Detection of bias in method comparison by regression analysis

Regression analysis is often applied to validate a newly developed method against a reference method. The present work investigates the risk of not detecting a systematic difference between two analytical methods (=β-error) and determines the number of points needed to detect a bias with a specified β-error. Approximate formulae are proposed to predict the sample size required to detect from a regression analysis a proportional or a constant bias, i.e. a bias in the slope or in the intercept. These results are compared with those of computer simulations. Three different designs to distribute the data are studied, namely, a normal and a rectangular distribution over the whole measurement range as well as an experimental design where the measurements are performed at three fixed concentration levels. For a known straight line relationship, it is demonstrated that this last design is to be preferred. A procedure is also proposed to simultaneously test slope and intercept of the orthogonal least-squares line. It is shown that, for a given number of data, an evaluation based on such a joint test allows a more reliable bias detection.