Introduction

Chronic kidney disease (CKD) has become a worldwide epidemic problem due to the significant increase in prevalence, serious complications, and the huge expense of management including treatment and care [1–5]. The glomerular filtration rate (GFR) is recognized as the best overall indication of renal function [6–8], because it can provide an excellent measure of kidney filtering capacity and it is an important parameter for adjusting the treatment plan and assessing prognosis. Unfortunately, the inulin clearance method, the gold standard for GFR determination, cannot be applied widely in clinical practice because of the complexity and cost. Therefore, several alternative measures for estimating GFR have been devised [9–14]. Although there is continuous discussion about which one is the most accurate method, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation developed by the Chronic Kidney Disease Epidemiology Collaboration in 2009 may be the most appropriate formula based on creatinine in determining GFR in Chinese patients with CKD [15–18].

A new modified CKD-EPI equation was developed by Liu in 2014 aimed to improve the performance of the GFR equation, and the results showed that the new modified equation achieved less bias, greater accuracy and parallel precision compared to the original CKD-EPI equation [19]. It seemed that the modified one should be preferred as the first choice instead of the original one. However, we found that the included subjects in the study were type 2 diabetic patients but not CKD patients. Moreover, the employed reference method was a calibration equation from 99mTc-diethylene triamine pentaacetic acid (99mTc-DTPA) renal dynamic imaging but not the genuine 99mTc-DTPA dual plasma sample clearance method that is recommended as the reference approach in determining GFR by the Nephrology Committee of the Society of Nuclear Medicine [20]. In order to validate the applicability of the new modified equation in determining GFR in Chinese patients with CKD and verify whether the CKD-EPI equation should be replaced by the new one, a well-designed paired cohort was set up and implemented.

Subjects and methods

Ethics statement

The study protocol was approved by Hebei Medical University ethical committee, and the written informed consent was obtained from each participant.

Patients

All enrolled participants met the diagnostic standard for CKD which was according to the National Kidney Foundation-Kidney Disease Outcomes Quality Initiative (K/DOQI) clinical practice guidelines [21], while the diagnosis of CKD did not depend on the GFR but depended on kidney damage irrespective of the level of GFR, and all patients were aged 18 years or older. Patients with complications related to acute kidney function deterioration, on renal replacement therapy, with edema, cardiac insufficiency, pleural or abdomen effusion, with a disabled limb, or on treatment with cimetidine or trimethoprim were excluded [22].

The true GFR (mGFR) measurement by the dual plasma sample clearance method has been described previously [22], and was estimated from a single exponential formula derived from the blood samples between 2 and 4 h after injection [23].

Measurement of serum creatinine

Serum creatinine (Scr) level was measured by the enzymatic method on an automatic biochemical analyzer (VITROS 5.1, Johnson & Johnson, New Brunswick, NJ, USA; reagents from the same company). The results of Scr were recalibrated with isotope dilution mass spectrometry.

GFR measurement by CKD-EPI equation (eGFRckdepi)

The CKD-EPI equation is as follows [11]:

For females:

  • With Scr concentration ≤0.7 mg/dl: eGFRckdepi = 144 × (Scr/0.7)−0.329 × (0.993)age;

  • With Scr concentration >0.7 mg/dl: eGFRckdepi = 144 × (Scr/0.7)−1.209 × (0.993)age;

For males:

  • With Scr concentration ≤0.9 mg/dl: eGFRckdepi = 141 × (Scr/0.9)−0.411 × (0.993)age;

  • With Scr concentration >0.9 mg/dl: eGFRckdepi = 141 × (Scr/0.9)−1.209 × (0.993)age.

GFR measurement by the new modified CKD-EPI equation (eGFRmodified)

For females:

  • With Scr concentration ≤0.7 mg/dl: eGFRmodified = 94 × (Scr/0.7)−0.511 × 0.998age;

  • With Scr concentration >0.7 mg/dl: eGFRmodified = 128 × (Scr/0.7)−543 × 0.992age;

For males:

  • With Scr concentration ≤0.9 mg/dl: eGFRmodified = 117 × (Scr/0.9)−0.277 × 0.994age;

  • With Scr concentration >0.9 mg/dl: GFR = 102 × (Scr/0.9)−0.558 × 0.994age.

