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A permutation test for independence of the event of interest and a prognostic factor in the competing risks framework
Journal of the Korean Data & Information Science Society 2018;29:1381-90
Published online November 30, 2018
© 2018 Korean Data and Information Science Society.

Jinheum Kim1 · Su-Hyun Kim 2

1Department of Applied Statistics, University of Suwon
Correspondence to: Professor, Department of Applied Statistics, University of Suwon, Hwaseong, 18323, Korea. E-mail :
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03028535).
Received October 8, 2018; Revised November 17, 2018; Accepted November 18, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In clinical studies, patients are often classified into low- and high-risk groups based on prognostic factors. Moreover, patients may experience several different types of events during follow-up under the competing risks framework. We propose a cutoff estimator as the value that yields the maximum of the absolute of the standardized linear rank statistic and also propose a maximally selected linear rank statistic for testing independence of the event of interest and the prognostic factor. The proposed test statistic converges in distribution to that of the supremum of a standardized Brownian bridge. Further, to overcome the conservativeness of the test based on an approximation of the asymptotic distribution, we also propose a permutation test based on permuted samples. We illustrate the proposed methods with two real datasets collected from Seoul Samsung hospital.
Keywords : Cumulative incidence function, diffuse large B-cell lymphoma, Gray’s statistic, hepatocellular carcinoma, linear rank statistic, permutation test.