Comparison of glomerular filtration rate estimating equations derived from creatinine and cystatin C: validation in the Age, Gene/Environment Susceptibility-Reykjavik elderly cohort

Abstract

Background

Validation studies comparing glomerular filtration rate (GFR) equations based on standardized creatinine and cystatin C assays in the elderly are needed. The Icelandic Age, Gene/Environment Susceptibility-Kidney cohort was used to compare two pairs of recently developed GFR equations, the revised Lund–Malmö creatinine equation (LMR_Cr) and the arithmetic mean of the LMR_Cr and Caucasian, Asian, Paediatric and Adult cystatin C equations (MEAN_LMR+CAPA), as well as the Full Age Spectrum creatinine equation (FAS_Cr) and its combination with cystatin C (FAS_Cr+Cys), with the corresponding pair of Chronic Kidney Disease Epidemiology Collaboration equations (CKD-EPI_Cr and CKD-EPI_Cr+Cys).

Methods

A total of 805 individuals, 74–93 years of age, underwent measurement of GFR (mGFR) using plasma clearance of iohexol. Four metrics were used to compare the performance of the GFR equations: bias, precision, accuracy [including the percentage of participants with estimated GFR (eGFR) within 30% of mGFR (P₃₀)] and the ability to detect mGFR <60 mL/min/1.73 m².

Results

All equations had a P₃₀ >90%. LMR_Cr and FAS_Cr yielded significantly higher precision and P₃₀ than CKD-EPI_Cr, while bias was significantly worse. LMR_Cr, FAS_Cr and CKD-EPI_Cr showed similar ability to detect mGFR <60 mL/min/1.73 m² based on the area under the receiver operating characteristic curves. MEAN_LMR+CAPA, FAS_Cr+Cys and CKD-EPI_Cr+Cys all exhibited consistent improvements compared with the corresponding creatinine-based equations.

Conclusion

None of the creatinine-based equations was clearly superior overall in this community-dwelling elderly cohort. The addition of cystatin C improved all of the creatinine-based equations.

INTRODUCTION

Accurate estimation of glomerular filtration rate (GFR) is essential in the elderly population for correct classification and management of chronic kidney disease (CKD) and for adjusting drug dosage. However, few validation studies comparing GFR equations that are based on serum creatinine or serum cystatin C, or a combination of the two markers, using standardized assays have been carried out in elderly populations [1–3]. In a recent study [3], several of the standardized GFR equations were validated and compared in the community-dwelling elderly Icelandic Age, Gene/Environment Susceptibility-Kidney (AGES-Kidney) cohort: the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) [4, 5], the Berlin Initiative Study (BIS) [1], the Caucasian, Asian, Paediatric and Adult (CAPA) [6] and Japanese equations [7, 8].

More recently developed European GFR equations that are based on standardized serum creatinine and serum cystatin C measurements, also merit comparison with the CKD-EPI equations in the Icelandic cohort, with additional analysis of their performance and ability to detect measured GFR (mGFR) <60 mL/min/1.73 m² in elderly patients. The revised Lund–Malmö equation (LMR_Cr) was developed in a Swedish population [9]. Combining LMR_Cr with the CAPA cystatin C equation (CAPA_Cys), which was partly developed in a Swedish population using the arithmetic mean of the two equations (MEAN_LMR+CAPA), has been shown to further improve the accuracy of the GFR estimates [10]. Recently, the Full Age Spectrum (FAS) equations, enabling estimation of GFR across the age spectrum from children to older adults based on serum creatinine (FAS_Cr) and serum creatinine combined with serum cystatin C (FAS_Cr+Cys) were established for healthy Europeans [11, 12]. It would therefore be of interest to compare these two pairs of European equations with the corresponding North American CKD-EPI equations (CKD-EPI_Cr and CKD-EPI_Cr+Cys), recommended by the Kidney Disease: Improving Global Outcomes (KDIGO) CKD guidelines [13], in an external validation cohort.

Thus the aim of the present study was to compare the bias, precision and accuracy of LMR_Cr and FAS_Cr with the CKD-EPI_Cr equation in the AGES-Kidney elderly cohort. An additional aim was to compare the impact of adding cystatin C to the creatinine-based GFR equations. The analysis included accuracy diagrams for straightforward interpretation and illustration of the uncertainty of estimated GFR (eGFR) in clinical practice [14]. Classification ability and probability diagrams to detect mGFR <60 mL/min/1.73 m² were used as additional validation tools [15].

