Brian H. Nathanson, Ph.D.

OptiStatim, LLC

Introduction:  The Glomerular Filtration Rate (GFR) is the best overall measure of kidney function. Abnormal GFR values may indicate Chronic Kidney Disease (CKD).  CKD is a major healthcare problem with an estimated 19 million Americans in its early stages.  Early detection and management can prevent kidney failure but patients in the early stages of CKD may have no symptoms and must rely on a diagnosis based partly on their GFR.   In patients with more advanced CKD, GFR values are used for drug dosing and the decision to seek a kidney transplant.   This study evaluates the amount of variation found in the three most commonly used equations to calculate GFR and proposes an alternative method based on linear programming.

Methods:  10,000 simulated patients with normally distributed variables for age, weight and serum creatinine were generated to replicate published values in 320 CKD patients (Annals of Internal Medicine 2004; 141:929-37).  40% were randomly assigned to be female and 20% African American.  The three GFR equations were Cockcroft-Gault (CG), Modification of Diet in Renal Disease (4-variable model) (MDRD), and the Mayo Clinic Quadratic Formula (MC).  GFRs were calculated using each equation and the results were analyzed with ANOVA and Chi-Square tests using Stata SE 8.2.

Results:  The mean GFRs from the three equations were different: CG = 59.3 (36.6) mL/min per 1.73 m2, MDRD = 50.8 (34.8), MC = 46.3 (28.6), p< 0.001.  The CG and MC methods were not statistically different (18.05% vs. 18.29% respectively, p = 0.66) in their proportion of patients with Stage 1 CKD (GFR > 90 mL/min per 1.73 m2) but both were higher than the MDRD method (11.03%, p <0.001).  The equations yielded significantly different proportions of patients with Stage 5 CKD (GFR < 15 mL/min per 1.73 m2, indicating kidney failure): CG = 1.33%, MDRD = 2.62%, MC = 4.21%, p<0.001.

Discussion:  This study shows that the GFR equations give different results which have clinical ramifications.   Though doctors are aware of this variability on specific subsets of patients from prior studies, no solution to this problem exists other than focusing on the relative changes in GFR per patient using the same equation.  Rather than using one regression based formula to predict GFR, a linear programming approach (using Data Envelopment Analysis) to measure the normal level of GFR (i.e., renal efficiency) based on a spectrum of healthy patients and then quantify the drop in GFR based on the progression of CKD may be more clinically informative.

Conclusion:  Existing GFR equations based on linear regression produce GFR values that statistically differ from each other.   Linear programming methods may be a superior alternative.