A two-stage semiparametric estimator is proposed to estimate the association measure for bivariate survival data that are subject to hybrid censoring: one event time is right censored and the other is observed as current status data, or subject to interval censoring case 1. The bivariate data are assumed to follow a copula model, in which the association parameter is of primary interest. The consistency and asymptotic normality of the proposed estimator are established based on empirical process theories. Simulation studies indicate that the estimator performs quite well with a moderate sample size. The method is applied to a motivating HIV example, which studies the effect of GB virus type C (GBV-C) co-infection on the survival of HIV infected individuals
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