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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Am J Kidney Dis. Author manuscript; available in PMC 2010 June 1.
Published in final edited form as:
PMCID: PMC2693296

Appraisal of GFR Estimating Equations Following Kidney Donation

Meghan Sebasky, M.D.,1 Alexandra Kukla, M.D.,1 Erin Leister, M.S.,1 Hongfei Guo, Ph.D.,2 Sanjeev K. Akkina, M.D.,1 Yasser El-Shahawy, M.D.,1 Arthur J. Matas, M.D.,3 and Hassan N. Ibrahim, M.D., M.S.1



It is not clear which serum creatinine-based glomerular filtration rate (GFR) estimating model performs best in kidney donors.

Study Design

Study of diagnostic accuracy.

Setting and Participants

From a population of 3,698 kidney donors, 255 donors underwent iohexol GFR measurement (mGFR).

Index Test (Intervention)

mGFR by the plasma disappearance of iohexol.

Reference Test or Outcome

eGFR was estimated using the Cockcroft-Gault equation, (eGFRCG), the Mayo Clinic equation (eGFRMC), and the MDRD Study equation (eGFRMDRD).


Mean mGFR was 71.8±11.8 mL/min/1.73m2 and 85.5% had mGFR > 60 mL/min/1.73m2. eGFRCG underestimated mGFR by 3.96±13.3 mL/min/1.73m2 and was within 30% of mGFR in 89.4% of the time. eGFRMC overestimated mGFR by 8.44±11.9 mL/min/1.73m2 and was within 30% of mGFR in 83.1% of cases. eGFRMDRD underestimated mGFR by only 0.43±11.7 mL/min/1.73m2 and the proportion within 30% of mGFR was the highest amongst the tested model; 94.1% of the time. The eGFRMC, however, was most accurate in classifying donors according to having eGFR < 60 mL/min/1.73m2.


Lack of ethnic diversity and response bias.


The MDRD Study equation is least biased and since it is routinely reported by most laboratories, is the best readily available model for estimating GFR in kidney donors.

Index Words: Glomerular filtration rate, kidney donor, Cockcroft-Gault, Modification of Diet in Renal Disease


The benefits of living donor transplantation are well established and current evidence suggests that kidney donors enjoy a favorable renal course and their life expectancy is preserved.15 A particular area of interest is how to best measure renal function in those who have donated a kidney. Serum creatinine-based glomerular filtration rate (GFR) estimating models such as the Cockcroft-Gault creatinine clearance (CG CCr), the Modification of Diet in Renal Disease (MDRD) Study equation, and the Mayo Clinic equation are superior to serum creatinine in estimating renal function, and in response to the effort by the National Kidney Disease Education Program (NKDEP) to standardize serum creatinine values, the MDRD Study equation was recently re-expressed for use with the isotope-dilution mass spectrometry (IDMS) standardized serum creatinine assay.610

We have previously reported on the performance of the CG CCr, 4-variable MDRD Study, and Mayo Clinic equations in a cohort of kidney donors who underwent iohexol GFR measurement and found that the MDRD Study equation was a reasonable substitute for, although clearly inferior to, formal GFR measurement.5 Herein, we report on the performance of serum creatinine-based GFR estimating equations in a larger number of donors and provide appraisal of the newly introduced MDRD Study equation that utilizes IDMS-traceable standardized serum creatinine, as well.


As of December 2007, a total of 3,698 living donor nephrectomies had been performed at the University of Minnesota. In December 2003, we initiated a comprehensive, multi-step effort to contact all donors by consulting phone and internet directories and also asking their recipient. We generated donor lists of those known to be alive and stratified them by sex and years after donation (in 3-year intervals). Using this sample frame, a random start was used to generate random numbers using SAS Macro to select 5% to 10% of donors from each strata to undergo GFR measurements. Between 2003 and 2007, 255 donors underwent GFR measurement. If the selected donor refused participation, a new donor from the same sex and time from donation strata, following the same scheme, was contacted. All donors who underwent GFR measurements donated in the year 2000 or earlier. In total, 1785 donors were approached to undergo GFR measurement to find 255 who were agreeable. All studies were approved by the University of Minnesota Institutional Review Board.

