A Stochastic Version of the EM Algorithm for Mixture Cure Model with Exponentiated Weibull Family of Lifetimes

In this paper, we propose a stochastic approximation to the well-studied expectation–maximization (EM) algorithm for finding the maximum likelihood (ML)-type estimates in situations where missing data arise naturally and a proportion of individuals are immune to the event of interest. A flexible family of three parameter exponentiated Weibull (EW) distributions is assumed to characterize lifetimes of the non-immune individuals as it accommodates both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub) hazard functions. To evaluate the performance of the proposed algorithm, an extensive simulation study is carried out under various parameter settings. Using likelihood ratio tests, we also carry out model discrimination within the EW family of distributions. Furthermore, we study the robustness of the proposed algorithm with respect to outliers in the data and the choice of initial values to start the algorithm. In particular, we show that our proposed algorithm is less sensitive to the choice of initial values when compared to the EM algorithm. For illustration, we analyze a real survival data on cutaneous melanoma. Through this data, we illustrate the applicability of the likelihood ratio test toward rejecting several well-known lifetime distributions that are nested within the wider class of the proposed EW distributions.