Proportional Odds under Conway-Maxwell-Poisson Cure Rate Model and Associated Likelihood Inference

Cure rate models are useful while modelling lifetime data involving long time survivors. In this work, we discuss a flexible cure rate model by assuming the number of competing causes for the event of interest to follow the Conway-Maxwell Poisson distribution and the lifetimes of the non-cured individuals to follow a proportional odds model. The baseline distribution is considered to be either Weibull or log-logistic distribution. Under right censoring, we develop the maximum likelihood estimators using EM algorithm. Model discrimination among some well-known special cases are discussed under both likelihood- and information-based criteria. An extensive simulation study is carried out to examine the performance of the proposed model and the inferential methods. Finally, a cutaneous melanoma dataset is analyzed for illustrative purpose.