Page 1

Universal GFR determination based on two time

points during plasma iohexol disappearance

Derek K.S. Ng1, George J. Schwartz2, Lisa P. Jacobson1, Frank J. Palella3, Joseph B. Margolick4,

Bradley A. Warady5, Susan L. Furth6and Alvaro Mun ˜oz1

1Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, USA;2Department of Pediatrics,

University of Rochester Medical Center, Rochester, New York, USA;3Department of Medicine, Northwestern University Feinberg School

of Medicine, Chicago, Illinois, USA;4Department of Molecular Microbiology and Immunology, Johns Hopkins Bloomberg School of Public

Health, Baltimore, Maryland, USA;5Department of Pediatrics, Children’s Mercy Hospital, University of Missouri-Kansas City School of

Medicine, Kansas City, Missouri, USA and6Department of Nephrology, The Children’s Hospital of Philadelphia, Philadelphia,

Pennsylvania, USA

An optimal measurement of glomerular filtration rate (GFR)

should minimize the number of blood draws, and reduce

procedural invasiveness and the burden to study personnel

and cost, without sacrificing accuracy. Equations have been

proposed to calculate GFR from the slow compartment

separately for adults and children. To develop a universal

equation, we used 1347 GFR measurements from two diverse

groups consisting of 527 men in the Multicenter AIDS Cohort

Study and 514 children in the Chronic Kidney Disease in

Children cohort. Both studies used nearly identical two-

compartment (fast and slow) protocols to measure GFR. To

estimate the fast component from markers of body size and

of the slow component, we used standard linear regression

methods with the log-transformed fast area as the

dependent variable. The fast area could be accurately

estimated from body surface area by a simple parameter

(6.4/body surface area) with no residual dependence on the

slow area or other markers of body size. Our equation

measures only the slow iohexol plasma disappearance curve

with as few as two time points and was normalized to

1.73m2body surface area. It is of the form: GFR¼slowGFR/

[1þ0.12(slowGFR/100)]. In a random sample utilizing a third

of the patients for validation, there was excellent agreement

between the calculated and measured GFR with low root

mean square errors being 4.6 and 1.5ml/min per 1.73m2for

adults and children, respectively. Thus, our proposed simple

equation, developed in a combined patient group with a

broad range of GFRs, may be applied universally and is

independent of the injected amount of iohexol.

Kidney International (2011) 80, 423–430; doi:10.1038/ki.2011.155;

published online 8 June 2011

KEYWORDS: glomerular filtration rate; iohexol; kidney disease; nephrology;

plasma disappearance curves; renal function

Glomerular filtration rate (GFR) can be determined accu-

rately by measuring the plasma clearance of a single intra-

venous injection of a contrast medium such as iohexol,

calculated from plasma sampling at multiple time points over

several hours1,2using an open two-compartment (slope–

intercept) mathematical model for the plasma disappearance

curve. The protocols to measure GFR in the Multicenter

AIDS Cohort Study (MACS) and Chronic Kidney Disease in

Children (CKiD) study involved four venous blood samples

after a single bolus injection of iohexol. To properly estimate

the two compartments, referred to hereafter as ‘fast’ for the

first compartment, and ‘slow’ for the second compartment,

two of the four blood samples were collected within B30min

of the injection (for the fast compartment) and the other two

were obtained X2h after the injection (for the slow

compartment). The ratio of the injected amount of iohexol

to the area under the disappearance curve is a direct measure

of GFR. This ‘gold-standard’ protocol is time intensive and

requires multiple blood draws, thereby increasing complexity

of large epidemiologic studies.2,3An optimal GFR measure-

ment should minimize the number of blood draws,

procedural invasiveness, burden to study personnel, and cost.

Restricting sampling to only the slow compartment of the

model has been proposed in adults4,5and children.2,6GFR

equations to quantify a universal relationship between the

one-compartment (slow) and the two-compartment (slow þ

fast) plasma disappearance models have been published,

based on diverse, but small, study samples (combining adults

and children) representing different clinical populations

(that is, varying levels of renal function).7–9Thus, the

purpose of the current study was to develop a formula to

determine the two-compartment GFR for studies where

samples in the fast compartment are not collected. To

accomplish this, we used iohexol-based studies that measured

both the slow disappearance curve and the fast disappearance

curve in two large-scale, clinically disparate populations.

