ML AND REML ESTIMATION IN SURVIVAL ANALYSIS WITH TIME-DEPENDENT CORRELATED FRAILTY

In the study of multiple failure times for the same subjects, for exam ple, recurrent infections for patients with a given disease, there are often subject effects, that is, subjects have different risks that ca nnot be explained by known covariates. Standard methods, which ignore subject effects, lead to overestimation of precision. The frailty mode l for subject effects is better, but can be insufficient, because it a ssumes that subject effects are constant over time. Experience has sho wn that the dependence between different time periods often decreases with distance in time. Such a model is presented here, assuming that t he frailty is no longer constant, but time varying, with one value for each spell. The main example is a first-order autoregressive process. This is applied to a data set of 128 patients with chronic granuiomat ous disease (CGD), participating in a placebo controlled randomized tr ial of gamma interferon (gamma-IFN), suffering between 0 and 7 infecti ons. It is shown that the time varying frailty model gives a significa ntly better fit than the constant frailty model. (C) 1998 John Wiley & Sons, Ltd.