Generalized Birnbaum–Saunders mixture cure frailty model: inferential method and an application to bone marrow transplant data

Cluster time data are commonly encountered in survival analysis due to unobservable factors such as shared environmental conditions and genetic similarity. In such cases, careful attention needs to be paid to model the possible correlation between the subjects within the same cluster. Moreover, some diseases are curable due to great advances on modern medical techniques and treatments. For tracking these issues, we consider here a mixture cure frailty model, with generalized Birnbaum–Saunders frailty distribution, and propose a marginal likelihood approach for the estimation of model parameter. We approximate the intractable integrals in the likelihood function by the use of Monte-Carlo method. Thereafter, the maximum likelihood estimates are numerically determined. A simulation study and model discrimination are then carried out for evaluating the performance of the proposed model. It is observed from this study that the proposed model provides more flexibility and the method of inference is quite robust. Finally, we conduct an analysis of the effects of allogeneic and autologous bone marrow transplant treatments on acute lymphoblastic leukemia patients to demonstrate the usefulness of the proposed model and the method of inference.