Our analysis includes large populations with a broad range of

GFRs and thus should provide a strong basis for a universally

applicable equation.

http://www.kidney-international.org

technical notes

& 2011 International Society of Nephrology

Received 22 November 2010; revised 15 March 2011; accepted 29

March 2011; published online 8 June 2011

Correspondence: Alvaro Mun ˜oz, Department of Epidemiology, Johns

Hopkins Bloomberg School of Public Health, 615 North Wolfe Street,

Room E7650, Baltimore, Maryland 21205, USA. E-mail: jvaldez@jhsph.edu

Kidney International (2011) 80, 423–430

423

Page 2

The protocol for measuring GFR in the MACS and CKiD

study used a two-compartment, four blood sample model of

plasma iohexol disappearance to calculate GFR (see Materials

and Methods). Two GFR values were calculated: one GFR

based on the slow compartment only (GFR0,2) and the other

GFR based on both the fast and slow compartments (GFR2,2;

see Variables subsection). As there is a close relationship

between GFR0,2 and GFR2,2, two approaches have been

proposed to estimate GFR2,2 from GFR0,2; this estimate

is denoted hereafter asd

typically in clinical guidelines5and epidemiological research;2

and (2) a new equation based on theoretical underpinnings

by Fleming7and Brochner-Mortensen and Jodal.8,9

In this study, we aimed to develop a formula to estimate

the fast component in GFR2,2not measured in GFR0,2(that

is, missing fast area). Once such a formula was developed, we

derived the corresponding formula to determine GFR2,2

based on GFR0,2, and we position our proposed equation in

the context of the recently improved principles.7–9The MACS

GFR2;2. These approaches are: (1) the

classical Brochner-Mortensen equation4that has been used

and CKiD studies provided an excellent opportunity to

develop a universal equation because the GFR-measuring

protocols were nearly identical (except for the time of the last

blood sample: 240min in the MACS and 300min in CKiD)

and included the same central biochemistry laboratory

(principal investigator GJS, University of Rochester Medical

Center, Rochester, NY) and the same data coordinating

center (co-principal investigators AM and LPJ, Johns

Hopkins Bloomberg School of Public Health, Baltimore,

MD), although the two populations studied were extremely

different. Agreement betweend

of a truly universal equation. Such a robust equation would

highlight any common dynamics between these two disparate

groups and permit future iohexol GFR studies in any

population to accurately determine GFR using only two

plasma samples.

GFR2;2and GFR2,2within each

study population, therefore, would assess the appropriateness

RESULTS

Table 1 presents descriptive statistics of the 527 adult men

from the MACS and the 514 children from the CKiD cohort

who were studied. In the CKiD data set, 63% of subjects

underwent one GFR2,2 study, 36% had two studies, and

1% had three studies (with repeated studies at B1-year

intervals), yielding a total of 820 GFR2,2studies. The two

cohorts differed substantially in most characteristics shown

in Table 1. The MACS subjects were adult men with a median

age of 51 years, and the CKiD subjects were children

(62% male) with a median age of 11 years. Human

immunodeficiency virus (HIV) infection was an exclusion

criterion for CKiD, but 70% of the MACS subjects were HIV

infected. In CKiD, a cohort of children with chronic kidney

disease, 21% had glomerular kidney disease.

Table 2 presents the plasma disappearance parameters by

study cohort and by training data set (for model develop-

ment using a 2/3 random sample) and validation data set

(for evaluation of agreement between observed and estimated

GFR using the remaining 1/3 random sample). All para-

meters were significantly different between the cohorts except

for the injected iohexol, which was B3200mg by the

common protocol. As expected, randomization yielded

Table 1|Descriptive statistics (percent or median (interquartile

range)) of clinical and demographic characteristics of the

MACS and CKiD populations at baseline

Characteristic MACS (n=527) CKiD (n=514)

Age (years)

Male

50.9 (46.0, 57.1)

100%

11.1 (7.7, 14.7)

62%

Race

White

Black

Other

Height (m)

Weight (kg)

BMI (kg/m2)

BSA (m2)

HIV infected

57%

35%

8%

66%

23%

12%

1.76 (1.71, 1.80)

80.7 (72.6, 90.4)

26.2 (23.9, 28.8)

2.00 (1.87, 2.14)

70%

1.40 (1.20, 1.58)

36.3 (23.7, 54.8)

18.3 (16.2, 22.0)

1.19 (0.89, 1.57)

0%

Serum creatinine (mg/dl)

GFR2,2(ml/min per 1.73m2)

0.92 (0.79, 1.08)

109.2 (94.9, 125.2)

1.30 (1.00, 1.80)

44.0 (32.8, 56.0)

Abbreviations: BMI, body mass index; BSA, body surface area; CKiD, Chronic Kidney

Disease in Children Cohort Study; GFR, glomerular filtration rate; HIV, human

immunodeficiency virus; MACS, Multicenter AIDS Cohort Study.