GFR was measured using the plasma disappearance of iohexol.5,1114 Via a small polyethylene catheter placed in an antecubital vein, we injected 5 mL of iohexol solution (647 mg of iohexol; 300 mg of iodine per mL). From the contralateral arm, via a second antecubital vein catheter, we then obtained serial samples at 120, 150, 180, 210, and 240 minutes (±15 sec). Plasma was stored at −20°C for high performance liquid chromatography determination of iohexol concentration. To analyze the plasma profile, we used a 1-compartment model system with all data fitted by a nonlinear regression iterative program. We chose the plasma disappearance of iohexol method because it does not require timed urine collections which may result in incomplete bladder emptying and lead to significant variability in the GFR measurement, and in view of its excellent correlation with inulin clearance which is the gold standard of measuring GFR.14 Moreover, utilizing the single compartment model corrected with the Brochner-Mortenson formula simplifies GFR calculation and produces a correlation with inulin GFR that is virtually identical to the 2-compartment model.14 The coefficient of variation of the mGFR at our center is consistently < 10%.

Serum creatinine was obtained on the morning of GFR measurement and after an 8–12 hour fast. Recognizing that large differences exist in serum creatinine assays across laboratories, we previously sent 25 serum creatinine samples ranging from 0.6 to 2.3 mg/dL to the Cleveland Clinic Biochemistry Laboratory in 2006.5,1517 This range was chosen since it would encompass the range observed in the overwhelming majority of donors, as we have shown in our previous studies.3,5,1819 The aforementioned laboratory is where serum creatinine was assayed for the Modification of Diet in Renal Disease (MDRD) Study using the Beckmann Rate Jaffe’/CXR Synchron method, which is based on the kinetic alkaline picrate reaction.20 We compared the Cleveland Clinic’s results with ours from the University of Minnesota laboratories which use an identical method and instrument. The results from both institutions were virtually identical. The mean serum creatinine at our laboratory was 0.95±0.41 mg/dL vs. 0.96±0.40 mg/dL at the reference laboratory; mean difference was 0.0125±0.03 mg/dL, the Pearson correlation coefficient between the measurements at the two institutions was 0.9965. Fitting a linear regression model with the University of Minnesota serum creatinine measurements as the outcome, revealed an intercept of −0.01376 and a slope of 1.00 (95% CI 0.967–1.042, SE 0.018). In May 2008 the creatinine assay at University of Minnesota laboratories changed from the Jaffe’/CXR Synchron method to the IDMS-traceable creatinine in compliance with the NKDEP recommendation to internationally standardize serum and urine creatinine measurements. The laboratory provided us with a formula for conversion of the Jaffe’ creatinine to the IDMS-traceable creatinine (IDMS creatinine in mg/dL= −0.111 + 0.964 · Jaffe’ creatinine in mg/dL) based on running creatinine assays by the two methods in a large number of samples. We used this formula to convert all creatinine values to IDMS-traceable values. To verify the accuracy of the conversion formula in our kidney donors, we randomly selected 50 serum samples from the pool of 255 donors and measured serum creatinine using the new IDMS traceable method. The average measured creatinine in these 50 samples was 0.95±0.25 mg/dL as compared to 1.10±0.26 mg/dL given by the older method and r = 0.95. Linear regression of the IDMS creatinine vs. the old method revealed an intercept of −0.03047 and a slope of 0.912 (95%CI 0.818–1.005, SE 0.046). The average creatinine predicted by the formula provided by the laboratory was 0.97±0.25 mg/dL. Since values provided by the regression formula provided serum creatinine values that were identical to the directly measured one in the 50 samples, we used the values obtained from it for this analysis.

