There has been much research on the study of associations among paired failure times. Most has either assumed time invariance of association or been based on complex measures or estimators. Little has accommodated failures arising amid competing risks. This paper targets the conditional cause specific hazard ratio, a recent modification of the conditional hazard ratio 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 researched, small sample performance evaluated, and methods applied to investigate familial association in dementia onset. The proposed methodology augments existing methodology with an approach that may be more readily applied and interpreted, thus facilitate dissemination of methodology addressing failure time associations into the substantive literature
Bandeen-Roche, Karen and Ning, Jing, "NONPARAMETRIC ESTIMATION OF BIVARIATE FAILURE TIME ASSOCIATIONS IN THE PRESENCE OF A COMPETING RISK" (November 2005). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 92.