A comparison of frailty and other models for bivariate survival data

Multivariate survival data arise when each study subject may experience multiple events or when study subjects are clustered into groups. Statistical analyses of such data need to account for the intra-cluster dependence through appropriate modeling. Frailty models are the most popular for such failure time data. However, there are other approaches which model the dependence structure directly. In this article, we compare the frailty models for bivariate data with the models based on bivariate exponential and Weibull distributions. Bayesian methods provide a convenient paradigm for comparing the two sets of models we consider. Our techniques are illustrated using two examples. One simulated example demonstrates model choice methods developed in this paper and the other example, based on a practical data set of onset of blindness among patients with diabetic Retinopathy, considers Bayesian inference using different models.