Frailty Models For Multiple Event Times

Abstract

In some clinical, epidemiologic and animal studies multiple events, possibly of different types, may occur to the same experimental unit at different times. Examples of such data include times to tumor detection, times from remission to relapse into an acute disease phase, and times to discontinuation of an experimental medication. Methods for the statistical analysis of such data need to account for heterogeneity between subjects. This can be achieved by incorporation of additional unobserved random effects into standard survival models. We concentrate on models including frailties — unobserved random proportionality factors applied to the time-dependent intensity function. In this paper we survey some such models, exhibit connections with extensions of the standard Andersen-Gill (1982) model for multiple event times that are reminiscent of the classical results of Greenwood and Yule (1920) on “accident — proneness”, and discuss methods of inference about the frailty distribution and regression parameters. The methods are illustrated by application to some animal tumor data of Gail, Santner and Brown (1980) and to data from a recently completed large multicenter clinical trial.