Bayesian semiparametric analysis of recurrent failure time data using copulas

The analysis of recurrent event data is of particular importance in medical statistics where patients suffering from chronic diseases often present with multiple recurring relapses or cancer patients experience several tumor recurrences. Whereas individual subjects can be assumed to be independent, the times between events of one subject are neither independent nor identically distributed. Apart from the marginal approach by Wei et al. (1989), the shared frailty model, see for example Duchateau and Janssen (2008), has been used extensively to analyze recurrent event data, where the correlation between sequential times is implicitly taken into account via a random effect. Oakes (1989) and Romeo et al. (2006) showed and exemplified the equivalence of frailty models for bivariate survival data to Archimedean copulas. Despite the fact that copula-based models have been used to model parallel survival data, their application to recurrent failure time data has only recently been suggested by Lawless and Yilmaz (2011) for the bivariate case. Here, we extend this to more than two recurrent events and model the joint distribution of recurrent events explicitly using parametric copulas within a Bayesian framework. This framework allows for parametric as well as a nonparametric modeling of the marginal baseline hazards and models the influence of covariates on the marginals via a proportional hazards assumption. Furthermore, the parameters of the copula may also depend on the covariates. We illustrate the flexibility of this approach using data from an asthma prevention trial in young children.