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Supplementary Material
GFR estimating equations referred to in the text

In all equations p-creatinine (pCr) is expressed in mol/L, p-cystatin C (pCysC) in mg/L, age in
years, weight in kilograms, height in centimetres and body surface area (BSA) in square meters.
ln = natural logarithm.

All creatinine equations except Cockcroft-Gault are based on IDMS-traceable creatinine assays.

All cystatin C equations are based on assays calibrated against the internationally certified
reference material ERM-DA471/IFCC [1].

All equations were developed based on Caucasian populations and include a factor for African
Americans in the MDRD and CKD-EPI creatinine equations and in the CKD-EPI combined
creatinine and cystatin C equation. The CAPA cystatin C equation were also based on an adult
Asian population.

Cockcroft-Gault and the Lund-Malmö equation with lean body mass (LM-LBMCREA) primarily
express eGFR in absolute values in mL/min, while remaining equations primarily express
relative GFR in mL/min/1.73 m2.
Body surface area (BSA) according to DuBois & Dubois [2]
BSA (m2) = (weight0.425 × height0.725) × 0.007184
Non-standardized creatinine equation for adults
Cockcroft Gault [3]
eGFR (mL/min) = 1.23 × [(140 – age) × weight/pCr] × 0.85 (if female).
Standardized creatinine equations for adults
Absolute Lund-Malmö with lean body mass (LM-LBMCREA) [4]
eGFR (mL/min) = eX - 0.0128 × age + 0.387 × ln(age) + 1.10 × ln(LBM)
X = –0.0111 × pCr
(if pCr < 150 mol/L)
X = 3.55 + 0.0004 × pCr - 1.07 × ln(pCr)
(if pCr  150 mol/L)
Lean body mass [5]
Women:
1.07 × weight – 148 × (weight/height)2
Men:
1.10 × weight – 128 × (weight/height)2
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Revised Lund-Malmö (LM-REVCREA) [6]
eGFR (mL/min/1.73 m2) =
eX – 0.0158  Age + 0.438  ln(Age)
Female
pCr < 150 mol/L:
X = 2.50 + 0.0121  (150 - pCr)
Female
pCr  150 mol/L:
X = 2.50 - 0.926  ln(pCr / 150)
Male
pCr < 180 mol/L:
X = 2.56 + 0.00968  (180 - pCr)
Male
pCr  180 mol/L:
X = 2.56 - 0.926  ln(pCr / 180)
MDRDCREA [7]
eGFR (mL/min/1.73 m2) =
175 × (pCr / 88.4)-1.154 × age-0.203 × 0.742 (if female) ×
× 1.210 (if African American)
CKD-EPICREA [8]
eGFR (mL/min/1.73 m2) =
Female
pCr ≤ 62 mol/L:
144  (pCr / 62)-0.329  0.993Age
Female
pCr > 62 mol/L:
144  (pCr / 62)-1.209  0.993Age
Male
pCr ≤ 80 mol/L:
141  (pCr / 80)-0.411  0.993Age
Male
pCr > 80mol/L:
141  (pCr / 80)-1.209  0.993Age
All expressions multiplied with 1.159 if African American.
Standardized creatinine equations for children
SchwartzCREA [9]
eGFR (mL/min/1.73 m2) = 36.5 × height (cm) / pCr
GaoCREA [10]
eGFR (mL/min/1.73 m2) = 60 × (height / pCr) - 6.25 × (height / pCr)2 + 0.48 × age – K
(K = 25.68 for females and 21.53 for males).
Standardized cystatin C equation for adults and children
CAPACYSC [11]
eGFR (mL/min/1.73 m2) =
130 × pCysC-1.069 × Age-0.117 – 7
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Standardized cystatin C equation for adults
CKD-EPICYSC [12]
eGFR (mL/min/1.73 m2) =
pCysC ≤ 0.8 mg/L:
133  (pCysC / 0.8)-0.499  0.996Age  0.932 (if female)
pCysC > 0.8 mg/L:
133  (pCysC / 0.8)-1.328  0.996Age  0.932 (if female)
Standardized combined creatinine and cystatin C equation for adults
CKD-EPICREA+CYSC [12]
eGFR (mL/min/1.73 m2) =
Female pCr ≤ 62
Female pCr ≤ 62
Male
Male
pCr ≤ 80
pCr ≤ 80
pCysC ≤ 0.8
130 × (pCr / 62)−0.248 × (pCysC / 0.8)−0.375 × 0.995Age
pCysC > 0.8
130 × (pCr / 62)−0.248 × (pCysC / 0.8)−0.711 × 0.995Age
pCysC ≤ 0.8
130 × (pCr / 62)−0.601 × (pCysC / 0.8)−0.375 × 0.995Age
pCysC > 0.8
130 × (pCr / 62)−0.601 × (pCysC / 0.8)−0.711 × 0.995Age
pCysC ≤ 0.8
135 × (pCr / 80)−0.207 × (pCysC / 0.8)−0.375 × 0.995Age
pCysC > 0.8
135 × (pCr / 80)−0.207 × (pCysC / 0.8)−0.711 × 0.995Age
pCysC ≤ 0.8
135 × (pCr / 80)−0.601 × (pCysC / 0.8)−0.375 × 0.995Age
pCysC > 0.8
135 × (pCr / 80)−0.601 × (pCysC / 0.8)−0.711 × 0.995Age
Standardized combined creatinine and cystatin C equation for children
ChehadeCREA+CYSC [13]
eGFR (mL/min/1.73 m2) = 0.42 × [height (cm) / (pCr / 88.4)] – 0.0004 × [height (cm) /
/ (pCr/88.4)]2 – 14.5 × cystatin C + 0.69 × age + K
(K = 18.25 for females and 21.88 for males).
GFR calculators
Easy available calculators exist for LM-REVCREA, CAPACYSC and their arithmetic mean MEANLMREV+CAPA
(egfr.se/eGFRen.html) as well as for the CKD-EPI equations
(www.kidney.org/professionals/kdoqi/gfr_calculator.cfm) and give the results for both single and
combined marker equations.
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Methods to Estimate and Measure Renal Function (Glomerular Filtration Rate).
Chapter 3.2, Validation of GFR estimating equations in large patient groups.
A systematic review by the Swedish Council on Health Technology Assessment,
Available at www.sbu.se/214, Accessed March 1, 2015.
Summary and conclusions in English is available at
http://www.sbu.se/en/Published/Yellow/Methods-to-Estimate-and-Measure-Renal-FunctionGlomerular-Filtration-Rate/, Accessed March 1, 2015.
The systematic search for studies ended in October 25, 2011.
Overall aim
The overall aim of Chapter 3.2. was to assess how accurate equations based on creatinine,
cystatin C or the combination of the two analytes estimate GFR. Using the PICO terminology, the
overall aim can be represented as:
P
Population
Large patient groups who had undergone GFR measurements
I
Index test
Estimated GFR based creatinine, cystatin C or equation combing
the two analytes.
C
Reference test (Control)
Renal clearance of inulin or another accepted clearance method
according to Chapter 3.1.
O
Outcome
Systematic error (bias), accuracy and classification ability.
Specific questions
1.
Which creatinine equation yields the most accurate estimate of GFR in large groups of adult
and child patients?
2.
Do cystatin C equations yield more accurate estimates of GFR than equations based on
creatinine?
3.
Do equations combining creatinine and cystatin C yield more accurate estimates than equations
based on the individual markers separately?
4.
How accurately is GFR estimated in subgroups divided according to kidney function, age, sex,
ethnicity, and BMI?
5.
How accurately is GFR estimated in populations that differ ethnically from the Swedish?
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Inclusion criteria
Population

