Cautionary Remarks When Testing Agreement between Two Raters for Continuous Scale Measurements: A Tutorial in Clinical Epidemiology with Implementation Using R

Background: When continuous scale measurements are available, agreements between two measuring devices are assessed both graphically and analytically. In clinical investigations, Bland and Altman proposed plotting subject-wise differences between raters against subject-wise averages. In order to scientifically assess agreement, Bartko recommended combining the graphical approach with the statistical analytic procedure suggested by Bradley and Blackwood. The advantage of using this approach is that it enables significance testing and sample size estimation. We noted that the direct use of the results of the regression is misleading and we provide a correction in this regard. Methods: Graphical and linear models are used to assess agreements for continuous scale measurements. We demonstrate that software linear regression results should not be readily used and we provided correct analytic procedures. The degrees of freedom of the F-statistics are incorrectly reported, and we propose methods to overcome this problem by introducing the correct analytic form of the F statistic. Methods for sample size estimation using R-functions are also given. Results: We believe that the tutorial and the R-codes are useful tools for testing and estimating agreement between two rating protocols for continuous scale measurements. The interested reader may use the codes and apply them to their available data when the issue of agreement between two raters is the subject of interest.