Normalization of GFR

The mGFR (ml/min) was normalized for a body surface area of 1.73 m2 according to Haycock’s equation [24].

Statistical analysis

Measurement data were expressed as \( \bar{x} \pm s \). T test and Wilcoxon’s test were used to compare quantitative variables. The diagnostic performance of eGFRckdepi and eGFRmodified was determined by calculating Passing-Bablok regression and Lin correlation. Additionally, the Bland-Altman method was employed to evaluate the agreement between estimated GFR (eGFR) and mGFR. The bias between mGFR and eGFR was defined as eGFRckdepi minus mGFR or eGFRmodified minus mGFR. The precision was measured by means of the standard deviation of bias. The accuracy was determined as the proportion of eGFR within 30 % deviation of mGFR. T test and F test for paired samples were applied to compare, respectively, bias and precision [25]. For the comparison of accuracy, the McNemar test was employed. A value of p < 0.05 was considered statistically significant. All statistical analyses were performed using SPSS (version 17.0, SPSS, Chicago, IL, USA) and Medcalc (version 4.3, Medcalc software, Mariekerke, Belgium) software.

Results

Characteristics of enrolled CKD patients

During the study time-frame, a total of 170 patients were enrolled including 82 males and 88 females with a mean age of 53 ± 17 and 58 ± 15 years, respectively (t = 1.770, p = 0.079). Patients’ demographic and clinical characteristics are presented in Table 1. A wide variety of clinical diagnoses causing CKD were observed, including chronic glomerulonephritis, diabetic nephropathy, chronic pyelonephritis, hypertensive nephropathy, chronic interstitial nephritis, immunoglobulin (Ig)A nephropathy, polycystic kidney disease, and other causes in the remaining three cases. It should be noted that the proportion of diabetic nephropathy in CKD was only 21 %.

Table 1 Characteristics of CKD patients
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Performance of the new modified CKD-EPI and the original one

The mean ± standard deviation (SD) index GFR for the 170 patients evaluated by the three methods was mGFR 58 ± 37, eGFRckdepi 56 ± 34 and eGFRmodified 61 ± 21 ml/min/1.73 m2, respectively. The concordance correlation coefficient for mGFR in the original CKD-EPI equation and the new modified CKD-EPI equation was 0.90 and 0.74, respectively. The Passing-Bablok regressions were constructed based on the scatter plot (Figs. 1, 2) and the regression equation of eGFRckdepi and eGFRmodified against mGFR was mGFR = 0.37 + 1.04 eGFRckdepi and mGFR = −49.25 + 1.74 eGFRmodified, respectively.

Fig. 1
figure 1

Scatter plot and Passing-Bablok regression of eGFRckdepi against mGFR in 170 subjects. eGFRckdepi estimated glomerular filtration rate by the original CKD-EPI equation, mGFR glomerular filtration rate determined by 99mTc-DTPA dual plasma sample clearance method

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Fig. 2
figure 2

Scatter plot and Passing-Bablok regression of eGFRmodified against mGFR in 170 subjects. eGFRmodified estimated glomerular filtration rate by the new modified CKD-EPI equation, mGFR glomerular filtration rate determined by 99mTc-DTPA dual plasma sample clearance method

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A comparison of GFR estimation equations is presented in Table 2. The bias of the original CKD-EPI equation was −1.80; in contrast, the result for the new modified one was 3.14 (t = 4.095, p < 0.001). The original CKD-EPI equation was more precise than the modified one (15.51 vs. 21.38 ml/min/1.73 m2, F = 24.808, p < 0.001). The overall percentages within 30 % of mGFR were 78.23 % for the original CKD-EPI equation and 52.15 % for the new modified one (p < 0.001). There was an obvious index that the slope of the original CKD-EPI equation was significantly much closer to the identical line and displayed the smaller intercept. Bland-Altman analysis showed a better agreement between the eGFRckdepi and mGFR and the 95 % limit of agreement for eGFRckdepi and mGFR was 60.80 ml/min−1/(1.73 m2)−1 (Figs. 3, 4).

