Prediction of random effects with misspecified AFT random effect models

Abstract

The accelerated failure time (AFT) model with random effects has been widely used for clustered or correlated time-to-event data as an alternative to frailty model which is the Cox’s proportional hazards model with random effects. The AFT random effect model usually assumes a normal distribution for random effect distribution. It is well known that the estimated regression parameters in the AFT model are robust against various violations of the assumed model. However, the impact of prediction (or estimation) of random effect, when the assumed normal random effect is misspecified, has been relatively less studied. In this paper, we investigate the impact of misspecification of normal random effect distribution on the prediction of random effect under the AFT random effect model. Here, the random effect is estimated using the hierarchical likelihood (h-likelihood) which is useful for the inference of random effects. The proposed method is demonstrated using simulation studies and a real data set.