The hazard level set. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Mao, Guangcai; Liu, Yanyan; Wu, Yuanshan; Yang, Qinglong
• Is Part Of: Journal of nonparametric statistics. Volume 34:Issue 1(2022)
• Page Start: 22
• Page End: 57
• Publication Date: 2022-01-02
• Subjects: Bootstrap -- empirical process -- Hausdorff distance -- random set -- set inference; 62G05 -- 62H12 -- 62N02; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2021.2015767
• Languages: English
• ISSNs: 1048-5252

Abstract

Abstract : The hazard rate function plays a fundamental role in survival analysis. Its statistical inference methods have been systemically and exclusively studied. When does the hazard rate reach a particular warning level? This is a basic question of interest to the investigator but largely left to be explored in practice. We define a level set of hazard rate to address this issue and propose a kernel smoothing estimator for such a level set. In terms of the Hausdorff distance, we establish the consistency, convergence rate and asymptotic distribution of the level set estimator. The validity of the proposed confidence set, based on the bootstrap method, for the level set of hazard rate function is theoretically justified. We conduct comprehensive simulation studies to assess the finite-sample performance of the proposed method, which is further illustrated with a breast cancer study.