Marginal Models for Clustered Time-to-Event Data with Competing Risks Using Pseudovalues

Many time-to-event studies are complicated by the presence of competing risks and by nesting of individuals within a cluster, such as patients in the same center in a multicenter study. Several methods have been proposed for modeling the cumulative incidence function with independent observations. However, when subjects are clustered, one needs to account for the presence of a cluster effect either through frailty modeling of the hazard or subdistribution hazard, or by adjusting for the within-cluster correlation in a marginal model. We propose a method for modeling the marginal cumulative incidence function directly. We compute leave-one-out pseudo-observations from the cumulative incidence function at several time points. These are used in a generalized estimating equation to model the marginal cumulative incidence curve, and obtain consistent estimates of the model parameters. A sandwich variance estimator is derived to adjust for the within-cluster correlation. The method is easy to implement using standard software once the pseudovalues are obtained, and is a generalization of several existing models. Simulation studies show that the method works well to adjust the SE for the within-cluster correlation. We illustrate the method on a dataset looking at outcomes after bone marrow transplantation.