SEMI-PARAMETRIC INFERENCE FOR COPULA MODELS FOR TRUNCATED DATA

We investigate the dependent relationship between two failure time vari- ables that truncate each other. Chaieb, Rivest, and Abdous (2006) proposed a semi- parametric model under the so-called "semi-survival" Archimedean-copula assump- tion and discussed estimation of the association parameter, the truncation prob- ability, and the marginal functions. Here the same model assumption is adopted but different inference approaches are proposed. For estimating the association pa- rameter, we extend the conditional likelihood approach (Clayton (1978)) and the two-by-two table approach (Wang (2003)) to dependent truncation data. We fur- ther 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.