A Paradox in Bland-Altman Analysis and a Bernoulli Approach

A reliable method of measurement is important in various scientific areas. When a new method of measurement is developed, it should be tested against a standard method that is currently in use. Bland and Altman proposed limits of agreement (LOA) to compare two methods of measurement under the normality assumption. Recently, a sample size formula has been proposed for hypothesis testing to compare two methods of measurement. In the hypothesis testing, the null hypothesis states that the two methods do not satisfy a pre-specified acceptable degree of agreement. Carefully considering the interpretation of the LOA, we argue that there are cases of an acceptable degree of agreement inside the null parameter space. We refer to this subset as the paradoxical parameter space in this article. To address this paradox, we apply a Bernoulli approach to modify the null parameter space and to relax the normality assumption on the data. Using simulations, we demonstrate that the change in statistical power is not negligible when the true parameter values are inside or near the paradoxical parameter space. In addition, we demonstrate an application of the sequential probability ratio test to allow researchers to draw a conclusion with a smaller sample size and to reduce the study time.