Estimating survival under a dependent truncation

• 成果类型: Article
• 署名作者: Chaieb, Lajmi Lakhal; Rivest, Louis-Paul; Abdous, Belkacem
• 署名单位: Laval University; Laval University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/93.3.655
• 发表日期: 2006
• 页码: 655669
• 关键词: PROPORTIONAL HAZARDS MODEL; association; inference; FAILURE; INDEPENDENCE; times

摘要

The product-limit estimator calculated from data subject to random left-truncation relies on the testable assumption of quasi-independence between the failure time and the truncation time. In this paper, we propose a model for a truncated sample of pairs (X-i,Y-i) satisfying Y-i > X-i. A possible dependency between the truncation time and the variable of interest is modelled with a parametric family of copulas. The model also features a distribution function F-X(.) and a survival distribution S-Y(.) associated with the marginal behaviours of X and Y in the observable region Y > X. Semiparametric estimators for these two functions are proposed; they do not make any parametric assumption about either F-X(.) or S-Y(.). We derive an estimator for the copula parameter alpha based on the conditional Kendall's tau. We generalise the copula-graphic estimators of Zheng & Klein (1995) to truncated variables. The asymptotic distributions of all these estimators are then investigated. The methods are illustrated with a real dataset on HIV infection by transfusion and by simulations.