An EM algorithm for the estimation of parameters of a flexible cure rate model with generalized gamma lifetime and model discrimination using likelihood- and information-based methods

In this paper, we consider the Conway-Maxwell Poisson (COM-Poisson) cure rate model based on a competing risks scenario. This model includes, as special cases, some of the well-known cure rate models discussed in the literature. By assuming the time-to-event to follow the generalized gamma distribution, which contains some of the commonly used lifetime distributions as special cases, we develop exact likelihood inference based on the expectation maximization algorithm. The standard errors of the maximum likelihood estimates are obtained by inverting the observed information matrix. An extensive Monte Carlo simulation study is performed to examine the method of inference developed here. Model discrimination within the generalized gamma family is also carried out by means of likelihood- and information-based methods to select the particular lifetime distribution that provides an adequate fit to the data. Finally, a data on cancer recurrence is analyzed to illustrate the flexibility of the COM-Poisson family and the generalized gamma family so as to select a parsimonious competing cause distribution and a lifetime distribution that jointly provide an adequate fit to the data.