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Multivariate survival distributions. (English) Zbl 1378.62121
Summary: 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 C. Genest and R. J. MacKay [Can. J. Stat. 14, 145–159 (1986; Zbl 0605.62049)]. 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.

MSC:
62N05 Reliability and life testing
62P10 Applications of statistics to biology and medical sciences; meta analysis
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