We estimated the re-expressed Cockcroft-Gault equation for estimation of GFR for use with standardized creatinine (eGFRCG), the Mayo Clinic equation (eGFRMC), and the MDRD Study equation (eGFRMDRD). eGFRCG was calculated using the formula (140age)·weight/(72×SCr)]×(0.85iffemale)(1.73BSA)6 multiplied by 0.8 to correct for the bias in the MDRD Study sample.20 eGFRMC was calculated using the quadratic equation that estimates logarithmic GFR from serum creatinine, age and gender and after indirectly calibrating serum creatinine by applying the following regression relation: IDMS-traceable creatinine = 0.906 [−0.213+(1.098*Mayo Clinic creatinine)].8,21 In the original cohort the eGFRMC was developed in, those with serum creatinine ≤ 0.8 mg/dL were assigned a value of 0.8 mg/dL. In this analysis, an individual with any value ≤ 0.60 mg/dL (0.8 × correction factor) was assigned a value of 0.66 mg/dL. eGFRMDRD was calculated using the following formula: 175 × standardized SCr−1.154 × age−0.203 × 1.210 (if black) × 0.742 (if female).9

We assessed the performance of eGFR from the three equations against mGFR in several ways:

  1. Bias: the average prediction error = Σ (eGFR − mGFR)/n, where n is the number of GFR studies performed (i.e. 255). Relative bias, % deviation from mGFR, was also calculated.
  2. Precision: the value of R2 from the linear regression of mGFR on eGFR, interquartile range of differences and root mean squared error (RMSE), and
  3. Relative accuracy: the percent of estimates falling within 10, 30 and 50% of mGFR.

The equations were compared statistically on each of these measures. The comparisons were made using a paired t-test for bias, a paired test of proportions for relative accuracy, 22 and the Hotelling-Williams test for precision, R2.23 All of these tests take into account that all equations were calculated for the same set of subjects. The equations were then compared using an average rank derived from these three criteria. Each equation was ranked from 1 to 3 based on its performance in terms of bias, precision, and relative accuracy.

Residual plots were performed for all equations. This sort of analysis plots the (eGFR – mGFR) on the y – axis against mGFR on the x – axis. Graphically, this depicts the mean difference between the two methods bracketed by the observed ± 2 standard deviations of the difference between the two methods which permits detection of a trend in bias.

We also compared these 3 models on their ability to accurately identify donors with mGFR < 60 mL/min/1.73m2 and assessed their performance in donors with hypertension, diabetes or albuminuria.

Results are expressed as mean ± standard deviation unless indicated otherwise. Statistical significance was assessed with a Bonferroni – adjusted threshold of 0.05/6 since 6 pairs of formulas were compared. Analyses and graphs were completed using statistical software SAS 9.1 (Cary, NC, SAS Institute) and R version 2.5.0.


Since 1963, 3698 patients donated a kidney at the University of Minnesota. Utilizing the Social Security Death Master File, we found that 3,404 are alive, 268 have died, and 26 of the donors were foreign nationals with missing Social Security numbers in whom vital status could not be ascertained. At the beginning of our efforts to contact all donors in December 2003, 2,199 returned health status updates and laboratory results. Of these 2,199 individuals, 255 were randomly selected for GFR measurement; roughly 1 out of 7 donors invited to undergo GFR measurement agreed (Figure 1). The 255 donors who underwent mGFR were similar to the donor population without formal GFR measurement (n = 3443) in current age and sex distribution. However, the donors with mGFR were older at donation (41.1±11.0 years vs. 38.4±11.7 years, p<0.001) and also had a shorter time from donation (12.2±9.2 years vs. 16.3±11.0 years, p<0.001). Roughly 62% of donors with mGFR were women, 98.8% were white, 24.7% reported a diagnosis and treatment for hypertension and 8% reported a diagnosis and treatment for diabetes with oral hypoglycemic agents and/or insulin (Table 1).

