Nonparametric estimation and test of conditional Kendall's tau under semi-competing risks data and truncated data

In this article, we focus on estimation and test of conditional Kendall's tau under semi-competing risks data and truncated data. We apply the inverse probability censoring weighted technique to construct an estimator of conditional Kendall's tau, . Then, this study provides a test statistic for , where . When two random variables are quasi-independent, it implies . Thus, is a proxy for quasi-independence. Tsai [12], and Martin and Betensky [10] considered the testing problem for quasi-independence. Via simulation studies, we compare the three test statistics for quasi-independence, and examine the finite-sample performance of the proposed estimator and the suggested test statistic. Furthermore, we provide the large sample properties for our proposed estimator. Finally, we provide two real data examples for illustration.