Covariate-adjusted Dependence Estimation on a Finite Bivariate Failure Time Region

Recently Fan and colleagues have proposed two measures of the strength of dependency between failure time variates over a finite region of the sample space; namely, an average relative risk measure and a finite region version of Kendall’s tau. Here, these dependency measures are generalized to accommodate regression effects on marginal hazard functions. Specifically, the dependency measures previously proposed are applied to possibly censored, estimated cumulative hazard variates, calculated under Cox model marginal hazard function models. The resulting dependency estimators use a nonparametric estimator of the bivariate survivor function and are shown to be consistent and asymptotically normally distributed, with consistent bootstrap variance estimators, for certain classes of covariates. The small sample properties of the estimators, and their variance estimators, are examined in simulation studies and the estimators are compared to corresponding homogeneous dependency estimators that do not condition on covariates.