A bivariate survival model with modified gamma frailty for assessing the impact of interventions

Bivariate survival analysis models that incorporate random effects or 'frailty' provide a useful framework for determining the effectiveness of interventions. These models are based on the notion that two paired survival times are correlated because they share a common unobserved value of a random variate from a frailty distribution. In some applications, however, investigators may have some information that characterizes pairs and thus provides information about their frailty. Alternatively, there may be an interest in assessing whether the correlation within certain types of pairs is different from the correlation within other types of pairs. In this paper, we present a method to incorporate 'pair-wise' covariate information into the dependence parameter of the bivariate survival function. We provide an example using data from the Framingham Heart Study to investigate the times until the occurrence of two events within an individual: the first detection of hypertension and the first cardiovascular disease event. We model the dependence between these two events as a function of the age of the individual at the time of enrollment into the Framingham Study.