Semi-parametric likelihood inference for Birnbaum–Saunders frailty model

Cluster failure time data are commonly encountered in survival analysis due to different factors such as shared environmental conditions and genetic similarity. In such cases, careful attention needs to be paid to the correlation among subjects within same clusters. In this paper, we study a frailty model based on Birnbaum–Saunders frailty distribution. We approximate the intractable integrals in the likelihood function by the use of Monte Carlo simulations and then use the piecewise constant baseline hazard function within the proportional hazards model in frailty framework. Thereafter, the maximum likelihood estimates are numerically determined. A simulation study is conducted to evaluate the performance of the proposed model and the method of inference. Finally, we apply this model to a real data set to analyze the effect of sublingual nitroglycerin and oral isosorbide dinitrate on angina pectoris of coronary heart disease patients and compare our results with those based on other frailty models considered earlier in the literature.