On Assessing the Association Relationship for Bivariate Current Status Data

We propose inference methods to study the association relationship for bivariate current status data. Although bivariate current status data can be viewed as cross sectional data, we nd that the odds ratio, as a conventional approach to study the association, does not provide useful information to summarize the relationship. Assuming that the two failure times of interest 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 semi-parametric estimator are studied which show that although the rst stage marginal estimators have only n 1=3 convergence rate, the resulting parameter estimator still converges to a normal random variable with the regular n 1=2 rate. The variance of the proposed estimator can be consistently estimated. Simulation results are presented. A community based study of cardiovascular diseases in Taiwan provides an example to illustrate the proposed methods.