Likelihood inference for Birnbaum–Saunders frailty model with an application to bone marrow transplant data

Cluster failure 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 the correlation among the subjects within the same cluster. In addition, some diseases are curable due to the advancement of modern medical techniques. In this paper, we extend the frailty model based on Birnbaum–Saunders frailty distribution to incorporate the cure proportion. In addition, the marginal likelihood approach using Monte Carlo approximation and Expectation-Maximization algorithm are also developed for the determination of the maximum likelihood estimates of the parameters of the proposed model. An extensive simulation study is carried out to evaluate the performance of the proposed model and the methods of inference. Finally, the proposed model is applied to a real data set to analyse the effect of allogeneic and autologous bone marrow transplant treatment on acute lymphoblastic leukemia patients.