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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Curr Opin Nephrol Hypertens. Author manuscript; available in PMC 2011 October 13.
Published in final edited form as:
PMCID: PMC3192437

Advances in Glomerular Filtration Rate Estimating Equations


Purpose of review

Estimated GFR is now commonly reported by clinical laboratories. Here we review the performance of current creatinine and cystatin C based estimating equations as well as demonstration of their utility in public health and clinical practice.

Recent findings

Lower levels of GFR are associated with multiple adverse outcomes, including acute kidney injury and medical errors. The new CKD-EPI equation improves performance and risk prediction compared to the MDRD Study equation. Current cystatin C based equations are not accurate in all populations, even in those with reduced muscle mass or chronic illness, where cystatin C would be expected to outperform creatinine. eGFR reporting has led to a greater number of referrals to nephrologists, but the increased numbers do not appear to be excessive or burdensome The MDRD Study equation appears to be able to provide drug dosage adjustments similar to the Cockcroft and Gault.


Estimated GFR and their reporting can improve and facilitate clinical practice for chronic kidney disease. Understanding strengths and limitations facilitates their optimal use. Endogenous filtration markers, alone or in combination, that less dependent on non GFR determinants of the filtration markers are necessary to lead to more accurate estimated GFR.

Keywords: glomerular filtration rate, creatinine, cystatin, prognosis


The level of glomerular filtrate rate (GFR) is accepted as the most useful index of kidney function in health and disease. Chronic kidney disease is defined as GFR less than 60 ml/min per 1.73 m2 as well as markers of kidney damage [1, 2]. Reduction in GFR is associated with symptoms and laboratory manifestations of kidney disease [2]; as well as cardiovascular disease [35]; and as has more recently been demonstrated, acute kidney injury [6] and medical errors [7]. Given the centrality of GFR to CKD diagnosis, evaluation and management, the National Kidney Education Detection Program (NKDEP) [8] in the United States and organizations in other countries recommend to laboratories to report estimated GFR (eGFR) using the MDRD study or other equation whenever a serum creatinine was ordered [911]. The reporting of eGFR has been received by some as a landmark in public health campaign for the improvement in care and outcomes for patients with CKD, while others have raised concerns that the limitations of the equations lead to misclassification of patients with CKD [1216]. Regardless of one’s opinion, it appears as if eGFR will be an increasingly important component of clinical practice. In the United States, recent data show that greater than 77% of laboratories report eGFR [17], and by the end of 2009 the vast majority of these laboratories will use standardized creatinine assays so as to improve the accuracy of these estimates. In addition, new recommendations from NKDEP state that eGFR calculated from the MDRD Study equation can be used for adjustment of medications based on kidney function [18]. In this review, we report on the recent literature (January 2008 to September 2009), which addresses the performance of estimating equations as well as demonstration of their utility in public health and clinical practice. Our perspective is that there are both strengths and limitations of GFR estimates, and while the introduction of eGFR reporting into widespread clinical practice has been an advance, optimal interpretation and use of GFR estimates requires attention to their limitations.


We first review the literature on the development and performance of estimating equations and then review the literature describing their use in clinical practice.

Measured GFR and rationale for estimating equations

The gold standard measurement for GFR requires urinary or plasma clearance of exogenous markers. These measurements are difficult to perform, and GFR is usually estimated from steady-state serum levels of endogenous filtration markers. Estimating equations incorporate demographic and clinical variables as surrogates of unmeasured physiologic processes that also affect the serum level [19, 20]. While equations are more accurate than the serum level of the marker, they only capture the average relationships between the marker and its non-GFR determinants, and, the relationship between the marker and its non-GFR determinants may vary across populations and over time. As such equations may be inaccurate when applied to different populations from which they were derived [20].

