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Article

Nonparametric Limits of Agreement for Small to Moderate Sample Sizes: A Simulation Study

1
Department of Toxicology, Charles River Laboratories Copenhagen A/S, 4623 Lille Skensved, Denmark
2
Department of Mathematics and Computer Science, University of Southern Denmark, 5230 Odense M, Denmark
3
Department of Nuclear Medicine, Odense University Hospital, 5000 Odense C, Denmark
4
Department of Clinical Research, University of Southern Denmark, 5000 Odense C, Denmark
*
Author to whom correspondence should be addressed.
Received: 7 August 2020 / Revised: 24 August 2020 / Accepted: 25 August 2020 / Published: 28 August 2020
(This article belongs to the Special Issue Robust Statistics in Action)
The assessment of agreement in method comparison and observer variability analysis of quantitative measurements is usually done by the Bland–Altman Limits of Agreement, where the paired differences are implicitly assumed to follow a normal distribution. Whenever this assumption does not hold, the 2.5% and 97.5% percentiles are obtained by quantile estimation. In the literature, empirical quantiles have been used for this purpose. In this simulation study, we applied both sample, subsampling, and kernel quantile estimators, as well as other methods for quantile estimation to sample sizes between 30 and 150 and different distributions of the paired differences. The performance of 15 estimators in generating prediction intervals was measured by their respective coverage probability for one newly generated observation. Our results indicated that sample quantile estimators based on one or two order statistics outperformed all of the other estimators and they can be used for deriving nonparametric Limits of Agreement. For sample sizes exceeding 80 observations, more advanced quantile estimators, such as the Harrell–Davis and estimators of Sfakianakis–Verginis type, which use all of the observed differences, performed likewise well, but may be considered intuitively more appealing than simple sample quantile estimators that are based on only two observations per quantile. View Full-Text
Keywords: agreement; Bland-Altman plot; coverage; limits of agreement; method comparison; quantile estimation; repeatability; reproducibility agreement; Bland-Altman plot; coverage; limits of agreement; method comparison; quantile estimation; repeatability; reproducibility
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MDPI and ACS Style

Frey, M.E.; Petersen, H.C.; Gerke, O. Nonparametric Limits of Agreement for Small to Moderate Sample Sizes: A Simulation Study. Stats 2020, 3, 343-355. https://0-doi-org.brum.beds.ac.uk/10.3390/stats3030022

AMA Style

Frey ME, Petersen HC, Gerke O. Nonparametric Limits of Agreement for Small to Moderate Sample Sizes: A Simulation Study. Stats. 2020; 3(3):343-355. https://0-doi-org.brum.beds.ac.uk/10.3390/stats3030022

Chicago/Turabian Style

Frey, Maria E., Hans C. Petersen, and Oke Gerke. 2020. "Nonparametric Limits of Agreement for Small to Moderate Sample Sizes: A Simulation Study" Stats 3, no. 3: 343-355. https://0-doi-org.brum.beds.ac.uk/10.3390/stats3030022

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