Multivariate survival distributions

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Abstract
When two or more observed survival times depend, via a proportional hazards model, on the same unobserved variable, called in this context a frailty, this common dependence induces an association between the observed times. This paper focuses on the class of multivariate survival distributions generated by such models. These turn out to be a subclass of the archimedean copula models described among others by Genest and Mackay (1986). A special case, important in survival analysis, is Gumbells (1960) Type B distribution of extreme values, which is obtained from a positive stable frailty distribution. We discuss characterizations of the frailty distribution via measures of association and methods for parametric and nonparametric inference from data possibly subject to censoring. We briefly contrast this situation with that obtained when repeated events can be observed on the same subject, leading to ordered failure time data.