Checking the adequacy of the gamma frailty model for multivariate failure times

Multivariate failure time data arise when the sample consists of clusters a nd each cluster contains several dependent failure times. The semiparametri c gamma frailty model (Vaupel, Manton & Stallard, 1979; Clayton, 1978; Oake s, 1982) for multivariate failure times characterises the intracluster depe ndence by the gamma frailty distribution while allowing the marginal distri butions to be unspecified. This paper develops both graphical and numerical techniques for checking the adequacy of this model. The proposed technique s are based on the posterior expectation of the frailty given the observabl e data. Two examples from genetics are provided.