A Bayesian Analysis for the Generalized Negative Binomial Log-logistic Cure Fraction Survival Model

In time-to-event studies, the occurrence of an event might be caused by one, among many, competing causes. Also, both the number of causes and the time-to-event associated with each cause may be not observed. Adding to this situation the existence of a proportion of individuals which is not susceptible to the occurrence of event of interesting, leading a scenario of competing causes with a cure fraction. In this paper, we propose a general survival model for accommodating data in the presence of competing causes and cure fraction. We assume the number of competing causes following a generalized negative binomial distribution while the times-to-event following a Log-logistic distribution. The advantage of this assumption is to incorporating in to the analysis characteristics of the treatment, such as the number of doses, the time interval between doses and the efficiency of each dose. The parameter estimation of the proposed model is straightforward via maximum likelihood estimation procedure. A simulation study was carried out in order to verify the coverage probabilities, the size and power of some hypotheses test under small and moderated sized samples. A real data on breast cancer is also provided.