On assessing the association for bivariate current status data

Assuming that the two failure times of interest with bivariate current status data follow a bivariate copula model, we propose a two-stage estimation procedure to estimate the association parameter which is related to Kendall's tau. Asymptotic properties of the proposed semiparametric estimator show that, although the first-stage marginal estimators have a convergence rate of only n^1/3, the resulting parameter estimator still converges to a normal random variable with the usual n^1/2 rate. The variance of the proposed estimator can be consistently estimated. Simulation results are presented, and a community-based study of cardiovascular diseases in Taiwan provides an illustrative example.