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-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 discussed. The extended model leads to a robust estimation result for the regression parameters against the mis-specification 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.