MATERIALS AND METHODS

The study was approved by the Icelandic National Bioethics Committee (NBC 00-063) and the Institutional Review Boards of the National Institute on Aging and Tufts Medical Center. All participants gave written informed consent. All procedures involving subjects and data were in accordance with the ethical principles for medical research involving human subjects established in the Helsinki Declaration of 1975, as revised in 2000. Samples and patient data were treated anonymously in all analyses.

Study population and laboratory methods

The AGES-Reykjavik Study originated from the Reykjavik Study cohort, a community-based sample comprising men and women born between 1907 and 1935 that was established in 1967 to prospectively investigate cardiovascular disease in Iceland [16]. Of the original cohort, 5764 individuals participated in the AGES-Reykjavik Study between 2002 and 2006, which was designed to examine risk factors for disease and disability in old age. At a follow-up visit (AGES II-Reykjavik Study) between 2007 and 2011, 3411 participants (71% of the AGES-Reykjavik survivors) underwent a repeat examination. Among the 3341 individuals who completed the second visit, 805 participated in a substudy to measure GFR between 2010 and 2011, the AGES-Kidney Study (see Supplementary data for details of the selection of participants and exclusion criteria). Measurement of GFR was carried out using plasma iohexol clearance. The AGES-Kidney cohort consisted of 450 females and 355 males between 74–93 years of age, of whom 39% had never smoked, 22% were obese, 11% were diabetics, 63% had hyperlipidaemia, 30% had cardiovascular disease and 90% had hypertension (75% on antihypertensive treatment) [17]. Patient characteristics are summarized in Table 1.

Table 1.

Characteristics of the AGES-Kidney cohort (n = 805)

Characteristics	Median values (2.5–97.5 percentiles)	Mean value (SD)
Age (years)	80 (75–90)	80 (4.0)
Weight (kg)	76 (52–108)	77 (14)
Height (cm)	167 (152–186)	168 (9)
Body mass index (kg/m2)	27 (20–38)	27 (4)
Body surface area (m2)	1.85 (1.49–2.24)	1.86 (0.20)
Serum creatinine (µmol/L)	82 (50–164)	88 (33)
Serum cystatin C (mg/L)	1.10 (0.75–2.25)	1.19 (0.38)
Measured GFR (mL/min/1.73 m2)	64 (28–91)	62 (16)
<30 mL/min/1.73 m2 [n = 28 (3.5%)]	26 (13–28)	24 (4.4)
30–59 mL/min/1.73 m2 [n = 286 (35.5%)]	49 (32–59)	48 (8.1)
60–89 mL/min/1.73 m2 [n = 458 (56.9%)]	70 (60–87)	71 (7.7)
≥90 mL/min/1.73 m2 [n = 33 (4.1%)]	93 (90–109)	95 (5.9)
Stratified by age
<80 years [n = 402 (50%)]	68 (33–95)	67 (15)
80–84 years [n = 279 (35%)]	61 (28–86)	59 (16)
≥85 years [n = 124 (15%)]	54 (23–83)	53 (17)
Stratified by sex
Females [n = 450 (56%)]	63 (26–91)	61 (17)
Males [n = 355 (44%)]	65 (32–92)	64 (16)

Serum creatinine was measured on the Roche Hitachi P Module instrument using the Roche Creatinine Plus enzymatic assay (coefficient of variation 2.3%), which is traceable to the National Institute of Standards and Technology creatinine standard reference material 909b [18]. Serum cystatin C was measured on the Siemens BN100 nephelometer using a particle-enhanced immunonephelometric assay (coefficient of variation 2.7% and 5.5% for intra- and inter-assay precision, respectively), traceable to international cystatin C calibrator ERM-DA471/IFCC [19, 20].

Measurement of GFR was carried out using plasma clearance of iohexol and was expressed per 1.73 m² body surface area. Details of the plasma iohexol clearance measurement procedure can be found in the Supplemental Methods of Fan et al. [3]. Briefly, 5 mL of iohexol was administered over a period of 30 s, followed by a 10 mL normal saline flush. Blood samples for plasma clearance measurements were taken from a second catheter at approximately 120, 180, 240 and 300 min, with the exact time points recorded. Plasma clearance of iohexol was calculated using the Bröchner–Mortensen equation [21].

