Abstract

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.

Clin Chem Lab Med 2008;46:1784–5.