| Abstract|| |
We determined the performance of estimated glomerular filtration rate equations (eGFR) including MDRD2-Isotope Dilution Mass Spectrometry (MDRD2-IDMS), Cockcroft-Gault (CG) and Virga to measure post-transplant chronic kidney disease (CKD) stages 1-4, using simultaneous isotope GFR (iGFR) measurement. The study was conducted in 97 patients. The eGFR results measured by CG and Virga were normalized to 1.73 m 2 . Analysis of relative and absolute bias, error, scatter, correlation coefficient of variance and accuracy within the 30% range from the reference iGFR result was performed using standard techniques. There were 135, 242, 314 and 82 scans, respectively, in CKD stages 1-4. Bias and accuracy of GFR estimators varied significantly across the CKD stages. In stages 1 and 2, CG had the best error of -12.7 and 0.2 mL/min/1.73 m 2 , respectively, while Virga had the highest accuracy of 74.3% and 85.5, respectively. In stages 3 and 4, MDRD2-IDMS had the best error of -0.52 and 5.8, respectively. Accuracy was the best at 75.1% for Virga in stage 3, while it was the highest of 70.7% for MDRD2-IDMS in stage 4. Virga had the highest accuracy of 75.2% in stage 4. The worst bias was for MDRD2-IDMS in stage 2 (-36.8 mL/min/1.73 m 2 ) and the best bias was for CG in stage 2 (-0.33 mL/min/1.73 m 2 ). The eGFR estimators have inconsistent performances in the various stages of CKD and, thus, another limitation is added to their validity to substitute for the gold standard methods.
|How to cite this article:|
Attia A, Zahran A, Shoker A. Comparison of equations to estimate the glomerular filtration rate in post-renal transplant chronic kidney disease patients. Saudi J Kidney Dis Transpl 2012;23:453-60
|How to cite this URL:|
Attia A, Zahran A, Shoker A. Comparison of equations to estimate the glomerular filtration rate in post-renal transplant chronic kidney disease patients. Saudi J Kidney Dis Transpl [serial online] 2012 [cited 2013 May 21];23:453-60. Available from: http://www.sjkdt.org/text.asp?2012/23/3/453/95701
| Introduction|| |
Consistency in estimating the glomerular filtration rate (GFR) at different levels of renal function is necessary for the longitudinal follow-up of kidney patients. For example, underestimation of GFR in patients with minimal renal dysfunction may erroneously suggest severe renal impairment. Likewise, over-estimation of GFR in patients with severe renal dysfunction may give a false sense of comfort that the patient does not have significant renal failure. Said another way, the current equations to estimate GFR are worthless if they do not demonstrate consistency in their performances across the different stages of chronic kidney disease (CKD). The National Kidney Foundation Kidney Disease Outcome Quality Initiative (K/DOQI) classifies CKD in native kidneys as well as transplant kidney into five well-known stages. This staging system is based primarily on estimation of GFR using modified diet in the renal disease equation measured by isotope dilution mass spectrometry (MDRD-IDMS) or Cockcroft-Gault (CG) equations. These equations have numerous limitations and they have been discussed elsewhere.  In brief, they have limited accuracy and higher bias, particularly in those with minimal renal dysfunction. With this in mind, we wished to test the hypothesis that the limitations associated with the current GFR equations translates into significant variation in their performance across various stages of CKD. To achieve our goal, we collected 787 isotope GFR (iGFR) values simultaneously along with the patient demographics as well as serum creatinine values to compare their performance in renal transplant patients with different GFRs.
| Materials and Methods|| |
We used an expanded data set, part of which has been published recently.  The protocol for this retrospective study followed the ethical standards of this institution. Blood was drawn on the same day for measuring radioisotope clearance as well as testing of serum creatinine. In addition, patients' demographics were recorded. All patients had stable renal function. We used the same inclusion criteria published recently, including iGFR performed after at least one month from the transplantation date. For this analysis, we included only patients who had iGFR studies starting within the first year following transplantation, and at least one month after the date of transplantation. We screened 1400 iGFR measurements performed in our center on 345 patients followed at our clinic. With these inclusion criteria in mind, 787 studies performed on 97 patients were eligible for analysis. During this period, there was no change in either the laboratory creatinine reference levels or the nuclear medicine protocols used. All studies were performed during the regular outpatient visits. iGFR was considered the reference to GFR. GFR estimation was calculated from three equations: CG, MDRD2-IDMS and Virga.
GFR Estimated by Isotope Scan
The GFR was calculated from the disappearance of radioactivity in three, timed plasma samples after a single injection of 99mTc DTPA. This method is precise, reproducible and independent of variations in the volume distribution of the isotope. Details of the methods of iGFR measurement and eGFR were presented previously.  Virga equation  was calculated using the following equations:
(69.4 - 0.59 × Age + 0.79 × Weight)/Scr - 3
(57.3 - 0.37 × Age + 0.51 × Weight)/Scr - 2.9
Measurement of Serum Creatinine Concentrations
The serum creatinine was measured with an enzymatic assay (SYNCHRON LX 20 Systems, Bachman, Coulter Inc., Fullerton, CA, USA) with a normal range of 60-110 μmol/L.
