Introduction of non-linearity by data transformation in method comparison and commutability studies.

Research paper by Dietmar D Stöckl, Linda M LM Thienpont

Indexed on: 01 Nov '08Published on: 01 Nov '08Published in: Clinical chemistry and laboratory medicine


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.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.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.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.