Introduction

Survival analysis is an important statistical field that is required for data analysis in different disciplines. There are a large number of textbooks on the basic concepts of survival analysis, e.g., Collett (2003) and Machin et al. (2006). In recent years a number of papers have been published extending the classical survival models to models that are suitable for the analysis of clustered survival data: frailty models. A wide variety of frailty models and several numerical techniques to fit these models have been studied in these papers. Only a limited number of textbooks have chapters devoted to frailty models, all of them containing only some specific aspects on frailty models. Klein and Moeschberger (1997) have a chapter on the use of the EM algorithm in semiparametric frailty models. Ibrahim et al. (2001) discuss both parametric and semiparametric frailty models but only in a Bayesian context. Hougaard (2000) discusses, among other techniques to model multivariate survival data, the frailty model mainly assuming a parametric model. Finally, Therneau and Grambsch (2000) discuss inference for the semiparametric frailty model using penalised partial likelihood.