A multinomial generalized linear mixed model for clustered competing risks data

Clustered competing risks data are a complex failure time data scheme. Its main characteristics are the cluster structure, which implies a latent within-cluster dependence between its elements, and its multiple variables competing to be the one responsible for the occurrence of an event, the failure. To handle this kind of data, we propose a full likelihood approach, based on generalized linear mixed models instead the usual complex frailty model. We model the competing causes in the probability scale, in terms of the cumulative incidence function (CIF). A multinomial distribution is assumed for the competing causes and censorship, conditioned on the latent effects that are accommodated by a multivariate Gaussian distribution. The CIF is specified as the product of an instantaneous risk level function with a failure time trajectory level function. The estimation procedure is performed through the R package Template Model Builder, an C++ based framework with efficient Laplace approximation and automatic differentiation routines. A large simulation study was performed, based on different latent structure formulations. The model fitting was challenging and our results indicated that a latent structure where both risk and failure time trajectory levels are correlated is required to reach reasonable estimation.