Statistical analyses

Creatinine-based and combined creatinine- and cystatin C-based equations (see Appendix) for computing eGFR were compared with mGFR. The corresponding equations based on cystatin C alone are included for completeness but without formal comparisons. The estimation error of the equations (eGFR−mGFR) was evaluated using the performance metrics bias, precision and accuracy, employing SPSS Statistics version 22 (IBM, Armonk, NY, USA) and STATA version 14 (StataCorp, College Station, TX, USA). Bias was calculated as the median estimation error in mL/min/1.73 m². Precision was expressed as the interquartile range (IQR) of the estimation error. Accuracy was expressed as the median absolute percentage estimation error (100 × |eGFR−mGFR|/mGFR in percent; absolute accuracy) and as P₃₀, the percentage of participants with eGFR within 30% of mGFR. Nonparametric and asymptotic 95% confidence intervals (CIs) were calculated for medians (bias and absolute percentage error) and proportions (P₃₀). CIs for IQR were estimated using bootstrap methods with 1000 replications. Bootstrapping was also used to examine the statistical significance of paired differences in bias, precision and absolute accuracy between LMR_Cr, FAS_Cr and CKD-EPI_Cr and between MEAN_LMR+CAPA, FAS_Cr+Cys and CKD-EPI_Cr+Cys. These comparisons were conducted both overall and stratified by mGFR (> and <60 mL/min/1.73 m²). Paired differences in P₃₀ were tested using McNemar’s exact test. Differences in the accuracy of each equation among females and males were assessed using the Mann–Whitney test (absolute accuracy) and Fisher’s exact test (P₃₀ accuracy). Results were also presented stratified by age (<80, 80–84 and ≥85 years).

Accuracy diagrams were constructed based on quantile regression to examine how the estimation error of the equations varied across mGFR (diagnostic correctness) and eGFR (diagnostic predictiveness) [14, 22]. In the diagrams, we express the estimation error for eGFR in mL/min/1.73 m² using the quantiles (percentiles) Q₁₀, Q₅₀ (median bias) and Q₉₀, where the accuracy interval (AI; Q₁₀–Q₉₀) reflects the largest estimation error with 80% certainty. The presentation was limited to eGFR in the range of 20–90 mL/min/1.73 m² since generally <5% of the patients had mGFR or eGFR outside this range. The constancy of bias stratified by eGFR in the accuracy diagrams is an indicator of how similar an equation behaves in a validation cohort compared with the original development cohort [14, 23].

The ability to detect mGFR <60 mL/min/1.73 m² was evaluated using sensitivity, specificity, positive and negative predictive values and the area under the receiver operating characteristic (ROC) curve. Differences in ROC area were assessed using the chi-square test (roccomp command in Stata). Probability diagrams were constructed using logistic regression with mGFR <60 mL/min/1.73 m² (yes/no) as the dependent variable and eGFR as an independent variable to illustrate the predicted probability at different levels of eGFR [15]. We also calculated threshold values of eGFR for each equation to rule in or rule out mGFR <60 mL/min/1.73 m² with 90% probability.

RESULTS

Direct comparisons of creatinine-based GFR equations (diagnostic correctness)

The four overall metrics—bias, precision and absolute and P₃₀ accuracy—used to compare the LMR_Cr, FAS_Cr and CKD-EPI_Cr equations are presented in Table 2. Compared with the other two equations, the performance of LMR_Cr was significantly better for precision and P₃₀ accuracy, similar for absolute accuracy and significantly worse for bias. The performance of FAS_Cr was significantly better than CKD-EPI_Cr in two metrics (precision and P₃₀) but worse in two (bias and absolute accuracy).

Table 2.

Bias (median eGFR−mGFR, mL/min/1.73 m²), precision (IQR, mL/min/1.73 m²), absolute accuracy (median, percent) and P₃₀ accuracy (percentage of GFR estimated within 30% of mGFR) of GFR estimating equations based on creatinine and the combination of creatinine and cystatin C in the AGES-Kidney cohort (n = 805)

