Piecewise linear approximations of baseline under proportional hazards based COM-Poisson cure models

Cure models are widely popular in modeling time-to-event data that are characterized by cure fraction owing to long-term survivors. Mixture cure models are perhaps the most studied cure models in the literature. In this article, however, we consider a competing risks scenario where the number of competing causes is modeled by flexible Conway-Maxwell (COM) Poisson distribution, and the lifetimes corresponding to the competing causes are assumed to be independently distributed following proportional hazards model. The baseline hazard function is modeled by a piecewise linear function, and hence, estimated non parametrically. Probability of obtaining zero competing causes is used to estimate the cure rate. Collectively, the resultant cure model is exceedingly general and flexible. The estimation of the parameters is carried out using maximum likelihood (ML) method by implementing the expectation-maximization (EM) algorithm, except for the dispersion parameter of the COM-Poisson distribution, which is estimated by the profile likelihood method. The performance of the model is tested under various settings of censoring rate, sample size and mean lifetime. Discrimination of models is performed and carried out with likelihood-based and information-based criteria. Performance of the proposed model is further illustrated using a real-world data on cutaneous melanoma.