Evaluating bias in method comparison studies using linear regression with errors in both axes

Abstract

Abstract This paper presents a theoretical background for estimating the probability of committing a β error when checking the presence of method bias. Results obtained at different concentration levels from the analytical method being tested are compared by linear regression with the results from a reference method. Method bias can be detected by applying the joint confidence interval test to the regression line coefficients from a bivariate least squares (BLS) regression technique. This finds the regression line considering the errors in the two methods. We have validated the estimated probabilities of β error by comparing them with the experimental values from 24 simulated data sets. We also compared the probabilities of β error estimated using the BLS regression method on two real data sets with those estimated using ordinary least squares (OLS) and weighted least squares (WLS) regression techniques for a given level of significance α. We found that there were important differences in the values predicted with WLS and OLS compared to those predicted with the BLS regression method. Copyright © 2002 John Wiley & Sons, Ltd.