Association measures for clustered competing risks

We propose a semiparameteric model for multivariate clustered competing risks data when the cause-specific failure times and the occurrence of competing risk events among subjects within the same cluster are of interest. The cause-specific hazard functions are assumed to follow Cox proportional hazard models, and the associations between failure times given the same or different cause events and the associations between occurrences of competing risk events within the same cluster are investigated through copula models. A cross-odds ratio measure is explored under our proposed models. Two-stage estimation procedure is proposed in which the marginal models are estimated in the first stage, and the dependence parameters are estimated via an expectation-maximization algorithm in the second stage. The proposed estimators are shown to yield consistent and asymptotically normal under mild regularity conditions. Simulation studies are conducted to assess finite sample performance of the proposed method. The proposed technique is demonstrated through an application to a multicenter Bone Marrow transplantation dataset.