Graphical Tests for the Frailty Distribution in the Shared Frailty Model

We extend a diagnostic plot for the frailty distribution in proportional hazards models to the case of shared frailty. The plot is based on a closure property of exponential family failure distributions with canonical statistics z and g(z), namely that the frailty distribution among survivors at time t has the same form, with the same values of the parameters associated with g(z). We extend this property to shared frailty, considering various definitions of a “surviving” cluster at time t. We illustrate the effectiveness of the method in the case where the “death” of the cluster is defined by the first death among its members.