Requiem for the Passing–Bablok nonparametric regression in assessing the agreement between two measurement methods
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Bruno Mario Cesana
und
Paolo Antonelli
Abstract
Objectives
Regulatory guidelines recommend non-parametric Passing–Bablok regression for evaluating the agreement between two measurement methods in laboratory settings. However, concluding for the agreement if the 95 % CI of the slope and of the intercept include 1 and 0, respectively is incorrect since the agreement assessment must focus on a null hypothesis of not equivalence and an alternative hypothesis of equivalence.
Methods
We exhaustively simulated appropriate structural models with several values of slope, intercept and measurement error by keeping equal variances and means of the two methods. We calculated the slope and intercept bias of four regressions: non-parametric Passing–Bablok, Theil, Ordinary Least Squares and Deming. In addition, we calculated the percentages of the agreement according to the not shareable Passing–Bablok suggestion. Furthermore, we calculated the percentages of the 95 % CI of the slope and of the intercept included within sensible equivalence thresholds for assessing the agreement.
Results
Passing–Bablok procedure gives unbiased estimates, a little more and less biased than those from Deming’s regression. The percentages of rejecting the hypothesis of no-agreement, according to the wrong Passing–Bablok’s approach are correctly near to 0.05 Type I error under the agreement and also for 0.990≤slopes≤1.005. However, they are too low for slopes >1.05 and <0.950.
Conclusions
The Passing–Bablok 95 % CIs are too wide for being included in sensible agreement thresholds according to a population equivalence model and, finally, this approach cannot be considered under the best agreement model of the individual equivalence.
Acknowledgments
The authors would like to thank Simona Ferraro PhD for many discussions about the agreement between measurement methods in the laboratory settings.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: B.M.C.: Conceptualization, writing original draft, statistical methodology data analysis; P.A.: writing, review and editing statistical methodology, supervision. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: None declared.
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Data availability: Not applicable.
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Supplementary Material
This article contains supplementary material (https://doi.org/10.1515/cclm-2025-0581).
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