A multivariate approach for the biometric comparison of analytical methods in clinical chemistry

The structural relationship model is recommended for the comparison of analytical methods in clinical chemistry. This model is based on the partition of the observed measurements of the different methods in 2 hypothetical random variables: the "expected values", which represent the correct value of the analyte with no error of measurement, and the "error term" representing the measurement errors. it is assumed, that both these variables are normally distributed. There exists a linear structural relation between different analytical methods for the same analyte, provided the correlation coefficient between each pair of the expected values of these models is 1. This linear structural relationship is expressed by the mean values mui and standard deviations alpha i of the expected values, whereas the standard deviations of the error terms determine the precision of the methods. As a measure of the precision the coefficient of determination R(2)i is recommended. The model of structural relationship is an extension of th well known regression models and gives a more realistic approach to the comparison of 2 or more analytical methods. With 2 methods the standardized principle component should therefore replace the regression analysis. The slope of this principle component is identical with the ratio sy/sx. Statistical methods for the estimation and for the tests of hypotheses of the parameters are derived and demonstrated with an example.