma distribution, we develop exact likelihood inference based on the EM algorithm. An extensive Monte Carlo simulation study is performed to examine the method of inference developed. Model discrimination between different cure rate models is carried out by means of likelihood ratio test and Akaike and Bayesian information criteria. Finally, the proposed methodology is illustrated with a cutaneous melanoma data.