Bland and Altman's limits of agreement have traditionally been used in clinical research to assess the agreement between different methods of measurement for quantitative variables. However, when the variances of the measurement errors of the two methods are different, Bland and Altman's plot may be misleading; there are settings where the regression line shows an upward or a downward trend but there is no bias or a zero slope and there is a bias. Therefore, the goal of this paper is to clearly illustrate why and when does a bias arise, particularly when heteroscedastic measurement errors are expected, and propose two new plots, the "bias plot" and the "precision plot," to help the investigator visually and clinically appraise the performance of the new method. These plots do not have the above-mentioned defect and still are easy to interpret, in the spirit of Bland and Altman's limits of agreement. To achieve this goal, we rely on the modeling framework recently developed by Nawarathna and Choudhary, which allows the measurement errors to be heteroscedastic and depend on the underlying latent trait. Their estimation procedure, however, is complex and rather daunting to implement. We have, therefore, developed a new estimation procedure, which is much simpler to implement and, yet, performs very well, as illustrated by our simulations. The methodology requires several measurements with the reference standard and possibly only one with the new method for each individual.
Keywords: Bland–Altman’s plot; Limits of agreement; best linear unbiased prediction; differential bias; empirical Bayes; measurement; method comparison; proportional bias.