Variables	LMRCr	FASCr	CKD-EPICr	MEANLMR+CAPA	FASCr+Cys	CKD-EPICr+Cys
Bias	−4.8	−5.7	2.7	−2.7	−5.9	0.6
	(−5.4 to − 4.2)a	(−6.3 to − 5.1)a	(2.1 to 3.3)	(−3.2 to − 2.1)a	(−6.5 to − 5.4)a	(−0.1 to 1.2)
Precision	10.8	10.7	12.1	9.3	10.0	10.2
	(10.1 to 11.5)b	(9.9 to 11.9)b	(11.2 to 13.4)	(8.5 to 10.1)c	(9.1 to 10.9)c	(9.0 to 11.1)
Absolute accuracy	11.4	12.1	10.2	8.5	11.3	8.1
	(10.3 to 12.3)c	(11.1 to 13.2)a	(9.3 to 11.0)	(8.0 to 9.2)c	(10.5 to 12.3)a	(7.5 to 8.9)
P30 accuracy	95.0	95.8	91.7	97.3	97.8	96.1
	(93.5 to 96.5)b	(94.4 to 97.2)b	(89.9 to 93.4)	(96.2 to 98.4)b	(96.7 to 98.8)b	(94.8 to 97.4)

Data are presented with 95% CIs.

^aSignificantly worse (P < 0.05) than corresponding CKD-EPI equation.

^bSignificantly better (P < 0.05) than corresponding CKD-EPI equation.

^cNo statistical difference (P ≥0.05) compared with corresponding CKD-EPI equation.

Results of the GFR equation metrics stratified by mGFR > and <60 mL/min/1.73 m² are shown in Supplementary Table S1. The magnitude of the bias was greater for LMR_Cr and FAS_Cr than for CKD-EPI_Cr at mGFR ≥60 mL/min/1.73 m². The improvement in precision observed for LMR_Cr and FAS_Cr compared with CKD-EPI_Cr was seen at an mGFR both > and <60 mL/min/1.73 m², whereas P₃₀ was only improved at mGFR <60 mL/min/1.73 m².

Accuracy diagrams stratified according to mGFR are presented in Figure 1A–C. The width of the 80% AIs at mGFRs of 30, 60 and 90 mL/min/1.73 m² were 18, 18 and 19 mL/min/1.73 m² for LMR_Cr; 12, 19 and 24 mL/min/1.73 m² for FAS_Cr; and 19, 25 and 17 mL/min/1.73 m² for CKD-EPI_Cr, respectively.

FIGURE 1.

Estimation errors (eGFR−mGFR, in mL/min/1.73 m² on the y-axis) at different levels of mGFR on the x-axis (diagnostic correctness) for (A) LMR_Cr equation, (B) FAS_Cr equation, (C) CKD-EPI_Cr equation, (D) arithmetic mean of LMR_Cr and CAPA_Cys (MEAN_LMR+CAPA), (E) FAS_Cr+Cys equation, and (F) CKD-EPI_Cr+Cys equation in the AGES-Kidney cohort (n = 805). The quantile regression curves for the estimation errors reflect bias (Q₅₀, solid line) and estimation error with 80% certainty (AI; Q₁₀–Q₉₀, dashed lines).

Diagnostic correctness of cystatin C–based GFR equations

The median bias of the CAPA_Cys, FAS_Cys and CKD-EPI_Cys equations was −0.1 (95% CI −0.6 to 0.7), −5.2 (95% CI −7.1 to −1.8) and −1.9 (95% CI −2.8 to −1.3) mL/min/1.73 m², respectively. The corresponding IQR values for precision were 11.8 (95% CI 10.8 to 12.9), 11.2 (95% CI 10.5 to 12.3) and 11.4 (95% CI 10.6 to 12.4) mL/min/1.73 m² and for accuracy (P₃₀) were 94.4% (95% CI 92.8 to 95.9), 95.9% (95% CI 94.5 to 97.3) and 93.8% (95% CI 92.0 to 95.4%), respectively.

Direct comparisons of combined creatinine- and cystatin C-based GFR equations (diagnostic correctness)

Combining cystatin C with creatinine in the GFR equations resulted in improved accuracy, both overall (Table 2) and stratified by mGFR > and <60 mL/min/1.73 m² (Supplementary Table S1). Among the four metrics, the performance of MEAN_LMR+CAPA was significantly better than CKD-EPI_Cr+Cys for P₃₀, similar for precision and absolute accuracy and significantly worse in the case of bias. FAS_Cr+Cys was significantly better than CKD-EPI_Cr+Cys for P₃₀, equal for precision and worse for bias and absolute accuracy.

The arithmetic mean of FAS_Cr and FAS_Cys yielded almost identical median bias (−5.7 mL/min/1.73 m²), precision (IQR 10.0 mL/min/1.73 m²), median absolute accuracy (11.0%) and P₃₀ (97.9%) as the combined FAS_Cr+Cys equation (Table 2). Also, the arithmetic mean of CKD-EPI_Cr and CKD-EPI_Cys resulted in a similar median bias (0.3 mL/min/1.73 m²), precision (IQR 9.6 mL/min/1.73 m²), median absolute accuracy (7.9%) and P₃₀ (96.6%) as the combined CKD-EPI_Cr+Cys equation (Table 2).

