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

Multivariate failure time data arise when the sample consists of clusters and each cluster contains several dependent failure times. The semiparametric gamma frailty model (Vaupel, Manton & Stallard, 1979; Clayton, 1978; Oakes, 1982) for multivariate failure times characterises the intracluster dependence by the gamma frailty distribution while allowing the marginal distributions to be unspecified. This paper develops both graphical and numerical techniques for checking the adequacy of this model. The proposed techniques are based on the posterior expectation of the frailty given the observable data. Two examples from genetics are provided.