On assessing the association for bivariate current status data

Abstract

Current status data are common especially in studies of epidemiology. In its univariate setting, the failure time variable of interest is never observed but can only be determined to lie below or above a random monitoring (censoring) time. Such a data structure is also called as interval censoring of case I in Groeneboom and Wellner (1992). In the talk, we discuss the bivariate case. The work was motivated by a community-based study of cardiovascular diseases in Taiwan conducted by Professor 潘文涵 at the Institute of Biomedicine, Academia Sinica. Pairwise associations between the onset ages of three chronic diseases, namely hypertension, diabetes mellitus and hypercholesterolemia are of interest while only current status data are available. In the talk, I will present the results based on my two papers jointly with Professor Adam Ding. In the first paper (Biometrika, 2000), we propose a semi-parametric inference method to estimate the association parameter for a copula model. In the second article, which is still under revision, we propose a nonparametric testing procedure to test independence between the two failure times. Both methods require plugging in the marginal nonparametric MLEs which have only n1/3 convergence rate. However the proposed estimators, which are smooth functionals of the marginal MLEs, still maintain the regular n1/2 convergence rate.