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

This paper presents a theoretical background for estimating the probability of committing a beta 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 13 error by comparing them with the experimental values from 24 simulated data sets. We also compared the probabilities of beta 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 alpha. 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 (C) 2002 John Wiley Sons, Ltd.