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Nonparametric Assessment of Differences Between Competing Risk Hazard Ratios: Application to Racial Differences in Pediatric Chronic Kidney Disease Progression

Authors Ng DK, Antiporta DA, Matheson MB, Muñoz A

Received 2 August 2019

Accepted for publication 18 December 2019

Published 20 January 2020 Volume 2020:12 Pages 83—93


Checked for plagiarism Yes

Review by Single anonymous peer review

Peer reviewer comments 4

Editor who approved publication: Professor Henrik Toft Sørensen

Derek K Ng, Daniel A Antiporta, Matthew B Matheson, Alvaro Muñoz

Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA

Correspondence: Alvaro Muñoz
Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, 615 Wolfe Street Room E7648, Baltimore, MD 21205, USA
Tel +1 410-955-2792

Abstract: Associations between an exposure and multiple competing events are typically described by cause-specific hazard ratios (csHR) or subdistribution hazard ratios (sHR). However, diagnostic tools to assess differences between them have not been described. Under the proportionality assumption for both, it can be shown mathematically that the sHR and csHR must be equal, so reporting different time-constant sHR and csHR implies non-proportionality for at least one. We propose a simple, intuitive approach using the ratio of sHR/csHR to nonparametrically compare these metrics. In general, for the non-null case, there must be at least one event type for which the sHR and csHR differ, and the proposed diagnostic will be useful to identify these cases. Furthermore, once standard methods are used to estimate the csHR, multiplying it with our nonparametric estimate for the sHR/csHR ratio will yield estimates of sHR which fulfill intrinsic linkages of the subhazards that separate analysis may violate. In addition, for non-null cases, at least one must be time dependent (i.e., non-proportional), and thus our tool serves as an indirect test of the proportionality assumption. We applied this proposed diagnostic tool to data from a cohort of children with congenital kidney disease to describe racial differences in the time to first dialysis or first transplant and extend methods to include adjustment for socioeconomic factors.

Keywords: survival analysis, nonparametric methods, competing risk analysis, cause-specific hazard ratios, sub-distribution hazard ratios, chronic kidney disease

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