Likelihood inference based on EM algorithm for the destructive length-biased Poisson cure rate model with Weibull lifetime

In this article, we consider the destructive length-biased Poisson cure rate model, proposed by Rodrigues et al., that presents a realistic and interesting interpretation of the biological mechanism for the recurrence of tumor in a competing causes scenario. Assuming the lifetime to follow the Weibull distribution and censoring mechanism to be non-informative, the necessary steps of the EM algorithm for the determination of the MLEs of the model parameters are developed here based on right censored data. The standard errors of the MLEs are obtained by inverting the observed information matrix. A simulation study is then carried out to examine the method of inference developed here. Finally, the proposed methodology is illustrated with a real melanoma dataset.