Modeling the association of bivariate interval-censored data using the copula approach

In a survival study, it may not be possible to record the exact event time but only that the event has occurred between two time points or still has to occur, leading to interval-censored survival times.Recently, Sun et al. (Scand. J. Stat. 2006; 33(4):637-649) suggested to fit a Clayton copula with nonparametric marginal distributions to estimate the association for bivariate interval-censored failure data. We propose here to model the marginal distributions with an accelerated failure time model with a flexible error term as suggested by Komárek et al. (J. Comput. Graph. Stat. 2005; 14(3):726-745) in combination with a one parameter copula. In addition, we allow the association parameter of the copula to depend on covariates.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 a longitudinal dental study.