Modeling the presence of immunes by using the exponentiated-Weibull model

In this paper the exponentiated-Weibull model is modified to model the possibility that long-term survivors are present in the data. The modification leads to an exponentiated-Weibull mixture model which encompasses as special cases the exponential and Weibull mixture models typically used to model such data. Inference for the model parameters is considered via maximum likelihood and also via Bayesian inference by using Markov chain Monte Carlo simulation. Model comparison is considered by using likelihood ratio statistics and also the pseudo Bayes factor, which can be computed by using the generated samples. An example of a data set is considered for which the exponentiated-Weibull mixture model presents a better fit than the Weibull mixture model. Results of simulation studies are also reported, which show that the likelihood ratio statistics seems to be somewhat deficient for small and moderate sample sizes.