Large groups of patients (adults and children), patients with chronic kidney disease, kidney
donors before and after donation, general populations and elderly who all had undergone GFR
measurements

Studies with at least 100 individuals or GFR measurements or at least 20 individuals or GFR
measurements in subgroups, e.g. elderly and children

Comparisons between creatinine and cystatin C equations and equations combining the two
analytes including stratification for kidney function, age, gender and BMI limited to Caucasians
Index test

GFR estimating equations based on creatinine, cystatin C or combinations of the analytes

Creatinine assays used in development and validation should be traceable to isotope dilution
mass spectrometry (IDMS) or calibrated against the method used at the laboratory (Cleveland
Clinic) where the original four-variable MDRD equation (MDRD-original) was developed.
Roche creatinine assays (Jaffe and enzymatic) are IDMS-traceable from year 2002 according to
the company and has been accepted for inclusion.
o For MDRD-original results are only accepted if the creatinine assays were calibrated
against the method used at Cleveland Clinic
o For MDRD-IDMS results are only accepted if the creatinine assays were IDMS-traceable
o Cockcroft-Gaults equation for adults and Schwartz original equation for children, both
from 1976, were included since they are still used in clinical routine, though they are not
based on today’s creatinine assays

Cystatin C equations were accepted for analysis only if the cystatin C assay was analyzed at the
same laboratory where the equation was developed due to lack of an international standard.
This implies that only results of internal validation (for definition see below) will be available.

