Nonparametric estimation of bivariate failure time associations in the presence of a competing risk

Most research on the study of associations among paired failure times has either assumed time invariance or been based on complex measures or estimators. Little has accommodated competing risks. This paper targets the conditional cause-specific hazard ratio, henceforth called the cause-specific cross ratio, a recent modification of the conditional hazard ratio designed to accommodate competing risks data. Estimation is accomplished by an intuitive, nonparametric method that localizes Kendall's tau. Time variance is accommodated through a partitioning of space into 'bins' between which the strength of association may differ. Inferential procedures are developed, small-sample performance is evaluated, and the methods are applied to the investigation of familial association in dementia onset.