A statistical note on extending Christensen's limits of agreement with the mean

Abstract: Limits of agreement with the mean (LOAM) can be used for assessing agreement of continuous measurements made by different observers. Definitions of a LOAM for measuring reproducibility has been introduced under a two-way random effects model without interaction between subject and observer. Here we extend that model framework to include a subject-observer interaction, allowing the separation of residual measurement error and systematic variation in how individual observers measure specific objects. Further, our framework extends the LOAM concept to two metrics: one quantifying reproducibility and the other repeatability. We supply estimates and confidence intervals for the reproducibility and repeatibility LOAM and discuss sample size calculations and a test to compare LOAMs between two groups. To make the text self-contained for a complete agreement analysis, we additionally provide estimates and confidence intervals for the variance components.