Model selection for frailty structures

Frailty models are now widely used for analyzing multivariate survival data. An open question is how best to determine how to select the most appropriate frailty structure supported by the data. Herein, we develop a proce- dure for selecting the optimal frailty structure from a set of (possibly) non-nested frailty models. Our focus is on the dispersion parameters which define the frailty structure. We propose two new AIC criteria: one based on the deviance for goodness of fit and the other on the extended restricted likelihood (ERL) of Lee and Nelder (1996). A simulation study shows that the AIC based on the extended restricted likelihood is better when attention is focussed on selecting the frailty structure.