The intra-assay and inter-assay coefficients of variation (CV) were <3%. This method has a small bias of ≤6 μmol/L as compared with IDMS. However, this difference is not considered significant in the estimation of GFR. 
Comparison between measured and estimated GFRs in different stages of CKD were performed using CG and Virga clearances, which were presented normalized to 1.73 m 2 ; MDRD2-IDMS was not.
| Statistical Evaluation of the Predictive Formulas|| |
Mean Percentage Error (MPE) as a Measure of Bias, Mean Absolute Percentage Error (MAPE), Precision, Coefficient of Variance, Scatter, Linear Correlation and Accuracy (Within 30% Range from Reference Method)
The MPE was calculated by the mean percentage difference between the calculated GFR and the measured GFR. The MPE is designed to allow comparison of the GFR values following different methods by using the percentage of error relative to the actual value. The MAPE was calculated by the average value of the absolute values of errors expressed in percentage terms. Smaller values for MPE and MAPE indicate less bias. 
Precision was defined as the standard deviation (SD) of the difference between the measured and estimated GFRs. Precision was assessed by calculating root mean square error (RMSE) ,, for each equation, which is the measure of the average distance between the predicted and measured GFR. The smaller the RMSE, the greater would be the precision of the formula. The CV for the equations was calculated by the ratio of the SD to the mean. It is a measure of dispersion of probability of distribution.  Scatter was measured by the median absolute difference (MAD) between calculated and measured GFR. A smaller value of MAD would indicate that the measured iGFR would be better reflected by the predicted eGFR. 
Accuracy  was used as the percentage of GFR estimates lying within 30% range of measured GFR.
where n is the total number of observations.
Accuracy of 100% means that the test identifies all true values correctly. Comparison of accuracy of eGFR across various stages of CKD was measured by the McNamara test. 
All statistical evaluations were performed for the total group as well as separately for patients with different stages of CKD. Both the T-test and ANOVA for paired data were used to compare the results of the eGFR equations versus the iGFR results. It should be noted that both gave similar results and, therefore, only the T-test findings were reported in this paper.
Continuous data is presented as mean ± SD and discrete variables as frequency (%). A P <0.05 was considered to be statistically significant. We used the Statistical Package of Social Science (SPSS, version 15), MedCalc Statistical Software (Mariakerke, Belgium, www.medcalc.be) and MS Excel to perform the analysis.
| Results|| |
Creatinine calibration Differences in calibration of the serum creatinine assay across laboratories can influence the accuracy and bias of creatinine-based formulae to estimate GFR. ,, Therefore, we compared the simultaneous measurement of serum creatinine at our laboratory and at Quintiles Laboratories Ltd., GA, USA, where the IDMS method is used. There was excellent parallelism between the local and central methods, with a mean difference of 1.06 μmol/L only; thus, no correction factor was needed to normalize our creatinine values. 
Using isotope GFR scan as a reference method, we simultaneously analyzed three published equations for the prediction of GFR slopes over a wide range of renal function in post-transplant CKD patients with Scr range from 0.49 to 12.93 mg/dL, with a mean ± SD of 1.66 ± 0.93 mg/dL. The data set consisted of 61 male and 36 female patients, with a total of 787 observations. Patients were on prednisolone, cyclosporine (a calcineurin inhibitor), mycophenolate mofetil, mycophenolate sodium or azathioprine. The cohort patients' demographics are summarized in [Table 1]. Our population comprised mainly middle- and old-aged individuals.
[Table 1] shows also the main descriptive results. The first iGFR was performed at a mean duration of 29.45 ± 47.65 months from the time of transplantation. Ten patients had four scans. Twenty-nine patients had five to six scans. Thirty-four patients had seven to 10 scans and 24 patients had 11-17 scans. The mean number of isotope scans/patient was 8.11 ± 3.13 scans. The mean duration between two scans was 18.7 ± 11.5 months (95% CI of 13.1-24.3). The mean duration of follow-up was 7.72 ± 6.72 years. As expected, the data set was not normally distributed (P-value from Kolmogorov-Smirnov tests was <0.05), with the majority of GFR values being <90 mL/ min/1.73 m 2 . The mean reference iGFR of the total population of 787 scans was 62.37 ± 30.34 mL/min. A total of 10% had iGFR between ≥15 and <30 mL/min/1.73 m 2 (stage 4), 40% had iGFR between ≥30 and <60 mL/min/1.73 m 2 (stage 3), 31% had iGFR between ≥60 and <90 mL/min/1.73 m 2 (stage 2) and 17% had iGFR above 90 mL/min/1.73 m 2 (stage 1). We had a small number of iGFR values (n = 14, 2%) in stage 5 (<15 mL/min/1.73 m 2 ) and, therefore, these were excluded from all analyses.
