Bivariate survival models induced by frailties.

*(English)*Zbl 0677.62094When two observed survival times depend via a proportional-hazards model on the same unobserved variable, called a frailty, this common dependence induces an association between the observed times. This article considers the class of bivariate survival distributions that can arise in this way, extends it to allow negative association, and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter. A cross-ratio function, easily estimated even from censored data, is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples. The models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data. The main distinguishing feature of survival data is the possibility of censoring, which makes the standard methods difficult to apply.

##### MSC:

62N05 | Reliability and life testing |