title: How to regress and predict in a Bland-Altman plot? Review and contribution based on tolerance intervals and correlated-errors-in-variables models.
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-variables regressions should not be avoided in method comparison studies, although the Bland-Altman approach is usually applied to avert their complexity. We argue that tolerance or predictive intervals are better alternatives than agreement intervals, and we provide guidelines for practitioners regarding method comparison studies. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Institut de Statistique, Biostatistique et sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays 20, Louvain-la-Neuve, 1348, Belgium.|Robertson Centre for Biostatistics, University of Glasgow, University Avenue, Level 11 Boyd Orr Building, Glasgow, G12 8QQ, Scotland, U.K.
authors.forename: Bernard G
authors.initials: BG
authors.lastname: Francq
authors.affiliation: Institut de Statistique, Biostatistique et sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays 20, Louvain-la-Neuve, 1348, Belgium.
authors.forename: Bernadette
authors.initials: B
authors.lastname: Govaerts
mesh_terms: D015982:Bias; D056808:Biostatistics; D001795:Blood Pressure Determination / Q000706:statistics & numerical data; D003198:Computer Simulation; D016001:Confidence Intervals; D000074099:Equivalence Trials as Topic; D006801:Humans; D015233:Models, Statistical; D011336:Probability; D012044:Regression Analysis
keywords: Bland-Altman; agreement; bivariate least square; correlated-errors-in-variables regressions; method comparison studies; prediction; tolerance interval