Multiple analytical method comparison using maximum livelihood principal component analysis and linear regression with errors in both axes

This paper discusses a new stepwise approach for comparing the results from several analytical methods which analyse a set of analytes at different concentration levels, taking into account all the individual uncertainties produced by measurement errors. This stepwise comparison approach detects the methods that provide outlying concentration results. The concentration results from each one of the remaining analytical methods are then compared to the ones from the others taken together, by using linear regression. To do this, the concentration results from the methods considered together and their individual uncertainties, are decomposed at each step to obtain a vector of concentrations. This is achieved by a maximum likelihood principal component analysis (MLPCA), which takes into account the measurement errors in the concentration results. The bivariate least squares (BLS) regression method is then used to regress the concentration results from the method being tested at a given step on the scores generated from the MLPCA decomposition (which have the information of the other remaining methods), considering the uncertainties in both axes. To detect significant differences between the results from the method being tested at a given step and the results from the other methods (MLPCA scores), the joint confidence interval test is applied on the BLS regression line coefficients for a given level of significance α. We have used four real data sets to provide application examples that show the suitability of the approach.