Quantile association for bivariate survival data

Bivariate survival data arise frequently in familial association studies of chronic disease onset, as well as in clinical trials and observational studies with multiple time to event endpoints. The association between two event times is often scientifically important. In this article, we examine the association via a novel quantile association measure, which describes the dynamic association as a function of the quantile levels. The quantile association measure is free of marginal distributions, allowing direct evaluation of the underlying association pattern at different locations of the event times. We propose a nonparametric estimator for quantile association, as well as a semiparametric estimator that is superior in smoothness and efficiency. The proposed methods possess desirable asymptotic properties including uniform consistency and root-n convergence. They demonstrate satisfactory numerical performances under a range of dependence structures. An application of our methods suggests interesting association patterns between time to myocardial infarction and time to stroke in an atherosclerosis study.