NDT Advance Access published online on August 28, 2008
Nephrology Dialysis Transplantation, doi:10.1093/ndt/gfn477
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Longitudinal analysis of performance of estimated glomerular filtration rate as renal function declines in chronic kidney disease
1 Department of Nephrology, Western Hospital, Melbourne, Victoria, Australia 2 Department of Nephrology, St Paul's Hospital, Vancouver, BC, Canada 3 Department of Renal Medicine, Gosford Hospital, Gosford, New South Wales, Australia
Correspondence and offprint requests to: Darren Lee, Department of Nephrology, Austin Health, Studley Road, Heidelberg, VIC 3084, Australia. Tel: +61-3-9496-5000; Fax: +61-3-9496-5123; E-mail: vrsadhkl{at}hotmail.com
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Abstract |
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Background. Numerous studies have assessed the accuracy of equations estimating glomerular filtration rate (eGFR) from serum creatinine in individuals with chronic kidney disease (CKD) in cross-sectional studies. Limited literature exists, however, on the consistency of performance of these equations in longitudinal studies as renal function declines.
Methods. Radionucleotide-measured GFR from 155 predialysis patients with stage 3–5 CKD was compared with eGFR derived from four equations [6-variable Modification of Diet in Renal Disease (6-MDRD), 4-variable MDRD (4-MDRD), Cockcroft–Gault (CG) and Cockcroft–Gault equations corrected for body surface area (CGC)] at baseline, 12 and 24 months. Bias (difference between eGFR and measured GFR) was used as a measure of performance. Restricted Maximum Likelihood (REML) models were used to identify variables potentially affecting the performance of estimating equations across time.
Results. Mean measured GFR (±SD) at baseline, 12 and 24 months was 25.9 ± 10.7, 23.1 ± 10.6 and 20.3 ± 10.1 mL/min/1.73 m2, respectively. There was a statistically significant negative association between bias and GFR for all four estimates (range: –0.76 to –0.71, P < 0.001 for all), indicating worsening underestimation and overestimation at higher and lower GFR, respectively. This negative association significantly reduced over the 24 months (P < 0.001); however, this was largely due to persistent underestimation of eGFR from individuals with GFR >50 mL/min/1.73 m2. For those with a baseline GFR <50 mL/min/1.73 m2, the change in bias for any of the four equations over 24 months was 
1.1 mL/min/1.73 m2, suggesting relatively preserved performance with time. The MDRD equations showed a sustained advantage in estimating renal function that was more evident as GFR declined.
Conclusion. GFR estimates are inexpensive and show an acceptable longitudinal performance for monitoring CKD patients with GFR <50 mL/min/1.73 m2. Inaccuracies appear more substantial above this level of GFR, and care with interpretation is required.
Keywords: Cockcroft–Gault; eGFR; longitudinal; MDRD
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Introduction |
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The health burden of chronic kidney disease (CKD) is extensive, yet the prevalence is frequently underestimated. In the United States alone, the total Medicare costs for CKD approached US$42 billion in 2005. For those who progressed to end-stage renal disease (ESRD), the costs neared US$21 billion, accounting for 6.4% of the entire budget consumed by <0.5% of Medicare recipients [1]. Prevention of progression of CKD to ESRD depends upon early detection and continued monitoring; hence a reliable and ready method of measuring kidney function is vital. Radionucleotide-derived glomerular filtration rate (GFR) is accurate but inconvenient and expensive to perform. Therefore, numerous GFR prediction equations, which include serum creatinine and various variables, have been developed to generate acceptable estimates of GFR. The most widely used equations include Cockcroft–Gault with or without corrected for body surface area (BSA) [2,3], and the 6- and 4-variable Modification of Diet in Renal Disease (MDRD) [4,5].
Whilst the use of the MDRD formula in CKD in particular has been extensively validated in cross-sectional cohorts [2,3,6–14], longitudinal studies examining its performance over time within the same cohort are lacking. Hence, this longitudinal study examined whether the performance of these four equations varied, compared with measured nuclear radiopharmaceutical clearance estimation of GFR, within a cohort comprising patients with established CKD (stages 3–5) over a 2-year period.
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Methods |
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Patient selection
Data were collected from a prospective multi-centre trial conducted in Australia and New Zealand, the details of which have been previously published [15]. Briefly, it was designed to assess the effect of early correction of anaemia with epoetin alfa (Johnson & Johnson, Langhome, Pennsylvania, USA) on left ventricular mass in patients with CKD. One hundred and fifty-five patients aged 18–75 were randomized to two different groups with target haemoglobin concentrations within the ranges of 120– 130 g/L and 90–100 g/L. All patients were required to have an eGFR between 15 and 50 mL/min estimated from the Cockcroft–Gault equation adjusted for BSA [3]. GFR measurements either by 51Cr-EDTA (51chromium ethylene diamine tetraacetate) or 99mTc-DTPA (99mtechnetium diethylene triamine pentaacetic acid) clearance, as well as serum albumin, urea, creatinine, height and weight (and BSA) were obtained at baseline, 12 and 24 months in the local research centres after randomization. Estimates of GFR at the three time points for the subjects were derived from these measurements using the following equations: (i) 6-variable MDRD (6-MDRD), (ii) 4-variable MDRD (4-MDRD), (iii) Cockcroft–Gault (CG) and (iv) Cockcroft–Gault corrected for BSA (CGC) [2–5].
