Aspects of the Armitage–Doll gamma frailty model for cancer incidence data

Abstract

AbstractUsing solid cancer incidence data from atomic bomb survivors in Japan, we examine some aspects of the Armitage–Doll gamma frailty (ADF) model. We consider the following two interpretations for lack of fit of the Armitage–Doll multistage (AD) model found with cancer data: the AD type individual hazards are heterogeneous or the individual hazards increase more slowly with age than the AD type hazards. In order to examine these interpretations, we applied the ADF model and the modified AD model to radiation‐related cancer incidence rates. We assessed the magnitude of frailty by a frailty parameter at the ADF model and departures from the AD‐type baseline hazard by a shape increment parameter at the modified AD model. Akaike's information criterion (AIC) was used to examine the goodness of fit of the models. The modified AD model provided as good a fit as the ADF model. Our results support both interpretations and imply that these interpretations may be practically unidentifiable in univariate failure time data. Thus, results from the frailty model for univariate failure time data should be interpreted carefully. Copyright © 2004 John Wiley & Sons, Ltd.