Robust frailty modelling using non-proportional hazards models

Correlated survival times can be modelled by introducing a random effect, or frailty component, into the hazard function. For multivariate survival data, we extend a non-proportional hazards (PH) model, the generalized time-dependent logistic survival model, to include random effects. The hierarchical likelihood procedure, which obviates the need for marginalization over the random effect distribution, is derived for this extended model and its properties are discussed. The extended model leads to a robust estimation result for the regression parameters against the misspecification of the form of the basic hazard function or frailty distribution compared to PH-based alternatives. The proposed method is illustrated by two practical examples and a simulation study which demonstrate the advantages of the new model.