Table 1 [2131] and Table 2 [23, 3033] describe the methods and results of the studies that have evaluated the performance of creatinine and cystatin C based equations, respectively, from January 2008 to September 2009. Performance of estimating equations can be described according to bias, precision, and accuracy, where bias is defined as systematic deviation of estimated GFR compared to measured GFR using the reference (“gold”) standard; imprecision is defined as random variation (or “spread”) of estimated GFR values centered about the measured values; and accuracy incorporates both bias and imprecision [34]. The specific metrics used for each of these parameters varied across each study. In order to compare across studies, in the tables, we provide a qualitative assessment of the equation that performs best for each of bias, precision and accuracy.

Table 1
Studies evaluating creatinine based GFR estimating equations*
Table 2
Studies evaluating cystatin C based glomerular filtration rate estimating equations*


Eleven studies described the development or evaluation of creatinine based equations (Table 1) [2131] Of those, 6 studies (55%) used standardized creatinine, which is an increase from our prior review where 28% of the studies used appropriate creatinine methods [35]. The three creatinine equations used in these studies were the MDRD Study, Cockroft-Gault and the Mayo Clinic equations [21, 36, 37].

General or diverse populations

Three studies evaluated equations in general or diverse population samples (Table 1). One study compare the MDRD study equation to the Mayo Clinic equation in the general population in New Zealand and showed the MDRD Study equation performed better across all three measures of performance This is inconsistent with the fact that Mayo clinic equation was developed in a population with and without CKD, whereas the MDRD Study equation was developed in populations with CKD. Another study evaluated the Cockroft-Gault and the MDRD Study equations in 2208 Europeans and showed lesser bias with the Cockroft-Gault equation but greater precision with MDRD Study equation [22]. In May 2009, a new equation, the CKD-EPI equation, was developed in a pooled dataset from 10 studies that included participants of diverse clinical characteristics, with and without kidney disease, and validated in a separate dataset pooled from 16 additional studies [21]. In the 16 studies used for its validation, the CKD-EPI equation was more accurate than the MDRD Study equation with lower bias especially at an estimated GFR greater than 60 ml/min per 1.73 m2; however precision was not substantially improved compared to the MDRD Study equation [21].

Special Populations


Three studies evaluated the performance of the estimating equations in patients with diabetes [2325]. Overall, there does not appear to be a clear consensus that one equation is better, but most studies did not use standardized creatinine and therefore optimal comparisons were not possible.

Kidney Donors

One study compared the performance of the Cockroft-Gault, MDRD Study and Mayo Clinic equations in 255 kidney donors [26]. The MDRD Study equation performed better than the Mayo Clinic and Cockroft-Gault equations, consistent with the findings from the study in the general population in New Zealand described above [27].


Matsuo and colleagues modified the MDRD Study equation for use in the Japanese population and standardized creatinine in 413 participants and validated in 350 participants[28]. The modification leads to a lower GFR estimate for the same level of creatinine. The new equation led to improved performance compared to the original MDRD Study equation as well as their prior modification of the MDRD Study equation for use with non-standardized creatinine methods [38].

Another study evaluated the performance of original MDRD Study equation and the MDRD Study equation modified with the Chinese and Japanese coefficients in a Chinese population [29]. In contrast to the Japanese coefficient, the Chinese coefficient leads to a higher GFR estimates for the same level of creatinine. In patients with eGFR greater than 90 ml/min per 1.73 m2, bias and accuracy improved with the use of the Chinese coefficient compared to the original MDRD Study; however, in the GFR range 30–59 ml/min per 1.73 m2, the use of the Chinese coefficient lead to worse bias and accuracy compared to the MDRD Study equation.

In the Chinese population, the Japanese coefficient had greater bias across all GFR levels. This has been posited to be due to differences in GFR measurement methods, creatinine calibration, or true differences in the study populations [39].