Studies of cystatin C equations were included only if there were comparisons with creatinine
based equations or equations combining creatinine and cystatin C

In comparative studies of creatinine and cystatin C equations, non-standardized creatinine
assays are accepted if the same laboratory and assay has been used for development and
validation

The time between the index (creatinine or cystatin C) and reference test (clearance
measurement) should have been performed within 24 hours
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Reference test

Renal clearance of inulin or other external clearance markers with sufficient accuracy (renal
clearance of iothalamate, iohexol, DTPA or 51Cr-EDTA, or plasma clearance of inulin, iohexol
or 51Cr-EDTA); see Table 1 in English summary or reference [14]
Outcome

Bias (systematic error) and accuracy (incorporates both bias and precision) in terms of
percentage of GFR estimates within 30% of measured GFR (P30) and classification ability of
different stages of chronic kidney disease
Exclusion criteria
Population

Specific disease groups. However, results concerning diabetes and organ transplants were
included if they were reported separately in studies of large groups of patients.

Patients undergoing dialysis treatment

For question 1-4 above only studies of populations that ethnically resemble a Swedish
population were included. For question 5 studies from all over the world were taken into
account.
Index test

GFR equations based on other biomarkers than creatinine and cystatin C

GFR equations based on bioimpedance for evaluation of lean body mass

Nomograms to estimate GFR

Creatinine assays where traceability is unclear or not described

Studies based on inhibition of tubular secretion of creatinine based on cimetidine

Studies on intra-individual variations, variation over time and reproducibility in estimated GFR

GFR equations ability to predict changes in renal function over time, morbidity, mortality or
other outcomes
Reference test

Not accepted reference test according to Chapter 3.1. (i.e. plasma clearance of iothalamate and
DTPA, and endogenous creatinine clearance); see Table 1 in English summary or reference [14]
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Outcome

Systematic errors and accuracy only presented in diagrams

Classification ability based ROC-area without presentation of correctly classified estimated
GFR

