Nonparametric Association Analysis of Bivariate Competing-Risks Data

Although nonparametric analyses of bivariate failure times under independent censoring have been widely studied, nonparametric analyses of bivariate competing-risks data have not yet been investigated. Such analyses are important in familial association studies, where multiple interacting failure types may violate the independent censoring assumption. We develop nonparametric estimators for the bivariate cause-specific hazards function and the bivariate cumulative incidence function that are natural analogs of their univariate counterparts and make no assumptions about the dependence of the risks. The estimators are shown to be uniformly consistent and to converge weakly to Gaussian processes. They provide the basis for novel time-dependent association measures, with the associated inferences yielding tests of cause-specific independence in pairs. The methodology performs well in simulations with realistic sample sizes. Its practical utility is illustrated in an analysis of dementia in the Cache County Study, where the nonparametric methods indicate that mother–child disease associations are strongly time-varying.