A multilevel model for hierarchical, repeated, and overdispersed time-to-event outcomes and its estimation strategies

Abstract

The aim of this article is to propose a multilevel combined model for repeated, hierarchical, and overdispersed time-to-event outcomes, extending the so-called combined model proposed by Molenberghs et al. (2010), and using three different estimation strategies: full likelihood, pseudo-likelihood, and Bayesian estimation. For the first two estimation methods, we implemented the alternating imputation posterior (AIP) algorithm (Clayton and Rasbash, 1999). It is shown that the multilevel combined model can be fitted nicely using all three estimation methods. In addition, the multilevel combined model has the advantage that it not only can capture the hierarchical structure of the data but also can accommodate overdispersion within the data set. From our simulation results, it follows that the multilevel combined model performs well in terms of point estimation and its precision, fitted with the three different estimation methods. We also observed that pairwise likelihood estimation, a particular form of pseudo-likelihood, is more time-intensive than full likelihood and Bayesian estimation. However, pseudo-likelihood estimation is less sensitive to starting values.