Proportional Odds COM-Poisson Cure Rate Model with Gamma Frailty and Associated Inference and Application

We introduce in this work a gamma frailty cure rate model for lifetime data by assuming the number of competing causes for the event of interest to follow the Conway-Maxwell-Poisson (COM-Poisson) distribution and the lifetimes of the non-cured individuals to follow a proportional odds model. The baseline distribution is taken to be either Weibull or log-logistic. Statistical inference is then developed under non-informative right censored data. We derive the maximum likelihood estimators (MLEs) with the use of Expectation Maximization (EM) method for all model parameters. The model discrimination among some well-known special cases, including Geometric, Poisson, and Bernoulli models, are discussed under both likelihood- and information-based criteria. An extensive Monte Carlo simulation study is carried out to examine the performance of the proposed model as well as all the inferential methods developed here. Finally, a cutaneous melanoma dataset is analyzed for illustrative purpose.