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Comparison of Kendall's tau estimators for bivariate censored data
Journal of the Korean Data & Information Science Society 2018;29:513-21
Published online March 31, 2018
© 2018 Korean Data and Information Science Society.

Jeong Jae Park1 · Hyemi Choi2

1Department of Statistics, Chonbuk National University
2Department of Statistics (Institute of Applied Statistics), Chonbuk National University
Correspondence to: Professor, Department of Statistics (Institute of Applied Statistics), Chonbuk National University, Jeollabuk-do 54896, Korea. E-mail: hchoi@jbnu.ac.kr
Received January 11, 2018; Revised February 26, 2018; Accepted March 5, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Kendall's τ is the important association measure and commonly used in biomedical application. Under censoring the estimation of τ has been challenging. Recently Hsieh (2010) replaced a censored event-time by a imputation with the conditional information and calculated the τ estimator based on the imputed data.We propose modified Hsieh's approach of the Kendall's tau statistic in the presence of univariate right censoring by implementing with the nonparametric bivariate survival function estimators in Lin and Ying (1993) and Wang and Wells (1997) with good performance under univariate (right)-censoring. Through simulation study the proposed estimators are compared with other practical estimators τ^MO (Oakes, 2008) and τ^LRB (Lakhal et al:, 2009). In the case of data under heavy censoring or with weak association, the modified Hsieh estimators show better performance compared to τ^LRB and τ^MO and seem comparable in other cases of the simulation. An illustrative analysis is also given.
Keywords : Bivariate survival function, Kendall's tau, univariate-censoring.