COM‐Poisson Cure Rate Models and Associated Likelihood‐based Inference with Exponential and Weibull Lifetimes

This chapter, by considering both the exponential and Weibull distributions for the time‐to‐event and assuming the number of competing causes related to the event of interest to follow the Conway‐Maxwell poisson (COM‐Poisson) distribution. It discusses the steps of the expectation maximization (EM) algorithm for the determination of the maximum likelihood estimates (MLEs) of the parameters of the cure rate survival model based on right censored data. It also discusses the applications of cure rate models in reliability and introduces the COM‐Poisson cure rate model. The form of the data and the likelihood function are presented. The author develops the estimation procedure for estimating the parameters of the COM‐Poisson cure rate model and some of its special cases. The asymptotic variance‐covariance matrix of the MLEs is derived. The chapter presents the results of the proposed methodology when the lifetime distribution is taken to be exponential and Weibull, respectively. expectation‐maximisation algorithm; exponential distribution; poisson distribution; Weibull distribution