Oakes, David Bivariate survival models induced by frailties. (English) Zbl 0677.62094 J. Am. Stat. Assoc. 84, No. 406, 487-493 (1989). When 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. Cited in 7 ReviewsCited in 264 Documents MSC: 62N05 Reliability and life testing Keywords:Kendall tau; life tables; rank invariance; proportional-hazards model; bivariate survival distributions; negative association; frailty distribution; cross-ratio function; characterization results; diagnostic plots; latent variable models; censoring PDFBibTeX XMLCite \textit{D. Oakes}, J. Am. Stat. Assoc. 84, No. 406, 487--493 (1989; Zbl 0677.62094) Full Text: DOI