The Problems of Empirical Formulas

Drug Therapy in Patients With Chronic Renal Failure by Dr. med. Bertram Hartmann, PD Dr. med. David Czock, Prof. Dr. med. Frieder Keller in volume 37/2010

The frequent use of the MDRD formula to estimate the GFR should not mislead us about the fact that it is an empirical formula. This is obvious from the failure of the measurement unit calculation: The units of measurement on the right hand side do not yield the unit of measurement of the GFR (mL/min/1.73 m²).

The MDRD formula in all its variants is the result of an estimate (regression analysis) of the ¹²⁵I-iothalamate clearance by using serum concentrations of creatinine and other patient data (1). If the data of an individual patient are entered, however, the result is not his or her individual GFR but the mean GFR of the cohort under investigation at the point that corresponds to the patient’s data.

The probability that this mean value is consistent with the individual GFR equals zero. The individual GFR can be captured with any certain probability only within a confidence interval. It is therefore incorrect to 0calculate using an empirical formula without confidence interval.

The problem is alleviated if the estimated GFR is not used per se but to determine a CKD stage, but it continues for the transitions between stages. Furthermore, in Table 1 the authors assigned to the CKD values GFR values with the unit of measurement mL/min and not mL/min/1.73 m², which means that the relation to the MDRD formula is misleading (2).

A further problem is the conversion of the GFR estimated with the MDRD formula into the absolute GFR by using the individual body surface area obtained with the Mosteller formula,—also an empirical formula (3). Mosteller did not report a confidence interval; but it can be presumed to be substantial. In the calculation, the confidence intervals of both formulas go into the end result and thus increase the uncertainty. In order to measure the absolute GFR, a clearance procedure seems to be more suitable.

DOI: 10.3238/arztebl.2011.0114a

Dr. med. Helmut Nocke

Institut für Physiologie

Otto-von-Guericke-Universität

Leipziger Str. 44

39120 Magdeburg, Germany

Conflict of interest statement

The author declares that no conflict of interest exists according to the guidelines of the International Committee of Medical Journal Editors.

References

1. Levey AS, Bosch JP, Lewis JB, Green T, Rogers N, Roth D: A more accurate method to estimate glomerular filtration rate from serum creatinine: a new prediction equation. Ann Intern Med 1999; 130: 461–70.

2. Hartmann B, Czock D, Keller F: Drug therapy in patients with chronic renal failure. Dtsch Arztebl Int 2010; 107(37): 647–56.

3. Mosteller RD: Simplified calculation of body-surface area. N Engl J Med 1987; 317: 1098.