Abstract

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.

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