Is Bland-Altman plot method useful without inference for accuracy, precision, and agreement?

Objective: Bland and Altman plot method is a widely cited and applied graphical approach for assessing the equivalence of quantitative measurement techniques, usually aiming to replace a traditional technique with a new, less invasive, or less expensive one. Although easy to communicate, Bland and Altman plot is often misinterpreted by lacking suitable inferential statistical support. Usual alternatives, such as Pearson's correlation or ordinal least-square linear regression, also fail to locate the weakness of each measurement technique. Method: Here, inferential statistics support for equivalence between measurement techniques is proposed in three nested tests based on structural regressions to assess the equivalence of structural means (accuracy), the equivalence of structural variances (precision), and concordance with the structural bisector line (agreement in measurements obtained from the same subject), by analytical methods and robust approach by bootstrapping. Graphical outputs are also implemented to follow Bland and Altman's principles for easy communication. Results: The performance of this method is shown and confronted with five data sets from previously published articles that applied Bland and Altman's method. One case demonstrated strict equivalence, three cases showed partial equivalence, and one showed poor equivalence. The developed R package containing open codes and data are available with installation instructions for free distribution at Harvard Dataverse at https://doi.org/10.7910/DVN/AGJPZH. It is possible to test whether two techniques may have full equivalence, preserving graphical communication according to Bland and Altman's principles, but adding robust and suitable inferential statistics. Decomposing the equivalence in accuracy, precision, and agreement helps the location of the source of the problem in order to fix a new technique.