Estimating survival under a dependent truncation

Lajmi Lakhal Chaieb, Louis-Paul Rivest and Belkacem Abdous

Biometrika, 2006, vol. 93, issue 3, 655-669

Abstract: 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-sub-i,Y-sub-i) satisfying Y-sub-i > X-sub-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-sub-X(.) and a survival distribution S-sub-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-sub-X(.) or S-sub-Y(.). We derive an estimator for the copula parameter α 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. Copyright 2006, Oxford University Press.

Date: 2006
References: Add references at CitEc
Citations: View citations in EconPapers (26)

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/93.3.655 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:93:y:2006:i:3:p:655-669

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().