Detecting proportional and constant bias in method comparison studies by using linear regression with errors in both axes

Constant or proportional bias in method comparison studies using linear regression can be detected by an individual test on the intercept or the slope of the line regressed from the results of the two methods to be compared. Since there are errors in both methods, a regression technique that takes into account the individual errors in both axes (bivariate least-squares, BLS) should be used. In this paper, we demonstrate that the errors made in estimating the regression coefficients by the BLS method are fewer than with the ordinary least-squares (OLS) or weighted least-squares (WLS) regression techniques and that the coefficient can be considered normally distributed. We also present expressions for calculating the probability of committing a β error in individual tests under BLS conditions and theoretical procedures for estimating the sample size in order to obtain the desired probabilities of α and β errors made when testing each of the BLS regression coefficients individually. Simulated data were used for the validation process. Examples for the application of the theoretical expressions developed are given using real data sets.