Accuracy diagrams for the combined equations, stratified by mGFR, are presented in Figure 1D–F. CKD-EPI_Cr+Cys had a more stable bias around zero compared with the other two combined equations. The width of the 80% AIs at mGFRs of 30, 60 and 90 mL/min/1.73 m² were 16, 17 and 21 mL/min/1.73 m² for MEAN_LMR+CAPA; 12, 16 and 21 mL/min/1.73 m² for FAS_Cr+Cys; and 14, 21 and 20 mL/min/1.73 m² for CKD-EPI_Cr+Cys, respectively.

Accuracy of GFR equations stratified by sex and age

The GFR equation metrics stratified by sex are shown in Supplementary Table S2. Both LMR_Cr and FAS_Cr had significantly better absolute accuracy among females than males [9.8 versus 13.1% (P <0.001) and 11.3 versus 12.9% (P = 0.04), respectively], while P₃₀ was similar [95.8 versus 94.1% (P >0.30) and 96.2 versus 95.5% (P >0.30), respectively]. For CKD-EPI_Cr the pattern was different, with worse absolute and P₃₀ accuracy among females compared with males [11.1 versus 9.1% (P = 0.02) and 89.3 versus 94.6% (P = 0.007), respectively].

Among the combined equations, both MEAN_LMR+CAPA and FAS_Cr+Cys had better absolute accuracy in females than males [8.1 versus 9.0% (P = 0.03) and 10.0 versus 12.5% (P < 0.001), respectively], while CKD-EPI_Cr+Cys had worse absolute accuracy in females compared with males [9.1 versus 7.2% (P = 0.001)]. P₃₀ accuracy showed small and insignificant difference in females and males for all three combined equations.

When stratified by age groups, similar bias was generally noted for all equations as in the overall results (Supplementary Table S3). All equations had a lower P₃₀ accuracy in the oldest age group (≥85 years).

Accuracy of GFR equations stratified by eGFR (diagnostic predictiveness)

Both LMR_Cr and MEAN_LMR+CAPA had a relatively constant negative bias across all levels of eGFR. The bias of the FAS equations first decreased and then increased with increasing eGFR, whereas it increased monotonically for the CKD-EPI equations with ascending eGFR (Figure 2). All three equation pairs showed increased imprecision with increasing eGFR as reflected by the width of the 80% AIs.

FIGURE 2.

Estimation errors (eGFR−mGFR, in mL/min/1.73 m² on the y-axis) at different levels of eGFR on the x-axis (diagnostic predictiveness) for (A) LMR_Cr equation, (B) FAS_Cr equation, (C) CKD-EPI_Cr equation, (D) arithmetic mean of LMR_Cr and CAPA_Cys (MEAN_LMR+CAPA), (E) FAS_Cr+Cys equation and (F) CKD-EPI_Cr+Cys equation in the AGES-Kidney cohort (n = 805). The quantile regression curves for the estimation errors reflect bias (Q₅₀, solid line) and estimation error with 80% certainty (AI; Q₁₀–Q₉₀, dashed lines).

Ability of GFR equations to detect measured GFR <60 mL/min/1.73 m²

Both LMR_Cr and FAS_Cr had a sensitivity close to or >90% and a noticeably lower specificity, while the pattern for CKD-EPI_Cr was converse (Table 3). Consequently, the number of patients classified as having mGFR <60 mL/min/1.73 m² varied considerably between the equations. Nevertheless, all three creatinine-based GFR equations demonstrated a similar ability to detect mGFR <60 mL/min/1.73 m² as assessed by the area under the ROC curve. Equations combining creatinine and cystatin C improved the classification ability compared with their creatinine counterparts. The combined GFR equations had similar ROC areas.

Table 3.

Sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV) and area under the ROC curve to detect mGFR <60 mL/min/1.73 m² using different GFR estimating equations in the AGES-Kidney cohort (n = 805)

	Sensitivity (%)	Specificity (%)	PPV		NPV		ROC (P-value)
	(n = 314)a	(n = 491)b	%	nc	%	nd
LMRCr	89.2	71.5	66.7	404	91.2	401	91.3 (0.16)
FASCr	92.4	64.2	62.2	461	92.9	344	91.7 (<0.001)
CKD-EPICr	76.2	91.6	85.4	276	85.7	529	91.0
MEANLMR+CAPA	85.4	79.8	73.0	353	89.5	452	93.2 (0.05)
FASCr+Cys	95.5	64.4	63.2	462	95.8	343	93.6 (0.70)
CKD-EPICr+Cys	81.8	88.8	82.4	306	88.4	499	93.6

P-values regarding differences in ROC area in relation to the corresponding CKD-EPI equation with the same filtration markers.

