Estimating local and global measures of association for bivariate interval censored data with a smooth estimate of the density

Measures of association for bivariate interval censored data have not yet been studied extensively. Betensky and Finkelstein (Statist. Med. 1999; 18:3101-3109) proposed to calculate Kendall's coefficient of concordance using a multiple imputation technique, but their method becomes computer intensive for moderate to large data sets. We suggest a different approach consisting of two steps. Firstly, a bivariate smooth estimate of the density of log-event times is determined. The smoothing technique is based on a mixture of Gaussian densities fixed on a grid with weights determined by a penalized likelihood approach. Secondly, given the smooth approximation several local and global measures of association can be estimated readily. The performance of our method is illustrated by an extensive simulation study and is applied to tooth emergence data of permanent teeth measured on 4468 children from the Signal-Tandmobiel study.