A New Biometrical Procedure for Testing the Equality of Measurements from Two Different Analytical Methods. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part I

TLDR

Procedures for evaluating method comparisons often require distributional assumptions that are rarely met. The paper proposes a new linear regression procedure that does not rely on distributional assumptions about samples or measurement errors. The method uses linear regression to test the relationship between two measurement methods, providing confidence limits for slope and intercept that are invariant to method assignment and are used to assess whether differences are statistically significant. The procedure yields assignment‑invariant confidence limits for slope and intercept, enabling determination of whether observed differences are due to chance.

Abstract

Procedures for the statistical evaluation of method comparisons and instrument tests often have a requirement for distributional properties of the experimental data, but this requirement is frequently not met. In our paper we propose a new linear regression procedure with no special assumptions regarding the distribution of the samples and the measurement errors. The result does not depend on the assignment of the methods (instruments) to X and Y. After testing a linear relationship between X and Y confidence limits are given for the slope beta and the intercept alpha; they are used to determine whether there is only a chance difference between beta and 1 and between alpha and 0. The mathematical background is amplified separately in an appendix.