Cystatin C

Cystatin C is under investigation as a replacement for serum creatinine in estimating the GFR [4042]. Prior studies demonstrated that the combination of cystatin C and creatinine provides the best estimate [43]. A convergence of evidence now suggests that, in contrast to early reports, there are non GFR determinants of its serum level [44, 45]. Nevertheless, these data also suggest that cystatin C is less dependent upon muscle mass than creatinine, and should provide more accurate GFR estimates particularly in populations with differences in muscle mass. We identified 5 studies that evaluated cystatin C based equations (Table 2) [23, 3033], two of which tested the performance in populations with decreased muscle mass.

CKD population

Sterner and colleagues compared the performance of MDRD Study equation to the Grubb cystatin C based equation [32, 46]. Cystatin C based equation performed superior in terms of bias; although accuracy was similar with the MDRD Study equation.


Willems and colleagues found the MDRD Study equation and the serum level of Cystatin C were similarly accurate [33]. Whereas, Rigalleau et al. showed that the composite equation with both cystatin C and creatinine performed better than any of the creatinine based equations [23].

Anorexia Nervosa

Delanaye and colleagues studied 27 patients with anorexia nervosa [30]. For eGFR less than 60 ml/min per 1.73 m2, the Rule cystatin C equation had the lowest bias. For all other levels of GFR, the Cockcroft and Gault equation had the lowest bias among all cystatin C and creatinine based equations. The improvement with Cockcroft and Gault over other creatinine based equations may be expected given the inclusion of weight in the numerator that leads to more accurate estimates in this extremely underweight population. However, the greater accuracy compared to cystatin C based equations is surprising and may suggest an independent relationship between weight and cystatin C.

Cystic Fibrosis

Beringer and colleagues compared the performance of cystatin based equations to the Cockroft-Gault and MDRD Study equations in patients with cystic fibrosis [31]. The cystatin C based equation outperformed the other equations in terms of precision and accuracy, however, bias was not substantially different among the three equations.

Use of Estimating Equations

GFR estimating equations can be used for detection, evaluation and management of kidney disease. Here, we describe the literature on their use for detection, assessment of change over time of kidney function, referral to nephrologist, drug dosage adjustment and cardiovascular disease prognosis.

Detection of Chronic Kidney Disease

Detection of CKD is important in studies of CKD prevalence and in screening populations at increased risk to detect patients for early treatment. Numerous studies now document the high prevalence of CKD around the world. Several recent studies highlight the difficulty in detecting CKD using estimating equations.

Levey and colleagues compared the distribution of estimated GFR and prevalence of CKD in US adults using the MDRD Study and CKD-EPI creatinine equations as applied to NHANES 1988–2006 [21]. As expected, due to the lesser bias of the CKD-EPI equation compared to the MDRD Study equation, the median eGFR for the population was higher (94.5 vs. 85.0 ml/min/1.73 m2) (Figure 1) and the overall prevalence was lower (11.5 vs. 13.1%, respectively).

Figure 1
Comparison of distribution of estimated GFR and Chronic Kidney Disease (CKD) prevalence by age (NHANES 1999–2004)

Astor and colleagues compared the distribution of eGFR and prevalence of CKD using the MDRD Study and CKD-EPI cystatin C equations in NHANES 1988–1994 [43, 47]. Compared to the MDRD Study equation, use of cystatin C alone or in combination with creatinine led to lower eGFR distributions and higher prevalence estimates of CKD. Foley and colleagues compared trends over time in the distribution of estimated GFR using creatinine and cystatin C in NHANES 1988–84 and 1999–2002 [48]. They found a decrease in eGFR based on creatinine, as had been reported previously [49], but not in eGFR based on cystatin C. Possible explanations for this discrepancy are differences over time in assay calibration of creatinine or cystatin C, or changes over time in the distribution of non-GFR determinants of these markers.

Monitoring Progression of Chronic Kidney Disease

All currently used estimating equations have been developed from cross-sectional databases. Prior analyses of the African American Study of Hypertension and Kidney Disease (AASK) demonstrated that eGFR leads to estimates of a slower but more precise slope of GFR decline than measured GFR. In this review period 3 additional studies evaluated the performance of estimating equations to estimate changes over time in measured GFR.