^aNumber of patients with measured GFR <60 mL/min/1.73 m².

^bNumber of patients with measured GFR ≥60 mL/min/1.73 m².

^cNumber of patients with estimated GFR <60 mL/min/1.73 m².

^dNumber of patients with estimated GFR ≥60 mL/min/1.73 m².

The probability diagrams together with the threshold values for ruling in or ruling out mGFR <60 mL/min/1.73 m² with 90% probability for the various GFR equations are presented in Figure 3. Using the MEAN_LMR+CAPA equation as an example, mGFR <60 mL/min/1.73 m² could be confidently ruled in and ruled out at eGFR <48 and >66 mL/min/1.73 m², respectively.

FIGURE 3.

Probability to detect mGFR <60 mL/min/1.73 m² as a function of eGFR based on (A) the LMR_Cr, FAS_Cr and CKD-EPI_Cr equations; and (B) arithmetic mean of the LMR_Cr and CAPA_Cys (MEAN_LMR+CAPA) equations, FAS_Cr+Cys equation and CKD-EPI_Cr+Cys equation in the AGES-Kidney cohort (n = 805). The lower and upper eGFR values (mL/min/1.73 m²) are for ruling in or ruling out mGFR <60 mL/min/1.73 m² with 90% probability.

DISCUSSION

All the GFR estimating equations met the 2002 Kidney Disease Outcomes Quality Initiative benchmark with an overall P₃₀ accuracy >90% [24]. The addition of cystatin C improved the accuracy compared with the corresponding creatinine-based equations. None of the three equation pairs was clearly superior overall. The more recently developed creatinine-based and combined equations were generally more accurate at mGFR <60 mL/min/1.73 m² but were less accurate at mGFR ≥60 mL/min/1.73 m² compared with the corresponding CKD-EPI equations.

The overall P₃₀ results of LMR_Cr compared with the CKD-EPI_Cr equation are consistent with two previous validations in Swedish clinical populations referred for GFR measurement, where LMR_Cr showed higher P₃₀ than CKD-EPI_Cr in all adults, as well as in elderly individuals ≥70 years of age [25, 26]. Stratifying by mGFR in the present study revealed that CKD-EPI_Cr was advantageous at mGFR >60 mL/min/1.73 m², while LMR_Cr and FAS_Cr had their strengths at mGFR <60 mL/min/1.73 m². These findings are also consistent with other validation studies [11, 12, 27, 28]. One explanation for the difference in the relative merits of the equations may be that LMR_Cr was developed with the explicit goal of improving the GFR estimates at low mGFR levels [9], whereas the objective of the CKD-EPI_Cr was to improve the estimations at higher levels of mGFR [4]. In addition, the CKD-EPI_Cr equation was developed in a cohort with only 4% of the individuals >70 years of age [4], while this percentage was 27% in the LMR_Cr development cohort [9]. The FAS_Cr equation was designed based on average GFR and age-normalized serum creatinine, valid for a healthy population [11], but nevertheless performed well in the present cohort of elderly individuals where CKD stages 3 and 4 were common. However, this result may not apply to younger adults with CKD. The initial validation of the FAS_Cr equation exhibited marked overestimation and unacceptable P₃₀ among adults between 18 and 70 years of age with an mGFR <60 mL/min/1.73 m² [11].

In line with a previous Swedish study [10], our findings suggest that the added benefit of equations combining creatinine with cystatin C tends to be larger in patient groups where the single-marker equations are inaccurate. The present validation also shows that the arithmetic mean of creatinine- and cystatin C-based equations performed as well as the composite equations including both filtration markers, which is consistent with previous studies [10, 29]. Using single-marker equations together with their arithmetic mean has an advantage over a composite equation, such as the FAS_Cr+Cys or CKD-EPI_Cr+Cys equations, in that the clinician can compare the agreement between the creatinine- and cystatin C-based equations and then choose the eGFR value that appears most accurate depending on the clinical context and patient characteristics or elect to measure GFR [10]. Some authorities have suggested that comparing the estimates obtained with creatinine- and cystatin C-based equations also allows the identification of ‘shrunken pore syndrome’, which is associated with high mortality [30–32]. Finally, an arithmetic mean of equations also has the advantage that a composite equation does not need to be developed, as the existing creatinine- and cystatin C-based equations can be relied on.

