A class of weighted dependence measures for bivariate failure time data

This paper considers a class of summary measures of the dependence between a pair of failure time variables over a finite follow-up region. The class consists of measures that are weighted averages of local dependence measure s, and includes the cross-ratio measure and finite region version of Kendal l's tau recently proposed by the authors. Two new special cases are identif ied that can avoid the need to estimate the bivariate survivor function and that admit explicit variance estimators. Nonparametric estimators of such dependence measures are proposed and are shown to be consistent and asympto tically normal with variances that can be consistently estimated. Propertie s of selected estimators are evaluated in a simulation study, and the metho d is illustrated through an analysis of Australian Twin Study data.