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Statistica Sinica 21 (2011), 349-367



Takeshi Emura, Weijing Wang and Hui-Nien Hung

National Chiao-Tung University

Abstract: We investigate the dependent relationship between two failure time variables that truncate each other. Chaieb, Rivest, and Abdous (2006) proposed a semi-parametric model under the so-called ``semi-survival" Archimedean-copula assumption and discussed estimation of the association parameter, the truncation probability, and the marginal functions. Here the same model assumption is adopted but different inference approaches are proposed. For estimating the association parameter, we extend the conditional likelihood approach (Clayton (1978)) and the two-by-two table approach (Wang (2003)) to dependent truncation data. We further show that the three estimators, including that proposed by Chaieb, Rivest, and Abdous (2006), differ in weights. The likelihood approach provides the formula for a good weight. Large sample properties of the proposed methods are established by applying the functional delta method, which can handle estimating functions that are not in the form of U-statistics. Analytic formulae for the asymptotic variance estimators are provided. Two competing methods are compared via simulations, and applied to the transfusion-related AIDS data.

Key words and phrases: Archimedean copula model, conditional likelihood, functional delta method, Kendall's tau, truncation data, two-by-two table.

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