A Marginalized Combined Gamma Frailty and Normal Random-effects Model for Repeated, Overdispersed, Time-to-event Outcomes

This article proposes a marginalized model for repeated or otherwise hierarchical, overdispersed time-to-event outcomes, adapting the so-called combined model for time-to-event outcomes of Molenberghs et al. (in press), who combined gamma and normal random effects. The two sets of random effects are used to accommodate simultaneously correlation between repeated measures and overdispersion. The proposed version allows for a direct marginal interpretation of all model parameters. The outcomes are allowed to be censored. Two estimation methods are proposed: full likelihood and pairwise likelihood. The proposed model is applied to data from a so-called comet assay and to data from recurrent asthma attacks in children. Both estimation methods perform very well. From simulation results, it follows that the marginalized combined model behaves similarly to the ordinary combined model in terms of point estimation and precision. It is also observed that the pairwise likelihood required more computation time on the one hand but is less sensitive to starting values and stabler in terms of bias with increasing sample size and censoring percentage than full likelihood, on the other, leaving room for both in practice.