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

TL;DR

This paper extends Christensen's limits of agreement with the mean (LOAM) model to include subject-observer interactions, enabling better assessment of measurement reproducibility and repeatability with new statistical tools.

Contribution

It introduces a new framework incorporating subject-observer interaction into LOAM, allowing separation of systematic and residual measurement errors.

Findings

Extended LOAM model to include interaction effects.

Provided estimates and confidence intervals for reproducibility and repeatability.

Discussed sample size calculations and comparison tests for LOAMs.

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.