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Handling missing values plays an important role in the analysis of survivaldata, especially, the ones marked by cure fraction. In this paper, we discussthe properties and implementation of stochastic approximations to theexpectation-maximization (EM) algorithm to obtain maximum likelihood (ML) typeestimates in situations where missing data arise naturally due to rightcensoring and a proportion of individuals are immune to the event of interest.A flexible family of three parameter exponentiated-Weibull (EW) distributionsis assumed to characterize lifetimes of the non-immune individuals as itaccommodates both monotone (increasing and decreasing) and non-monotone(unimodal and bathtub) hazard functions. To evaluate the performance of the SEMalgorithm, an extensive simulation study is carried out under various parametersettings. Using likelihood ratio test we also carry out model discriminationwithin the EW family of distributions. Furthermore, we study the robustness ofthe SEM algorithm with respect to outliers and algorithm starting values. Fewscenarios where stochastic EM (SEM) algorithm outperforms the well-studied EMalgorithm are also examined in the given context. For further demonstration, areal survival data on cutaneous melanoma is analyzed using the proposed curerate model with EW lifetime distribution and the proposed estimation technique.Through this data, we illustrate the applicability of the likelihood ratio testtowards rejecting several well-known lifetime distributions that are nestedwithin the wider class of EW distributions.

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