Table 2 Comparison of the equations in determining glomerular filtration rate
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Fig. 3
figure 3

Bland–Altman plot showing the disagreement between eGFRckdepi and mGFR. The solid long line indicates the mean of difference and the dotted long line represents the 95 % limits of agreement (2 SD). eGFRckdepi estimated glomerular filtration rate by the original CKD-EPI equation, mGFR glomerular filtration rate determined by 99mTc-DTPA dual plasma sample clearance method, SD standard deviation

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Fig. 4
figure 4

Bland–Altman plot showing the disagreement between eGFRmodified and mGFR. The solid long line indicates the mean of difference and the dotted long line represents the 95 % limits of agreement (2 SD). eGFRmodified estimated glomerular filtration rate by the new modified CKD-EPI equation, mGFR glomerular filtration rate determined by 99mTc-DTPA dual plasma sample clearance method, SD standard deviation

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Discussion

Accurate estimation of GFR is essential for the diagnosis and treatment of patients with CKD. A large number of methods have been developed to determine GFR more simply and accurately in view of the impracticality of the gold standard method. The CKD-EPI equation is the most frequently used and favored one in North America, Europe, Australia and China [15, 26]. Recently, a new modified CKD-EPI equation was developed and it seemed that the new modified equation was much better than the original one. But the included objects of the new equation were Chinese patients with type 2 diabetes. As is known to all, type 2 diabetes is only one of the causes of CKD. So it is necessary to assess the applicability of the new one in the patients with CKD.

In this study, we evaluated the accuracy of the new modified equation to estimate GFR in Chinese patients with CKD. Based on the dual plasma sample clearance method of 99mTc-DTPA, we found that either the new modified or the original one could be a good choice to determine GFR of CKD patients. This finding is consistent with the previous research of Liu [19].

In terms of bias, precision and accuracy, the most important three indicators in evaluating the validity of the method in determining GFR [27], the new modified formula did not outperform the original one in this study. Furthermore, the concordance correlation coefficient, intercept and slope of eGFR against mGFR and Bland-Altman analysis also supported the conclusion that the new modified formula was not better than the original one. However, the accuracy within 30 % of the original CKD-EPI remains unsatisfied in this study, which was consistent with the previous study [17, 18, 22]. But there is no working method to overcome the shortcomings of the equation as yet.

Our findings were contrary to those of Liu’s research, which might due to the following two reasons. First, the enrolled subjects of Liu’s research were patients with type 2 diabetes but not CKD patients, which may account for the difference in bias, precision and accuracy. The serum glucose level and body mass index of patients with type 2 diabetes are drastically different from those of “ordinary” CKD patients, which might affect the accuracy of GFR [28–30]. Another reason may be the difference of the selected reference method to determine true GFR. A calibration equation from 99mTc-DTPA renal dynamic imaging was employed as the reference method in Liu’s research. However, 99mTc-DTPA renal dynamic imaging can be affected by a large number of factors such as the sketching of region of interest [31] and the dosage of administration [32]. Moreover, it may overestimate the true GFR and be less accurate than the CKD-EPI equation. So 99mTc-DTPA renal dynamic imaging may be unsuitable to use as the reference method in determining GFR, even the linear regression equation derived from it. Accordingly, in this study we used the 99mTc-DTPA dual plasma sample clearance method, which may provide a perfect true GFR resulting in more a reliable conclusion.

The limitation of the present study is that the sample size was so small that it was inadequate to compare the application of the two equations according to CKD stage, causes of CKD, and the age of patients.

In conclusion, the new modified CKD-EPI equation did not show an improved performance with respect to the original one. Therefore, we propose that the modified equation be ignored and the original CKD-EPI equation remain the first choice for the measurement of GFR in Chinese CKD patients, in spite of the unsatisfactory accuracy within 30 %.