On the dependence structure of bivariate recurrent event processes: Inference and estimation

Bivariate or multivariate recurrent event processes are often encountered in longitudinal studies in which more than one type of event is of interest. There has been much research on regression analysis for such data, but little has been done to measure the dependence between recurrent event processes.We propose a time-dependent measure, termed the rate ratio, to assess the local dependence between two types of recurrent event processes. We model the rate ratio as a parametric function of time, and leave unspecified all other aspects of the distribution. We develop a composite likelihood procedure for model fitting and parameter estimation. We show that the proposed estimator is consistent and asymptotically normal. Its finite sample performance is evaluated by simulation and illustrated by an application to a soft tissue sarcoma study.