Testing independence of bivariate interval‐censored data using modified Kendall's tau statistic

Abstract

In this paper, we study a nonparametric procedure to test independence of bivariate interval censored data; for both current status data (case 1 interval-censored data) and case 2 interval-censored data. To do it, we propose a score-based modification of the Kendall's tau statistic for bivariate interval-censored data. Our modification defines the Kendall's tau statistic with expected numbers of concordant and disconcordant pairs of data. The performance of the modified approach is illustrated by simulation studies and application to the AIDS study. We compare our method to alternative approaches such as the two-stage estimation method by Sun et al. (Scandinavian Journal of Statistics, 2006) and the multiple imputation method by Betensky and Finkelstein (Statistics in Medicine, 1999b).

Robust Rank Canonical Correlation Analysis for Multivariate Survival Data

“…The key idea is to construct an unbiased estimator of the rank correlation for the pairwise underlying population. For instance, we can cope with multivariate interval-censored data using modified Kendall's τ statistic (Kim et al, 2015) in our formulation.…”

A spline-based nonparametric analysis for interval-censored bivariate survival data

“…For this case, the dependence test statistic can be constructed based on a functional of the NPMLEs for the marginal distribution functions. Kim et al (2015) adopted the approach for bivariate right censoring by Brown et al (1974) and developed an association test based on estimating Kendall s τ for bivariate interval-censored data.…”

“…However, the asymptotic normality of the test statistic given by Kim et al (2015) seems difficult to justify theoretically when the majority of censoring rectangles are overlapped. It is noted that all aforementioned inferences for interval-censored data were either under specific model structure for the joint distribution (Wen and Chen, 2013;Zeng et al, 2017;Zhou et al, 2017;Hu et al, 2017;Wang and Ding, 2000;Sun et al, 2006), or to deal with special cases of interval-censored data (Ding and Wang, 2004;Jewell et al, 2005) or was quite ad-hoc (Kim et al, 2015). To the best of our knowledge there is no rigorously justified model-free nonparametric method in the literature for the inference of association between bivariate interval-censored time-to-event data.…”