Seminars

Nonparametric analysis of multivariate competing risks data

While nonparametric analyses of bivariate failure times have been widely studied, nonparametric analyses of bivariate competing risks data have not been investigated. Such analyses are important in familial association studies, where multiple interacting failure types may invalidate nonparametric analyses for independently censored clustered survival data. We develop nonparametric estimators for the bivariate cause-specific hazards function and the bivariate cumulative incidence function, which are natural extensions 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. Summary association measures are proposed and yield formal tests of independence in clusters. The  estimators and test statistics perform well in simulations with realistic sample  sizes. Their practical utility is illustrated in an analysis of dementia in the  Cache County Study.