Bivariate Survival Models Induced by Frailties
研究了当两个生存时间通过比例风险模型依赖于同一未观测变量（脆弱性）时，由此产生的双变量生存分布类，并扩展至允许负相关，证明了可观测分布能确定未观测脆弱性分布至一个尺度参数。
Abstract 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. The procedures developed here work well with censored data. Although the present work is restricted to problems involving a random sample from a single bivariate distribution, extensions to problems involving higher-dimensional distributions and/or additional measured covariates are undoubtedly possible. Key Words: AssociationCensoringCross ratiosDiagnostic plotsKendall's tauLatent variable modelsLife tablesRank invariance