Development validations, i.e. results based on the same cohort of patients without separation in
a development and test cohort
Quality assessment of included studies
The quality assessment of included studies was based on three different aspects: 1) type of
validation (see next paragraph), 2) number of measurements, 3) study quality according to a
modified QUADAS template with 11 items (Quality Assessment of Diagnostic Accuracy Studies)
[15, 16]. The quality was classified as high, moderate or low according to the following criteria:
High quality
External validation of at least 500 clearance measurements (≥ 100
measurements in subgroups) and at least seven out of eleven quality points.
Moderate quality
At least 100 clearance measurements (≥ 40 measurements in subgroups) and at
least four out of eleven quality points.
Low quality
Studies that does not fulfil the criteria of moderate or high quality.
Requirements of bias and accuracy
Bias was considered acceptable if it was less than 10% in mean or median [17]. Accuracy was
regarded sufficient if at least 75% of the GFR estimates were within 30% of measured GFR (P30)
according to National Kidney Foundation [18]. To be regarded as statistically certain, the lower
95% confidence limit of P30 should be ≥75%.
Definition of validations
Study quality depends on characteristics of the validation procedure. External validation has the
highest quality followed by internal validation. Development validation has the lowest quality.
External validation
Validation performed in a different population and at a different laboratory than where the equation
was developed. The validation is not regarded as external if its results are allowed to influence the
final functional form or coefficients, or which one of alternative equations that is advocated.
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Internal validation
The expression of the equation and its coefficients is determined from a subset of a certain
population (development cohort) and then tested in another subset of the same population
(validation cohort). A validation performed in a different population than that used to develop the
equation but at the same laboratory is also regarded as internal. In an internal validation the results
are allowed to affect the final expression of the equation and which one of alternative equations that
is advocated.
Development validation
Validation results presented for the same cohort that was used to develop the final expression of the
equation and its coefficients.
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Supplementary Figures and Tables based on the SBU systematic review
Figure S1. Comparison performed by Equalis AB (External quality assessment for clinical
laboratory investigations, www.equalis.se/en) of reported plasma concentrations of creatinine in
µmol/L (Y-axis) between about 100 Swedish laboratories from 2003 to 2011 (year-week on the Xaxis) using a certified creatinine sample (71 µmol/L, 95% confidence interval 69.6 - 71.5 µmol/L).
Median value, 1st and 3rd quartile (box plot), 5% and 95% percentiles, and maximum and
minimum values (+) are illustrated. Dotted lines indicate the certified creatinine concentration.
During the same time interlaboratory variation coefficient from measurements of the certified
creatinine sample decreased from 10% to 5%. Adapted from Figure 1.5 in reference [19].
Permission granted for publication from the Swedish Council on Health Technology Assessment.
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Figure S2. Estimated GFR (eGFR) in mL/min/1.73 m2 (Y-axis) based on MDRD, CKD-EPI and
the original (LM-original) and revised Lund-Malmö (LM-revised) equations at a plasma creatinine
concentration of 80 µmol/L in girls and females 1-30 years of age. eGFR based on the LM
equations decreases with decreasing age at a given creatinine level, which reflects decreasing renal
function when muscle mass (creatinine production) also decreases at the same time. On the other
hand, MDRD and CKD-EPI will markedly overestimate GFR in children. The markedly different
performance of the LM equations vs. MDRD and CKD-EPI may be attributed to the noticeable
difference in the age coefficients [20]. Adapted from Figure 3.2.16 in reference [19]. Permission
granted for publication from the Swedish Council on Health Technology Assessment.
MDRD
CKD-EPI
LM-original
LM-revised
(GFR (mL/min/1.73 m2)
150
120
90
60
30
0
1
5
10
15
18
Age (years)
20
30
40
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Table S1. Meta-analysis of creatinine based equations in children regarding P30 accuracy (95%
confidence intervals), i.e. percent of GFR estimates within 30% of measured GFR. Adapted from
Table 3.2.10. based on studies with details given in Table 3.2.29 (English text) in reference [19].
Comparisons
Type of validation
Number
SchwartzIDMS vs.
Schwartz
original
External in the same
cohorts [20, 21]
337
SchwartzIDMS
80 (76-84)
SchwartzIDMS vs.
LM-original
External and internal in
the same cohorts [20, 22]
267
58 (53-64)
SchwartzIDMS
External [20-24]
700
74 (70-77)
Schwartzoriginal
24 (19-28)
SchwartzExternal and internal
807
74 (71-77)
IDMS
[9, 20-23, 25]
Schwartz-IDMS = Schwartz equation based on IDMS traceable creatinine assays.
Schwartz original = the original Schwartz equation [26].
LM-original = the original Lund-Malmö equation [4].
LM-original
69 (63-74)
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Table S2. Meta-analysis of creatinine based equations in adults regarding P30 accuracy (95% confidence intervals), i.e.
percent of GFR estimates within 30% of measured GFR. Results are based on pair wise comparisons and adapted from Table
3.2.4. which in turn is based on studies with details given in Table 3.2.17 (English text) in reference [19].
Comparisons
Type of validation
Number
CG
MDRD
CG/MDRD
External [4, 27-29]
3 267
75 (74-77)
85 (83-86)
CG/MDRD
External (CG)
Extern and internal (MDRD)
[4, 27-30]
8 771
71(70-72)
84(83-85)
CKD-EPI/
MDRD
External [28, 31, 32]
7 485
78 (77-79)
79(78-80)
CKD-EPI/
MDRD
External and internal
[8, 28, 31-33]
14 131
80 (79-80)
81(80-82)
External [31]
1 397
80 (77-82)
79 (77-81)
MDRD/CKD-EPI/
LM
CG = Cockcroft-Gault equation normalized to 1.73 m2 body surface area
MDRD = Modification of Diet in Renal Disease Study equation
CKD-EPI = Chronic Kidney Disease Epidemiology Collaboration equation
LM = Lund-Malmö equation
CKD-EPI
LMoriginal/
reviderad
82 (80-84)/
84(82-86)
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Table S3. Meta-analysis of the best performing cystatin C and creatinine equation in each study as
well as equations combining the two analytes in adults regarding P30 accuracy (95% confidence
intervals), i.e. percent of GFR estimates within 30% of measured GFR. Results are based on pair
wise comparisons and adapted from Table 3.2.9. which in turn is based on studies with details given
in Table 3.2.28 (English text) in reference [19].
Type of validation
Cystatin C
equation
Creatinine
equations
83 (80-86)
(n=760)
Arithmetic
mean equation*
Composite
equation**
83 (80-85)
(n=760)
83 (80-86)
(n=760)
89 (86-91)
(n=760)
90 (87-93)
(n=438)
89 (88-91)
(n=1617)
89 (88-90)
(n=4713)
External [29, 34]
External and internal [29, 34]
External, internal and
82 (81-83)
84 (83-85)
developmental [29, 34, 35]
(n=5035)
(n=5035)
*Arithmetic mean of one cystatin C and one creatinine equation.
**Single equation based on both cystatin C and creatinine.
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