In the MDRD Study, there was a 28% slower mean rate of decline in eGFR vs. measured GFR and only dietary protein affected the difference between estimated and measured GFR slope [50]. Nonetheless, differences in slope estimates were greater than 2.0 ml/min/173 m2 per year in 41% of patients, due either to differences in non-GFR determinants of serum creatinine or imprecision in measured GFR. A second study compared eGFR using several equations with measured GFR over time in 155 patients in Australia [51]. Over time, the mean difference between estimated and measured GFR was relatively stable, especially in patients with lower GFR. Finally, Abraham and colleagues developed an equation to estimate longitudinal change in GFR from prior measured GFR and changes over time in covariates in children participating in the Chronic Kidney Disease in Children Cohort Study (CKiDS) [52]. Changes in height and serum creatinine were the most important covariates. Notably, when initial GFR measurement was not used, addition of changes in covariates did not add to the accuracy of estimates based on a cross-sectional equation.

Referral to Nephrologists

Three recent reports have described the impact of eGFR reporting on referral to nephrologists. After implementation of eGFR reporting in Ontario, Canada, non-urgent nephrology referrals increased from 134 per nephrologist per year to 156 per nephrologist per year [53, 54]. The 22 additional consults per nephrologist per year translates into an increase in the rate of referral by 2.9 consults per 100,000 population, with a greater increase in women and the elderly, consistent with bias in these groups by serum creatinine. In an evaluation of eGFR reporting in Australia, monthly referrals increased by 40% following the introduction of eGFR reporting [55]. The appropriateness of nephrology referrals fell criteria, although a greater number of CKD patients were appropriately referred [56]. In a UK study, there was an initial increase in the number of referrals following institution of eGFR reporting, which was reversed by the introduction of a referral management program.

Use of GFR estimating equations for drug dosage adjustment

In its Guidance to Industry, the FDA states that the method for assessment of kidney function that is most widely used in clinical practice ought to be the method used for adjustment of drug dosages [57]. At the time, the Cockcroft and Gault was widely used and the FDA provided this equation as an example an estimate that could be used. Since then, the MDRD Study equation is now more widely reported and creatinine assays are standardized to gold standard methods [17].

Several studies have compared the two equations for drug dosing purposes. Table 3 lists the studies that have compared the two equations for this purpose since January 2006 [5866]. There is substantial heterogeneity in the methods used among the studies, which, complicates comparison of the two equations. First, most studies used Cockcroft and Gault as the gold standard by which to compare the drug dosages. However, since the value determined from the equation is dependent upon the creatinine assay used, this is an inappropriate gold standard [18, 67]. Prior to availability of standardized creatinine assays, there was substantial variation in the creatinine assay used, which caused differences in dosing recommendations resulting from pharmacokinetic studies, even for drugs with the same pharmacokinetics. For the same medications, variation in creatinine assays among clinical laboratories caused differences in drug exposure among patients, even if drug dosing recommendations are followed. Therefore, even if the same equation used in the pharmacokinetic studies was used to assign a drug dosage, the assigned drug dosage would likely be different than intended. Only two studies compared the estimates to the gold standard of measured GFR. Second, three studies mentioned whether creatinine method used was standardized and of those, only two used standardized creatinine value. Third, five studies expressed GFR in ml/min (as appropriate for drug dosing). Finally, of the eight studies, five used actual body weight in the Cockcroft Gault equation, whereas five used ideal body weight.

