Introduction of non-linearity by data transformation in method comparison and commutability studies.
BACKGROUND
Logarithmic transformation is recommended in method comparison or commutability studies when the standard deviation of the measurement results is heteroscedastic. We show that in the case of a considerable constant difference in the relationship between the x- and y-data, logarithmic transformation introduces non-linearity.


METHODS
We used a simulated bivariate dataset [n=50; no systematic differences between the x- and y-data; x-data without error and y-data with concentration-dependent random, normally distributed error (CV=7%)], from which we generated two new sets of data: one by i) multiplying the y-data by 1.1, and the second by ii) adding a constant value of 15 to the y-data.


RESULTS
The runs test (p<0.001) confirms that logarithmic transformation of the second dataset introduces non-linearity. Consequently, applying a linear regression model to the transformed data would result in erroneous decisions about commutability and in erroneously high estimates of the limits of agreement in method comparison studies.


CONCLUSIONS
We recommend applying a linearity test after logarithmic transformation of bivariate data and, if necessary, to calculate the prediction intervals of a non-linear regression function.
Stöckl
Dietmar
D
Laboratory for Analytical Chemistry, Faculty of Pharmaceutical Sciences, Gent University, Gent, Belgium.
Thienpont
Linda M
LM
D003198:Computer Simulation; D012016:Reference Values; D012044:Regression Analysis; D012107:Research Design / Q000706:statistics & numerical data*