Frailty modeling for clustered competing risks data with missing cause of failure

Competing risks data often occur within a center in multi-center clinical trials where the event times within a center may be correlated due to unobserved factors across individuals. In this paper, we consider the cause-specific proportional hazards model with a shared frailty to model the association between the event times within a center in the framework of competing risks. We use a hierarchical likelihood approach, which does not require any intractable integration over the frailty terms. In a clinical trial, cause of death information may not be observed for some patients. In such a case, analyses through exclusion of cases with missing cause of death may lead to biased inferences. We propose a hierarchical likelihood approach for fitting the cause-specific proportional hazards model with a shared frailty in the presence of missing cause of failure. We use multiple imputation methods to address missing cause of death information under the assumption of missing at random. Simulation studies show that the proposed procedures perform well, even if the imputation model is misspecified. The proposed methods are illustrated with data from EORTC trial 30791 conducted by European Organization for Research and Treatment of Cancer (EORTC).