Table 3
Summary of Studies Comparing Kidney Function Estimates for Drug Dosage Adjustment

Studies also differences in the metric used for comparison of the equations. Four studies compared concordance for drug specific dosing levels, with concordance rates ranged from 64 to 89%. Four studies also compared the equations according to predefined CKD stages or eGFR target levels, with reported concordance rates of 37 to 99%. In the two studies that compared estimated GFR to measured GFR, both showed that the MDRD Study equation had greater concordance with measured GFR than the Cockcroft and Gault [58, 59]. One study of inpatients receiving aminoglycoside or vancomycin compared the area under the curve for actual drug levels to the eGFR and showed greater precision for the MDRD Study equation [60]. Importantly, no study looked at adverse outcomes, side effects of ineffective doses.


A number of studies have shown a J-shaped relationship of GFR estimated from serum creatinine and total mortality in studies of the general population [68, 69]. This is likely due to confounding by chronic diseases associated with malnutrition and inflammation causing low creatinine generation and overestimation of measured GFR [70]. These results are especially important in evaluating the risk associated with eGFR <60 ml/min/1.73 m2, since the risk in the reference group is not uniform [71]. When evaluating risk of eGFR 45–59 ml/min/1.73 m2, it is more appropriate to use a more narrow reference group, such as eGFR of 75–89 or 90–104 ml/min/1.73 m2, rather than eGFR >60 ml/min/1.73 m2.

Two recent studies compared the risk of eGFR 45–59 using general population studies. The Atherosclerosis Risk in Communities (ARIC) and the Australian Diabetes, Obesity and Lifestyle study (AusDiab) using the CKD-EPI equation rather than the MDRD Study equation, due to reclassification of low risk patients to higher eGFR when using the CKD-EPI equation [72, 73].

Astor and colleagues compared risk prediction for all cause and cardiovascular disease mortality in NHANES 1999–1994 based on CKD-EPI cystatin C equations and MDRD Study equation [47]. GFR estimates using cystatin C or cystatin C plus creatinine provided more accurate predictions than the MDRD Study equation. In particular, the risk relationship of estimated GFR computed using either cystatin C or cystatin C plus creatinine to mortality was more steep at eGFR >60 ml/min/1.73 m2 compared to the MDRD Study equation.


In the current era, there are advances in our understanding of the performance and utilization of GFR estimation. First, the new CKD-EPI equation developed in people with and without kidney disease, and that which uses the same four variables as the MDRD Study equation, but which improves bias and risk prediction, without a decline in accuracy in people with CKD, is an important step forward. The CKD-EPI equation should replace the MDRD Study equation for routine clinical use. Second, there is now recognition that there are non GFR determinants of cystatin C, and therefore while a better predictor of risk, is not necessarily a more accurate estimate of GFR, even in populations with low muscle mass. Indeed, the two studies that evaluated estimating equations in populations with reduced muscle mass, did not clearly show cystatin C to an improvement over creatinine based equations. New GFR estimates that are less 14 dependent upon nonGFR determinants are required to improve GFR estimates across populations as well as within populations over time. Third, the availability of GFR reports has a substantial effect on clinical practice. However, the impact needs to be further studied and education programs as to use these estimates needs to be developed.


Sponsorship statements

Lesley Stevens: Research support from the NIH, National Kidney Foundation and Gilead Inc

Smita Padala: none declared

Andrew Levey: Research support from the NIH, National Kidney Foundation, Gilead Inc and Amgen

We are grateful to Aghogho Okparavero MBBS, MPH for his assistance in preparation of the manuscript


Conflict of Interest: none declared


Papers of particular interest, published within the period of review, have been highlighted as:

*of special interest

**of outstanding interest

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47* Astor BC, Levey AS, Stevens LA, Van Lente F, Selvin E, Coresh J. Method of glomerular filtration rate estimation affects prediction of mortality risk. J Am Soc Nephrol. 2009;20:2214–2222. This study evaluated the risk of cardiovascular mortality in the National Health and nutrition examination survey 1988–1994. Compared to the MDRD Study equation, use of cystatin C alone led to lower eGFR distributions and higher prevalence estimates of CKD. [PubMed]
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