Bland–Altman Limits of Agreement from a Bayesian and Frequentist Perspective

Abstract

Bland–Altman agreement analysis has gained widespread application across disciplines, last but not least in health sciences, since its inception in the 1980s. Bayesian analysis has been on the rise due to increased computational power over time, and Alari, Kim, and Wand have put Bland–Altman Limits of Agreement in a Bayesian framework (Meas. Phys. Educ. Exerc. Sci. 2021, 25, 137–148). We contrasted the prediction of a single future observation and the estimation of the Limits of Agreement from the frequentist and a Bayesian perspective by analyzing interrater data of two sequentially conducted, preclinical studies. The estimation of the Limits of Agreement θ1 and θ2 has wider applicability than the prediction of single future differences. While a frequentist confidence interval represents a range of nonrejectable values for null hypothesis significance testing of H0: θ1 ≤ −δ or θ2 ≥ δ against H1: θ1 > −δ and θ2 < δ, with a predefined benchmark value δ, Bayesian analysis allows for direct interpretation of both the posterior probability of the alternative hypothesis and the likelihood of parameter values. We discuss group-sequential testing and nonparametric alternatives briefly. Frequentist simplicity does not beat Bayesian interpretability due to improved computational resources, but the elicitation and implementation of prior information demand caution. Accounting for clustered data (e.g., repeated measurements per subject) is well-established in frequentist, but not yet in Bayesian Bland–Altman analysis.