Statistical analysis
Genstat 9 (2006, VSNi, Hemel Hempstead, UK) and Mini- tab 14 (2004, Minitab Inc, Stage College, Pennsylvania, USA) were the statistical software packages used to analyse data and produce graphs, respectively. Bias (difference between eGFR and measured GFR) was used as a measure of performance. The mean bias from each estimating equation was compared at baseline, 12 and 24 months. The analysis was further categorized into various stages of CKD according to the measured GFR values, namely stages 3 (30.0–59.9 mL/min/1.73–m2), 4 (15.0–29.9 mL/min/1.73 m2) and 5 (<15.0 mL/min/1.73 m2). The patients whose measured GFR at 12 and/or 24 months was less than that at baseline were re-categorized as necessary to the appropriate new CKD stage for calculation at 12 and/or 24 months.
The bias values from each of the four estimating equations were plotted on the y-axis as a function of measured GFR values on the x-axis, graphed separately for each of the three time points (baseline, 12 and 24 months). Linear regression lines were then fitted through these data points, one for each equation. Should there be a relationship between bias and measured GFR, the slope of the regression line would be either downwards or upwards. If there was no change in the performance of the equations with time, the relationship between bias and measured GFR should be unchanged, and the three regression lines at different time points for each equation would be similar in terms of slope and location.
A Restricted Maximum Likelihood (REML) algorithm, which is a method of analysis for linear mixed models, was used to assess statistically the similarity of the regression lines for each time point. A separate linear mixed model was fitted for each equation, incorporating the variables potentially affecting the performance (measured as bias): (i) measured GFR value, (ii) time point (baseline, 12 and 24 months), (iii) interaction effect between GFR and time point, (iv) race (Caucasians or non-Caucasians), (v) presence of diabetes, (vi) haemoglobin (Hb) level at time point (g/L), (vii) parathyroid hormone (PTH) level at baseline (pmol/L), (viii) systolic blood pressure at time point and (ix) diastolic blood pressure at time point. The coefficients represented the strength of the effect of each explanatory variable on the performance of the estimating equations. Statistical significance would be achieved at a P-value of <0.05.
Estimated GFR values were plotted on the y-axis as a function of measured GFR values, graphed separately for each of the four equations. Linear regression lines were fitted through these data points, one for each time point. The R2-values of the regression lines for each equation, as a measure of degree of correlation and precision, were compared across the three time points.
Data were censored as follows: three patients were excluded from the original study due to unsatisfactory echocardiographic images and six with incomplete data for measured GFR at any of the three time points and/or eGFR at baseline. One hundred and forty-six patients were therefore available for analysis.
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Results |
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The baseline characteristics of the study cohort are shown in Table 1. The mean measured GFR (±SD) at baseline, 12 and 24 months was 25.9 ± 10.7, 23.1 ± 10.6 and 20.3 ± 10.1 mL/min/1.73 m2, respectively. Most subjects (63%) had stage 4 CKD at baseline. The 14 (9.6%) non-Caucasians included were of indigenous ethnic background from Australia, New Zealand and the Pacific Islands with the exception of one Asian and one African American.
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Table 2 shows the mean bias (±SD) derived from the four GFR estimating equations with measured GFR at three time points in the study cohort. The two MDRD equations initially underestimated GFR, a tendency that reduced with time. The two Cockcroft–Gault equations (particularly if not adjusted for BSA) overestimated GFR and showed no consistent change over 2 years.
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Regardless of the equation used, low GFR was overestimated (positive bias values) whereas high GFR was underestimated (negative bias values) (Figure 1). There was a strong negative association between the bias and GFR at all three time points, which was most evident for CG with the greatest negative coefficient representing the gradient of the regression line (Table 3). Despite this generalization, at the same level of GFR, CG was more likely to overestimate true function compared with the MDRD equations (Figure 1).
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When the regression lines were compared at each time point for all equations, the gradient became progressively less steep with time, suggesting that the performance of the equations changed over time. However, the bias difference between equations remained constant at each time point and over the range of renal function measured. This is illustrated in Figure 1, where the slopes for the four equations were virtually parallel at all three time points.