Figure 1
Participant flow.
Table 1
Characteristics of Study Population

Serum creatinine at the time of GFR measurement was 1.1±0.2 mg/dL, and eGFRMDRD was 84.0±13.6 mL/min/1.73m2 at donation and 71.4±14.8 mL/min/1.73m2 at the time of this study. mGFR in these 255 donors was 71.8±11.8 mL/min/1.73m2 as compared to 67.9±16.3 mL/min/1.73m2 for eGFRCG, 80.3±15.5 mL/min/1.73m2 for eGFRMC and, as mentioned above, 71.4±14.8 mL/min/1.73m2 for eGFRMDRD. Reassuringly, 85.5% of donors had a mGFR > 60 mL/min/1.73 m2, 14.5% had a mGFR between 30–60 mL/min/1.73m2, and no donor had a mGFR of <30 mL/min/1.73m2. Moreover, 87.3% of donors were normoalbuminuric at the time of GFR measurement, as assessed by first void urinary albumin-creatinine ratio, 11.5% were microalbuminuric, and only 1.2% were macroalbuminuric. None of the donors had both a mGFR < 45 mL/min/1.73m2 and albuminuria. The distribution of donors by the presence of hypertension, diabetes and albuminuria according to mGFR levels is shown in Table 2; 83 donors had at least one of these three conditions, 3 had both diabetes and hypertension, 11 had both hypertension and albuminuria, 1 donor had diabetes and albuminuria but none had all three conditions. None of the diabetic or albuminuric donors had an mGFR less than 45 mL/min/1.73m2 and only 2 hypertensive donors fell within this range. The majority (66/83) of hypertensive, diabetic and albuminuric donors had mGFR > 60 mL/min/1.73m2. mGFR was inversely related to age; there was a 0.49 mL/min/1.73m2/year decline in mGFR [95% CI,(−0.62) − (−0.34)]. In men the decline was 0.34 [95%CI (−0.55) − (−0.14)] and in women, −0.60 [95%CI (−0.78) − (−0.43)] (Figure 2).

Figure 2
Age vs. measured GFR depicted as a regression line and 95% C.I.; 2a: Entire cohort, 2b: Men, 2c: Women.
Table 2
Distribution of donors according to mGFR by the presence of hypertension, albuminuria and diabetes

eGFRCG underestimated mGFR by 3.96±13.3 mL/min/1.73 m2 and had a relative bias of -5.18±17.9% (Figure 3a, b). The precision, or R2 estimate, was 0.35. eGFRCG fell within 10%, 30%, and 50% of mGFR in 37.3%, 89.4%, and 98.8% of the cases, respectively (Table 3).

Figure 3
eGFRCG vs. mGFR; 3a: Scatterplot, 3b: Residual plot.
Table 3
Overall performance of eGFRCG, eGFRMC and eGFRMDRD in kidney donors

eGFRMC overestimated mGFR by 12.43±17.5 mL/min/1.73 m2 (Figure 4a) and the residual plot revealed a wide ± 2SD interval (Figure 4b). Precision was 0.42. The relative accuracy of eGFRMC was similar to eGFRCG as 36.9%, 83.1% and 97.7% fell within 10%, 30% and 50%, respectively (Table 3).

Figure 4
eGFRMC vs. mGFR; 4a: Scatterplot, 4b: Residual plot.

eGFRMDRD was the least biased. In fact, it had a bias of only −0.43±11.7 mL/min/1.73m2 and the relative bias was −0.10±16.2% (Figure 5a). The residual plot demonstrates a much narrower variability around the difference between mGFR and eGFRMDRD, Figure 5b. eGFRMDRD was similar in its precision to the other two models; R2 = 0.41. eGFRMDRD was within 10%, 30%, and 50% of mGFR in 45.5%, 94.1%, and 99.2% of cases, respectively (Table 2). In all, its relative accuracy and precision were most comparable to that of eGFRCG.

Figure 5
eGFRMDRD vs. mGFR; 5a: Scatterplot, 5b: Residual plot.

We next assessed the performance of these 3 models in donors who developed diabetes, hypertension or albuminuria after donation. As mentioned previously, there were 83 such donors. The results were almost identical to those observed in the entire cohort (Table 4).

Table 4
Overall performance of eGFR (CG), eGFRMC and eGFRMDRD in kidney donors with albuminuria, hypertension, or diabetes

Finally, we compared the percentage of donors who had an eGFR < 60 mL/min/1.73m2 by the different models. 14.5% had a mGFR<60 mL/min/1.73m2, 33.3% by eGFRCG, 10.2% by eGFRMC and 24.3% by eGFRMDRD (Figure 6). All estimation equations yielded results which were significantly different from mGFR with the exception of eGFRMC. Very comparable results were observed in the 83 donors with hypertension, diabetes or albuminuria; i.e. eGFRMC was least likely to misclassify this high risk group as having eGFR < 60mL/min/1.73m2.

Figure 6
Percentage of donors with GFR < 60 mL/min/1.73m2. Different letters represent statistically significant differences (McNemar’s test); Grey bars: All donors, Black bars: Donors with hypertension, diabetes, or albuminuria.