The accuracy diagrams provide straightforward assessments of bias, precision and accuracy of the GFR equations [14]. They provide unambiguous interpretations, not only when the equation performance is stratified by mGFR, but also in clinical situations where only eGFR is available. Despite satisfactory P₃₀ overall, the width of the 80% AIs depicted in the diagrams indicates that large estimation errors could not be ruled out with certainty for any of the equations evaluated. CKD-EPI_Cr+Cys was the only equation with a relatively stable bias across all mGFR levels. However, only LMR_Cr and MEAN_LMR+CAPA showed a stable bias at all levels of eGFR in the accuracy diagrams, suggesting that improved performance and compatibility in behaviour between the validation and development cohorts could be achieved for this pair of equations after a simple (constant) bias correction. By contrast, the bias of the CKD-EPI and FAS equations varied across eGFRs, making such corrections complicated.

Discrepancies in the performance of the GFR estimating equations may also be due to the use of different clearance methods and exogenous filtration markers used for determination of mGFR when the equations were developed. The CKD-EPI equations were developed using renal clearance of iothalamate [4], while single-sample plasma iohexol clearance was used for the development of the LMR_Cr equation [9]. No mGFR reference method was used when the FAS equations were established [11, 12]. Remaining differences in the calibration of creatinine and cystatin C assays, despite the use of international standards, may also contribute to variations in the performance of the GFR equations [6, 33–37]. Furthermore, the CKD-EPI equations were to a large extent developed in North American and European adult populations [4, 5], whereas the LMR_Cr equation was developed in a more homogeneous Swedish adult population [9] that is more likely to be comparable to Icelanders. The CAPA_Cys equation was established in a mixed population of children and adults from Sweden, the Netherlands and Japan [6].

The creatinine-based GFR equations showed similar ability to detect mGFR <60 mL/min/1.73 m² based on the area under the ROC curve. Adding cystatin C improved the classification ability of the estimating equations. A drawback of standard binary GFR classification > or <60 mL/min/1.73 m² is that it yields predictive values that are constant, irrespective of the individual eGFR value [15]. By contrast, our probability diagrams show how the probability of mGFR <60 mL/min/1.73 m² varies with eGFR. For example, the probability of mGFR <60 mL/min/1.73 m² for the MEAN_LMR+CAPA equation increased from 35 to 95% when the eGFR decreased from 59 to 45 mL/min/1.73 m² (Figure 3B). The range of GFR estimates where mGFR <60 mL/min/1.73 m² could not be ruled in or out with acceptable certainty was generally wide for all equations. The information from the probability curves may help the clinician decide when to request a direct measurement of the GFR or refer the patient to a nephrologist. It should nonetheless be stressed that the clinical (pre-test) probability markedly affects the left-to-right position of the probability curves and the width of the eGFR interval, where mGFR > and <60 mL/min/1.73 m² cannot be separated with adequate certainty [15]. We appreciate that a cut-off level of 60 mL/min/1.73 m² has been debated and that the curves may also be constructed with a cut-off level of 45 mL/min/1.73 m², which might be more suitable since the risk of both cardiovascular disease and CKD increase substantially below that level [38].

In conclusion, the current study comparing the LMR_Cr and FAS_Cr equations with the CKD-EPI_Cr equation in a community-dwelling elderly Nordic cohort suggests that none of the equations are clearly superior overall, but there are differences in performance between subgroups. All equations combining serum creatinine with serum cystatin C demonstrated improved performance compared with their creatinine counterparts.

SUPPLEMENTARY DATA

Supplementary data are available online at http://ndt.oxfordjournals.org.

APPENDIX

For all the GFR estimating equations below, age is expressed in years and eGFR in mL/min/1.73 m² body surface area. ln = natural logarithm.

