How to regress and predict in a Bland-Altman plot? Review and contribution based on tolerance intervals and correlated-errors-in-variables models

Statistics in Medicine
Bernard G Francq, Bernadette Govaerts

Abstract

Two main methodologies for assessing equivalence in method-comparison studies are presented separately in the literature. The first one is the well-known and widely applied Bland-Altman approach with its agreement intervals, where two methods are considered interchangeable if their differences are not clinically significant. The second approach is based on errors-in-variables regression in a classical (X,Y) plot and focuses on confidence intervals, whereby two methods are considered equivalent when providing similar measures notwithstanding the random measurement errors. This paper reconciles these two methodologies and shows their similarities and differences using both real data and simulations. A new consistent correlated-errors-in-variables regression is introduced as the errors are shown to be correlated in the Bland-Altman plot. Indeed, the coverage probabilities collapse and the biases soar when this correlation is ignored. Novel tolerance intervals are compared with agreement intervals with or without replicated data, and novel predictive intervals are introduced to predict a single measure in an (X,Y) plot or in a Bland-Atman plot with excellent coverage probabilities. We conclude that the (correlated)-errors-in-variab...Continue Reading

References

Feb 1, 1997·Clinical and Experimental Pharmacology & Physiology·J Ludbrook
Jun 13, 2002·Clinical and Experimental Pharmacology & Physiology·John Ludbrook
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Citations

Sep 3, 2016·Statistical Methods in Medical Research·Andrew Carkeet, Yee Teng Goh
Nov 22, 2018·Pediatric Nephrology : Journal of the International Pediatric Nephrology Association·Niels ZiegelaschKatalin Dittrich
Jun 21, 2019·Journal of Oral Science·Essam A AlsanawiAshraf A El-Metwally
Apr 26, 2019·Statistical Methods in Medical Research·Patrick Taffé
Jun 20, 2020·Therapeutic Innovation & Regulatory Science·Colleen RussellSusan Wong
Oct 30, 2019·Statistics in Medicine·Bernard G FrancqWalter Hoyer
Apr 4, 2017·Journal of Oral Science·Ayako OkadaNobuhiro Hanada
Jul 23, 2020·Journal of Hypertension·Michael BöhmLuis M Ruilope
Mar 23, 2021·Expert Review of Pharmacoeconomics & Outcomes Research·Kanyarat KatanyooArthon Riewpaiboon

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