Estimation of association parameters in copula models for bivariate left-truncated and right-censored data

We investigate the problem of estimating the association between two related survival variables when they follow a copula model and bivariate left-truncated and right-censored data are available. By expressing truncation probability as the functional of marginal survival functions, we propose a two-stage estimation procedure for estimating the parameters of Archimedean copulas. The asymptotic properties of the proposed estimators are established. Simulation studies are conducted to investigate the finite sample properties of the proposed estimators. The proposed method is applied to a bivariate RNA data.