TABLE OF CONTENTS One of the ways in which it was suggested that non-proportionality might come about was in a context in which individuals varied in their risk of death in ways not reflected in the included covariates. This lack of homogeneity has been conceptualised as implying the presence of a random effect in the hazard function and has been termed frailty. The sharing of frailty may also be a useful way of considering the correlation in response of patients that have been formed into matched groups similar on a set of prognostically relevant variables, sampled by a multi-stage process (e.g. individuals within families) or the correlations among repeated or multivariate survival times that might arise from experimental response time measurements. A number of authors have investigated the impact of frailty on estimated effects (eg., Chastang et al., 1988; Pickles and Crouchley, 1995) and this can be large for endogeneous variables. This issue also relates to the possible presence of long-term survivors or cured individuals (Farewell, 1982). Pickles and Crouchley (1994) also considered models in which dose-response was a random effect. Such models can now be relatively easily fitted using multilevel modelling software (Goldstein, 1991). We illustrate in Chapter 9 the Bayesian estimation of a frailty model for the matched pairs data.
It is very tempting to interpret the hazard function as saying something about the development of risk within the individual. A decreasing hazard rate is often interpreted as expressing a biological phenomenon associated with the individual in...