GFR estimating equations based on creatinine

LMR_Cr equation [9]

Serum creatinine (SCr) is expressed in µmol/L

$${\mathrm{e}}^{x-0.0158\times \mathrm{Age}\mathrm{+}\mathrm{0}\mathrm{.438}\times \ln \left(\mathrm{Age}\right)}$$

Female	SCr <150:	x = 2.50 + 0.0121 × (150 − SCr)
Female	SCr ≥150:	x = 2.50 − 0.926 × ln(SCr/150)
Male	SCr <180:	x = 2.56 + 0.00968 × (180 − SCr)
Male	SCr ≥180:	x = 2.56 − 0.926 × ln(SCr/180)

FAS_Cr equation [11]

Serum creatinine (SCr) is expressed in mg/dL

$$[1\mathrm{0}7.3/(\text{SCr}/{\mathrm{Q}}_{\text{Cr}})]\times 0.{988}^{(\text{Age}–4\mathrm{0})}(\text{if }4\mathrm{0}\text{ years or older})$$

Female	QCr = 0.7 mg/dL
Male	QCr = 0.9 mg/dL

CKD-EPI_Cr equation [4]

Serum creatinine (SCr) is expressed in mg/dL

$$141\times \text{min}(\text{SCr}/\kappa ,1)\alpha \times \text{max}{(\text{SCr}/\kappa ,1)}^{-1.209}\times 0.{993}^{\text{Age}}\times 1\mathrm{.0}18(\text{iffemale})\times 1.159(\text{ifblack})$$

κ is 0.7 for females and 0.9 for males, α is − 0.329 for females and −0.411 for males, min is the minimum of SCr/κ and 1 and max is the maximum of SCr/κ and 1.

GFR estimating equations based on cystatin C

Serum cystatin C (SCys) is expressed in mg/L for all equations

CAPA_Cys equation [6]

$$130\times \mathrm{SCy}{\mathrm{s}}^{-1.069}\times \mathrm{Ag}{\mathrm{e}}^{-0.117}–7$$

FAS_Cys equation [12]

$$\begin{array}{c}[1\mathrm{0}7.3/(\text{SCys}/{\mathrm{Q}}_{\text{Cys}})]\times 0.{988}^{(\text{Age}–4\mathrm{0})}(\text{if }4\mathrm{0}\text{ years or older})\\ {\mathrm{Q}}_{\text{Cys}}=0.82\text{mg}/\mathrm{L}\text{ if }<7\mathrm{0}\text{ years}\\ {\mathrm{Q}}_{\text{Cys}}=0.95\text{mg}/\mathrm{L}\text{ if }\ge 7\mathrm{0}\text{ years}\end{array}$$

CKD-EPI_Cys equation [5]

SCys ≤0.8	133 × (SCys/0.8)−0.499 × 0.996Age [× 0.932 if female]
SCys>0.8	133 × (SCys/0.8)−1.328 × 0.996Age [× 0.932 if female]

GFR estimating equations based on creatinine and cystatin C

Arithmetic mean of the LMR_Cr and the CAPA_Cys equations (MEAN_LMR+CAPA)

$$({\text{LMR}}_{\text{Cr}}\hspace{0.17em}+\hspace{0.17em}{\text{CAPA}}_{\text{Cys}})/2$$

FAS_Cr+Cys equation for adults [12]

Serum creatinine (SCr) is expressed in mg/dL and serum cystatin C (SCys) in mg/L

$$1\mathrm{0}7.3/(\mathrm{\alpha }\times \text{SCr}/{\mathrm{Q}}_{\text{Cr}}+(1-\mathrm{\alpha })\times \text{SCys}/{\mathrm{Q}}_{\text{Cys}})\times 0.{988}^{(\text{Age}-4\mathrm{0})}(\text{if}4\mathrm{0}\text{yearsorolder})$$

An α-factor of 0.5 was used. For Q_Cr and Q_Cys values see above.

CKD-EPI_Cr+Cys equation [5]

Serum creatinine (SCr) is expressed in mg/dL and serum cystatin C (SCys) in mg/L

$$\begin{array}{c}135\times \text{min}(\text{SCr}/\kappa ,1)\alpha \times \text{max}{(\text{SCr}/\kappa ,1)}^{-0.601}\times \text{min}{(\text{SCys}/0.8,1)}^{0.375}\times \\ \text{max}{(\text{SCys}/0.8,1)}^{-0.711}\times 0.{995}^{\text{Age}}\times 0.969(\text{iffemale})\times 1\mathrm{.0}8(\text{ifblack})\end{array}$$

κ is 0.7 for females and 0.9 for males, α is − 0.248 for females and −0.207 for males, min is the minimum of SCr/κ and 1, and the minimum of SCys/0.8 and 1, and max is the maximum of SCr/κ and 1, and the maximum of SCys/0.8 and 1.