TITLE: Short- and Long-Term Effects in Prostate Cancer Survival: Analysis of Treatment Efficacy and Risk Prediction PRINCIPAL INVESTIGATOR:

Introducing a random effect into the Cox model is a useful tool forbuilding hierarchical families of univariate semiparametric regressionsurvival models. Hougaard [1984] used the Laplace transform to buildfrailty models with explicitly defined survival functions and random ef-fects. The family derived from stable distributions was then extended[Aalen, 1992] to frailty variables following a Discrete–Continuous com-pound (Poisson–Gamma) structure. Still, in this form the techniquesapplies only to a subset of frailty models. In this paper we extend theidea of compounding first to arbitrary frailty models and then to non-frailty Nonlinear Transformation Models (NTM). EM algorithm canbe used to provide inference with frailty models. Motivated by sec-ond moment properties of frailty models, Tsodikov [2003] generalizedthe EM algorithm into a non-frailty frame represented by the Quasi-EM algorithm (QEM). We derive a chain rule showing that QEMwill fit any model constructed using the new composition technique,provided it is applicable to the submodels. Simulations, real dataand a variety of models are used to illustrate the composition tech-nique. Non-identifiability aspect of semiparametric frailty models isdiscussed. Many important modelling issues and links are highlighted.