estimating kendall's τ when both times are subject to interval censoring

A common challenge in working with longitudinal data is dealing with incomplete data‎. ‎according to the existing studies on the dependence structure of survival times‎, ‎it is a riveting topic for researchers to estimate survival functions and dependence parameters‎, ‎especially in biology and medical research‎. ‎some researchers have studied the aforementioned subjects with left‎- ‎or right-truncated or censored data‎. ‎when the data involves interval censoring‎, ‎the mentioned issues still need to be solved or modified‎. ‎in this article‎, ‎we propose two alternative approaches to the estimation of a dependence parameter and kendall's τ‎, ‎given an interesting covariate and interval-censored dataset‎. ‎more precisely‎, ‎these approaches include non-parametric and semi-parametric methods to estimate the copula dependence parameter and kendall's τ‎, ‎which are evaluated by simulation‎. ‎finally‎, ‎we apply the mentioned approaches to a real-world dataset and copula's goodness-of-fit tests.