Using the REML models (Table 3), GFR (P < 0.001), time point (P < 0.001) and the interaction effect between GFR and time point (P < 0.02) were all statistically significant factors. An increase in Hb concentration was associated with a modest but statistically significant overestimation (P < 0.001), whilst an increase in the PTH level was associated with a small underestimation of GFR (P < 0.001). Race did not significantly affect the performance of any of the four equations with time.
Figure 2 illustrates the data points for bias from the four equations at three time points where measured GFR values were categorized as stages 3, 4 and 5, the mean bias values of which are also presented in Table 2. The two MDRD equations underestimated GFR to a greater degree in stage 3 CKD. CG generally overestimated GFR, particularly for stage 5 CKD where MDRD equations were more reliable in comparison.
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Figure 3 shows the regression lines for GFR estimates from the four equations as a function of measured GFR. R2 values for MDRD equations were greater than those for CGC and CG at all time points (0.49–0.66 versus 0.33–0.59). Regardless of the equations, superior correlation between estimated and measured GFR was demonstrated with time, suggesting improved performance.
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Figure 2 highlights the five outliers for 6-MDRD and 4-MDRD and three outliers for CG and CGC in stage 3 disease at baseline, representing underestimation of GFR by >20 mL/min/1.73 m2. These outliers corresponded to the individuals with measured GFR values >50 mL/min/ 1.73 m2 at baseline in Figure 1. There were six subjects whose GFR was overestimated by >18 mL/min/1.73 m2 by all four equations. Table 3 shows the mean bias from the equations in the current study if these six individuals were excluded. Exclusion of these subjects reduced the inaccuracy of GFR estimates at baseline particularly by the MDRD equations, making the apparent improvement in underestimation from the baseline to 12 months much less evident. For GFR <50 mL/min/1.73 m2, the change in the mean bias by any equation over the 24-month period was only
1.1 mL/min/1.73 m2, reduced from 1.9 mL/min/ 1.73 m2, indicating relatively preserved reliability of all four equations across the three time points (Table 2). However, the change in performance with time remained statistically significant for all equations (P < 0.001) using the REML models. |
Discussion |
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This is the first study to examine the consistency of performance of eGFR with time in a cohort comprising predominantly a Caucasian population with GFR <60 mL/ min/1.73 m2. One previous study analysed a cohort of autosomal dominant polycystic kidney disease with GFR >70 mL/min/1.73 m2 [16], whilst another study included only African Americans with a mean GFR of 46 ± 13 mL/min/1.73 m2 [17,18], compared to initial results of 25.9 ± 10.7 mL/min/1.73 m2 in this present study. Both of these previous studies evaluated the validity of eGFR-based outcomes as surrogate end-points in longitudinal studies when compared to measured GFR for research purposes. In contrast, the aim of this study was to examine the longitudinal performance of eGFR for clinical practice.
With the exception of Caucasians and African Americans, GFR estimates have not been well validated in other ethnic groups. Small studies provided evidence that the MDRD equations, without modifications, did not perform well in Chinese or Japanese populations [19–21]. Less than 10% of the study cohort that was non-Caucasian comprised predominantly an indigenous ethnic background. The REML models did not demonstrate race as a statistically significant factor affecting the performance of any of the equations in the present study; however, none of these equations has been adequately studied in indigenous populations in Australia, New Zealand and the Pacific Islands, and a type II error cannot be excluded given the small subject numbers.
A consistent finding of this study was the strong negative association between bias and GFR. The higher the GFR, the more likely it would be underestimated regardless of the equations or time points, and vice versa. However, CG (particularly if not corrected for BSA) overestimated at a much higher GFR compared to MDRD (Figures 1 and 2). This is consistent with previous studies where MDRD equations significantly underestimated GFR in patients with near-normal renal function [7,8]; however, when GFR was <60 mL/min/1.73 m2, performance was superior to the Cockcroft–Gault formula [7,9–11], (originally derived from a population with a mean GFR of 72.7 mL/min/1.73 m2, calibrated against creatinine clearance [2]). When corrected for BSA, the Cockcroft–Gault formula has been shown to improve accuracy, especially with creatinine clearance <50 mL/min [3], similar to our findings as shown in Table 2.
An unexpected finding from this study was that the reliability of all four equations varied with time. The progressively less steep gradients of bias versus GFR from baseline to 24 months suggested improving performance with time (Figure 1). The steeper gradient at baseline, however, was at least partially influenced by the six outliers with an initial GFR >50 mL/min/1.73 m2 compared to one at 12 months and none at 24 months. After excluding patients with GFR >50 mL/min/1.73 m2, the change in the mean bias over 24 months was 1.1 mL/min/1.73 m2, compared to 1.9 mL/min/1.73 m2 (Table 2). This suggested that these underestimating outliers at baseline contributed to the apparent improved performance with time. Despite the modest change remaining statistically significant, it would be unlikely to affect clinical decision making for an individual patient. Similarly, the apparently improved correlation between GFR estimates and measured GFR with time was at least partially influenced by the decline in GFR (Figure 3). At a given time point, both MDRD equations provided more precise GFR estimates compared with CG and CGC as evident by greater R2 values, consistent with previous literatures [4,6].
