JSM 2004 - Toronto

Abstract #301539

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Activity Number: 435
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: SSC
Abstract - #301539
Title: Estimating Survival Function under Dependent Truncation
Author(s): Lajmi Lakhal*+
Companies: Universite Laval
Address: Departement de Mathematiques et Statistique, Quebec, PQ, G1K 7P4, Canada
Keywords: survival estimator ; semi-survival copulas ; dependent truncation ; Martingales ; Archimedean copulas
Abstract:

Left-truncated data arise when failure is observed only when it is greated or equal to some random quantity. The product-limit estimator for data subject to random truncation rely on the testable assumtion of quasi-independence between failure time X and truncation time T. We present a method to estimate the failure survival function S_X when it is related to the truncation time cumulative distribution function F_T by a known archimedean semi-survival copula. After defining the semi-survival copulas, we will show that the survival estimator can be expressed in terms of the unknown probability c=P(X > T) estimator. This estimator as well as its asymptotic properties are presented. Finally, we will investigate our survival estimator properties.

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