Sample Size for Agreement Studies on Quantitative Variables

Abstract

We reviewed the statistical assessments of the agreement between two measurement methods of continuous variables together with their recent contributions about the sample size calculation based on the “two one side t-tests (TOST) extensions to the individual equivalence. We generalized a restricted null hypothesis that constitutes a particular case in finding the supremum of the probability of rejecting the equivalence under the null hypothesis (H0) and which, obviously, limits its applicability.
Particularly, we devise and propose an exact procedure for calculating the sample sizes for individual equivalence, as an expression of the agreement between two measurement methods, by using a size a test (that is, with adequate control of Type I error), based on the non-central bivariate t distribution with correlation equal to 1 and to the related functions for calculating a and 1-b probabilities.
Furthermore, our devised procedure allows to calculate the sample sizes by choosing between two most suitable formulations of the global parameters space of the null and alternative hypotheses; indeed, they are based on the portion of the distribution of the differences between the two measurement methods or on appropriately chosen agreement thresholds.
Thereafter, we compared our theoretical results with the recently published proposals of the sample size calculation for the Bland and Altman agreement analysis by means also of simulation studies.
Finally, a program written in the open-source R language to perform sample size calculations according to our procedure is available upon request.