Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family

Recently, a new cure rate survival model has been proposed by considering the Conway–Maxwell Poisson distribution as the distribution of the competing cause variable. This model includes some of the well-known cure rate models discussed in the literature as special cases. Cancer clinical trials often lead to right censored data and so the EM algorithm can be used as an efficient tool for the estimation of the model parameters based on right censored data. By considering this Conway–Maxwell Poisson-based cure rate model and by assuming the lognormal distribution for the time-to-event variable, the steps of the EM algorithm are developed here for the estimation of the parameters of different cure rate survival models. The standard errors of the MLEs are obtained by inverting the observed information matrix. An extensive Monte Carlo simulation study is performed to illustrate the method of inference developed. Model discrimination between different cure rate models is addressed by the likelihood ratio test as well as by Akaike and Bayesian information criteria. Finally, the proposed methodology is illustrated with a real data on cutaneous melanoma.