Dependence estimation over a finite bivariate failure time region.

This article concerns nonparametric estimation of association between bivariate failure times. In the presence of independent right censoring, the support for failure time variates may be restricted and measures of dependence over a finite failure time region may be of particular interest. To this end, the reciprocal cross ratio function, weighted by the bivariate failure time density, is proposed as a summary measure of dependence over a failure time region. This 'relative risk' estimator is shown to be consistent and asymptotically normally distributed, with consistent bootstrap variance estimator. A finite-region version of Kendall's tau, which is suitable for censored failure time data, is also proposed, and corresponding asymptotic distribution theory is noted. The accuracy of these asymptotic approximations is studied in simulations and an illustration is provided.