Discrete CKD stage, similar to GFR, had a significant relationship with equation reliability. The tendency for greater underestimation in stage 3 disease at baseline compared with the other two time points could again be explained by the outliers with initial GFR >50 mL/min/1.73 m2. After exclusion of individuals with GFR >50 mL/min/ 1.73 m2, the decline in mean GFR in stage 3 CKD from baseline to 12 months reduced substantially from 3.9 to 1.6 mL/min/1.73 m2. Within the same CKD stage (after exclusion of outliers), the consistency of the performance of the four equations was relatively preserved across time (Figure 2). However, as renal function deteriorated, the MDRD equations provided more reliable GFR estimates than CG, which significantly overestimated GFR in stage 5 CKD.
A significant number of patients had GFR values changing from one stage to another, mostly progressing from stage 3 to 4 or stage 4 to 5 as their renal function declined, not to mention the 39 patients who commenced dialysis during the study period and were therefore excluded from the original study at 12 and/or 24 months. As a consequence, the characteristics of patients included in the same stage at different time points could have changed significantly, potentially influencing the performance of the equations. For instance, the mean GFR in stage 3 at baseline was 39.3 mL/min/1.73 m2 compared with 35.1 mL/min/1.73 m2 at 24 months, and the sample sizes of stage 3 and stage 4 at 24 months were almost half that at baseline whereas that of stage 5 was more than doubled (Table 2).
Haemoglobin and PTH concentrations were expected to decrease and increase, respectively, as GFR declined, when eGFR would tend to overestimate these measurements. Counterintuitively, however, each g/L increase in Hb concentration was associated with an overestimation of GFR of <0.13 mL/min/1.73 m2, whilst an increase of 1 pmol/L in the PTH level was associated with an underestimation of <0.17 mL/min/1.73 m2 (Table 3). No clear explanation was identified for these statistically significant relationships, and the possibility of a type I error could not be excluded. Regardless of the explanation, again they were unlikely clinically relevant given the minor degree of error associated with the change in Hb and PTH concentrations.
There are several limitations to this study. Firstly, the study cohort predominantly comprised middle-aged Caucasians with mainly stage 4 CKD at baseline, with less than one quarter due to diabetic nephropathy (Table 1). Therefore, the current findings may not apply to some individuals. Secondly, even though race was not found to affect the performance of the equations, generalization of the results to indigenous populations, accounting for <10% of the study cohort, should be done with caution until these estimating equations are validated in larger studies. Thirdly, despite including numerous variables in the analysis, other variables that were not incorporated in the models could potentially influence the outcome. Serum creatinine assays were not calibrated, and the serum creatinine samples were processed in different research centres although by the same laboratory for each patient. Inconclusive results have been reported from small studies in the 1960s and 1970s regarding the accuracy of 51Cr-EDTA and 99mTc-DTPA clearances [22–28], but no recent human studies have directly compared the clearances of the two radionucleotides against the gold standard, inulin. In the present study, one or other radionucleotide was used to measure GFR, and the same agent was used for each individual. Finally, the challenge with the analyses in this study has been to control for the potential change in mean GFR with time and different stages of CKD in the subcohorts. Due to a significant number of patients dropping out of the study as they commenced dialysis, and the deterioration of GFR over the 2-year study period, there was an inevitable shift to a lower range of GFR from baseline to 24 months (Table 2). Since the performance of the equations changed depending on the level of GFR, the findings of the differences with time could be at least partially influenced by the decline in GFR.
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Conclusion |
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The MDRD equations have been extensively validated in multiple studies to provide superior performance in estimating GFR <60 mL/min/1.73 m2 when compared to the Cockcroft–Gault formula in cross-sectional cohorts. This longitudinal study identified statistically significant but generally modest changes in the performance of all four equations with time. This was largely explained by the decline in GFR in the study cohort. Importantly, the consistency of estimation was relatively preserved for a GFR <50 mL/min/1.73 m2. Further longitudinal studies examining a larger cohort will help verify the consistency of the performance of these equations.
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Acknowledgments |
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The authors would like to thank the other investigators of the Australian Predialysis Study involved in part of the data collection. We would also like to thank Janssen–Cilag for the sponsorship of statistical analysis and the original study.
Conflict of interest statement. Simon D. Roger is members of the advisory boards and speakers bureau for F. Hoffmann-La Roche Ltd and Amgen. The remaining authors have no conflict of interest to declare.
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Accepted in revised form: 31. 7.08
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