Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods

Chapter 11

Frailty Models

Andreas Wienke

11.1 Introduction

The notion of frailty provides a useful way for modeling unobserved heterogeneity and associations in survival analysis. In its simplest form, frailty is an unobserved random proportionality factor that modifies the hazard function of an individual or related individuals. In essence, the frailty concept goes back to the work of Greenwood and Yule [1] on “accident proneness.” The notion of frailty itself was coined by Vaupel et al. [2] for univariate survival data, and the approach was substantially promoted by its extension to multivariate survival models by Clayton [3] on chronic disease incidence in families (without using the notion of frailty).

Frailty models are extensions of the proportional hazards Cox model [4], the most popular model in survival analysis. Normally, survival analysis implicitly assumes a homogeneous population to be studied (except for observed covariates), which means that all individuals sampled in that study are subject in principle under the same risk (e.g., risk of death, risk of disease recurrence). In many applications, the study population cannot be assumed to be homogeneous but must be considered as a heterogeneous sample (i.e., a mixture of individuals with different hazards). For example, in many cases, it is impossible to measure all relevant covariates related to the outcome of interest, sometimes because of economic, ethical, or clinical reasons, sometimes because the importance of ...