Study of bias, precision, CV, scatter, correlation and accuracy
[Table 2] presents the main findings. A bias of up to ±10% from the measured GFR value is considered clinically acceptable.  All GFR estimators showed a marked bias to estimate GFR in CKD stage 1. Both CG and Virga demonstrated excellent bias in stage 2, while the MDRD2-IDMS demonstrated a good bias of -5.23 and 5.84 mL/min/1.73 m 2 in stages 3 and 4, respectively. Precision as measured by RMSE, coefficient of variance and scatter showed similar trends. The correlative analysis, with the reference iGFR, showed a limited R value of no more than 0.52 mL/min/1.73 m 2 at any stage. The correlative analysis of each formula showed a wide difference across stages. For example, the MDRD2-IDMS demonstrated an R value of 0.14 and 0.46 in stages 2 and 3, respectively. Our results showed a higher accuracy by Virga equation in all stages except in stage 4, where MDRD2-IDMS showed highest accuracy. The MDRD2-IDMS had the lowest accuracy, 36.7%, in stage 1, while the CG demonstrated the lowest accuracy, 40%, in stage 4. Importantly, the results demonstrated significant differences in bias, precision and accuracy of each of the three estimators across the various stages of CKD when compared using the McNamara test.
|Table 2: Performance of mathematical equations to measure glomerular filtration rate across various stages of chronic kidney disease.|
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| Discussion|| |
In this study, we utilized the two most commonly used equations as well as the Virga equation,  which performs well in our hand.  Performances of iGFR across the K/DOQI stages raise an interesting point for discussion. Comparison of bias, precision and accuracy across the stages showed frequent and statistically different results when compared with the reference iGFR, concluding a detrimental effect of the stage of CKD on performance of the GFR equations. Accuracy within 30% of the true GFR was consistently higher across CKD stages 1-3 for the Virga equation. There was fluctuation in the level of accuracy across the stages. For example, accuracy of the MDRD2-IDMS equation within stage 1 was low at 36.7% compared with 70.7% in stage 4. Similarly, accuracy at stage 4 for the Virga equation was low at 48.7% compared with 85.5% at stage 2. There was also marked fluctuation in analysis of bias across all stages. For example, bias was low at 0.2 for CG in stage 2 while it increased dramatically to 41.3 in stage 4.
[Figure 1] shows a graphical presentation of variation in accuracy and bias of the three estimators. The results exposed the limitation of the current equations to sensitively predict GFR across CKD stages. In particular, and consistent with the literature,  all three estimators demonstrated poor sensitivity in stages 1 and 2. Improved sensitivity in stages 3 and 4 are of less practical use. It is possible, then, that in the less-stable population, increased variability in rates of decline in renal function may masquerade significant unseen differences in rates of decline in kidney function across the various CKD stages.
|Figure 1: Analysis accuracy (A) and bias (B) across various stages of chronic kidney disease.|
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In one of our previous works using inulin to measure GFR, we concluded that the current equations lack consistent good performance to define CKD.  We demonstrated that the IDMS equation missed 30%, although it demonstrated a high specificity. Other researchers reached similar conclusions. , Based on the limited performance to estimate CKD, White et al suggested that prospective studies are needed to determine whether the adoption of these equations for classification would lead to improved recognition of CKD complications or patient care. 
The K/DOQI CKD classification scheme was designed in part to offer guidelines for intervention based on different levels of GFR. Although it remains useful in epidemiological studies and general guidelines, the current findings are disturbing as accuracy to stage GFR remains low.
Recently, the pitfalls in use of kidney equations have been discussed.  Based on these limitations, there is an increasing awareness that other markers that can predict course of kidney failure should be added to the staging system, such as albuminuria. ,, As such, our paper would strengthen the argument for looking for markers other than GFR equations in staging patients with kidney disease.
Our findings have clinically important relevance. Recently, Eriksen et al  suggested that the addition of a chronicity criterion is an important determinant of the characteristics of the population of patients with CKD stage 3 and 4. In addition, Kukla et al  found that death rates were no different in stage 3 compared with stage 2 CKD, suggesting that eGFR and the current staging classification have a limited value to predict patient death in this cohort.
| Limitations|| |
Several limitations of this analysis deserve comments. Firstly, we selected a patient population from one center. Independent observations by other centers would be helpful to support our conclusions. Secondly, it was a retrospective study and therefore subjected to investigative bias. Thirdly, GFR tests were not routinely performed on all patients and, therefore, we cannot extrapolate actual or estimated rates of decline in kidney function in our center. Fourthly, we did not calibrate serum creatinine. A small systematic error in serum creatinine measurement can affect the results of GFR.  Hallan et al  previously showed that the bias due to a missing calibration decreases as serum creatinine increases. This is crucial as our cohort comprised a considerable percentage of patients with abnormal serum creatinine levels. Stevens et al  suggested that creatinine calibration to IDMS resolved most of the over- and under-estimation of GFR when using the MDRD formula without calibration. We calibrated our method to the IDMS method, and we have found that the error is too small to cause a large error in interpretation. 
| Conclusion|| |
Our results highlight the significant variation of the current GFR estimators to accurately and precisely estimate transplant function across various stages of CKD. Gold standard techniques are therefore necessary to determine GFR, particularly in clinical studies.
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Director of Transplant Program, Department of Medicine, Division of Nephrology, University of Saskatchewan, 103 Hospital Drive, Saskatoon, SK S7N 0W8
[Table 1], [Table 2]