These results confirm and extend our previous observation that the majority of donors had a mGFR > 60 mL/min/1.73m2, were normoalbuminuric and the rate of mGFR decay with age is not accelerated. The MDRD Study equation was least biased and was reasonably precise. The eGFRCG underestimated mGFR but this bias was comparable to that observed with eGFRMC. In regard to its precision and relative accuracy, it was very comparable to that of the MDRD study equation. When assessed on their ability to accurately classify kidney donors by eGFR < 60 mL/min/1.73m2 the eGFRMC was most reliable. In all, the MDRD Study equation was least biased and had the highest likelihood of being within 30% of mGFR, the 3 models have comparable precision and eGFRMC was least likely to result in misclassification of donors according to the conventional 60 mL/min/1.73m2 GFR cutpoint. Similar results were obtained in donors who developed post-donation hypertension, diabetes, or albuminuria.

Serum creatinine-based GFR estimation models were developed in specific subgroups in populations which are different than this study population. Nevertheless, they seem to perform well in patients who have undergone uninephrectomy for donation. The CG CCr formula was developed in a population of 249 patients with renal disease; furthermore, it predicts creatinine clearance which overestimates GFR due to creatinine secretion.6 In our previous assessment of this model, we found it to be a reasonable estimate of mGFR as it overestimated mGFR by only 3.35±13.6 mL/min/1.73m2.5 It is clear that correcting the CG CCr for the bias in the MDRD study sample to produce eGFRCG does not alter its precision but reverses the direction of its bias. The MDRD Study equation was developed in patients with CKD.7 In contrast, the group from Mayo Clinic used a population of 580 healthy individuals combined with 320 patients with chronic kidney disease to develop their quadratic equation.8 The current results demonstrate improvement over our previous results when it comes to eGFRMC. This may stem directly from the indirect calibration of serum creatinine. Most recently, the MDRD Study equation has been re-expressed for use with the standardized IDMS-traceable creatinine in an effort to standardize results between various laboratories.9 This represents a major improvement as this new equation reduced the underestimation of mGFR by over 6 mL/min/1.73m2 when compared to the older version of the MDRD study equation. Unfortunately it did not enhance its precision.5 Overall, it seems possible that GFR prediction formulas behave differently in patients with chronic kidney disease when compared to healthy people and perhaps also individuals who have previously donated a kidney.

These data also show that the majority of former kidney donors have a GFR > 60 mL/min/1.73m2. Importantly, the donors at highest risk for reduced GFR (hypertensive, diabetic and albuminuric donors) also enjoyed preserved GFR since only 2 out of 83 such donors had a GFR less than 45 mL/min/1.73m2, 15 donors between 45–60 mL/min/1.73m2 and the rest were above 60 mL/min/1.73m2. Longer follow-up is, of course, needed in these high risk donors. These studies also confirm the inverse relationship between GFR and age as donors lost 0.5 mL/min/year; a rate that is comparable to what has been described in people with full complement of nephrons.24 We hope that our planned future studies that entail serial measurement of GFR in donors will better quantify the rate of GFR decay as the cross-sectional nature of this data is not an ideal way of assessing longitudinal changes in GFR.

While, to our knowledge, this is the largest series to report on mGFR in donors, it is still small in size and from a single center. In addition, the population is 98.8% white. Although we selected donors randomly for formal GFR measurement, there were significant differences in this population when compared to the donor population as a whole: the donors with measured GFR were older and had a shorter period of elapsed time since donation. Moreover, this data suffers not only from response bias but also survival bias.

The three studied models have reasonable performance in those who donated a kidney in the past but in the absence of formal GFR measurement, the MDRD Study equation provides the least biased estimate of GFR, provides improvement over previous equations and should be the preferred model of estimating GFR. Accurately estimating renal function in studies of subjects who have undergone nephrectomy would improve our ability to counsel future donors regarding their level of post-donation kidney function.


We would like to acknowledge Robert Bailey and his staff for their efforts in locating donors. Most of all, we would like to thank our kidney donors themselves.

Support: Funding for this study was provided by National Institutes of Health grant PO1DK13083 and grant MO1-RR00400 from the General Clinical Research Center at the University of Minnesota.


Financial Disclosure: None.

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