Table 2|Median (interquartile range) of plasma disappearance parameters of iohexol studies for the training and validation

data sets from the MACS and CKiD populations

Training data set (2/3 random sample)Validation data set (1/3 random sample)

MACS (n=350)CKiD (n=546)P-valuea

MACS (n=177)CKiD (n=274)

Iohexol injection (mg)

Fast areab(mg min/ml)

Slow areac(mg min/ml)

GFR0,2d(ml/min per 1.73m2)

GFR2,2e(ml/min per 1.73m2)

3180 (3151, 3243)

3.2 (2.6, 3.9)

21.9 (18.6, 25.5)

125.3 (105.5, 149.0)

108.6 (93.8, 126.2)

3190 (3156, 3223)

5.7 (4.0, 8.1)

107.6 (73.9, 156.2)

45.3 (33.4, 59.2)

42.9 (32.0, 54.8)

0.426

o0.001

o0.001

o0.001

o0.001

3185 (3127, 3223)

3.4 (2.8, 4.1)

21.3 (18.7, 25.0)

128.3 (110.0, 150.1)

112.1 (96.3, 124.9)

3192 (3160, 3228)

5.3 (3.7, 8.2)

97.5 (63.8, 142.8)

47.7 (36.2, 63.6)

45.4 (34.6, 58.6)

Abbreviations: CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; MACS, Multicenter Aids Cohort Study.

aWilcoxon rank-sum test comparing MACS and CKiD in training data set; bold indicates statistically significant (Po0.05).

bBased on plasma samples at 10 and 30min after iohexol injection.

cBased on plasma samples at 120 and 240min for MACS and 120 and 300min for CKiD after iohexol injection.

d(Iohexol injection/slow area)?(1.73/BSA).

e(Iohexol injection/total area)?(1.73/BSA).

424

Kidney International (2011) 80, 423–430

technical notes

DKS Ng et al.: Two-sample iohexol GFR for diverse populations

Page 3

similar parameters for the training and validation data sets

for each cohort. For CKiD, these parameters indicated renal

insufficiency. In contrast, most of the MACS had normal

renal function: 81% of these subjects had a GFR2,2X90ml/

min per 1.73m2.

Predictors of the fast area

The left side of Table 3 shows the regression coefficients and

R2for the univariate regressions with the dependent variable

being the fast area in the log scale. All variables showed

substantial associations with the fast area. In particular, the

fast area was inversely proportional to body surface area

(BSA; that is, coefficient of BSA was close to, and not

statistically different from, –1). Furthermore, there was a

strong positive relationship between the slow and fast areas,

with the slow area explaining close to 34% of the variability

in fast area. Given the strong relationship between the fast

area and BSA, we explored the predictive power of variables

in Table 3 on the variability of the fast area unexplained by

BSA. The right side of Table 3 shows that none of the

predictors explain the variability of residuals of the regression

of fast area on BSA. In particular, the strong univariate

association between slow and fast area completely disap-

peared when the dependent variable was BSA-adjusted

fast area (regression coefficient¼?0.018 (P¼0.194), R2¼

0.2%). Further evidence of the lack of association between

the fast and slow area conditional on BSA is the fact that the

R2¼34% observed in the overall univariate relationship

between the fast and slow area reduced to 0.6, 0.1, 0.7, and

1.6% in four strata defined by quartiles of BSA.

Figure 1a shows that the relationship between fast area and

BSA (R2¼56%) is given by fast area¼6.46?(BSA)?1.023.

More importantly, Figure 1b shows that once the variability

of fast area due to BSA has been accounted for, there is no

additional information from the slow area (R2¼0.2%).

Hence, the fast area depends on BSA, but not on the slow

area once BSA has been taken into account.

Formula to determine GFR2,2from GFR0,2

Not only does the fast area not depend on the slow area once

BSA has been taken into account, but the relationship

between the fast area and BSA can be simplified to

fast area ¼ 6:4/BSA

and we can derive an equation to determine GFR2,2in terms

of GFR0,2. Specifically, by simply dividing both sides of the

above equation by the slow area and multiplying and

dividing the right-hand side of the equation by 1.73?I

(where I is the injected amount of iohexol), the equation

becomes

fastarea=slowarea ¼ ð6:4=ð1:73?IÞÞ?GFR0;2:

As by protocol, I is close to 3200 and has very low variability

(see Table 2), 6.4/(1.73?I) is equal to 0.00116 (which

hereafter we round to 0.0012). In addition, the ratio of fast to

slow area is simply (GFR0,2/GFR2,2) – 1.

Table 3|Univariate linear regression models used to

determine the percent of explained variance of

BSA-unadjusted and BSA-adjusted fast area for the

combined MACS (n=350) and CKiD (n=546) training data set

Dependent variable

BSA-unadjusted

fast areab

BSA-adjusted

fast areac

Independent variablea

Regression

coefficient R2

Regression

coefficientR2

BSA (m2)

Slow area (mg min/ml)

GFR0,2(ml/min per 1.73m2)

Height (m)

Weight (kg)

BMI (kg/m2)

Age (years)

Male gender

?1.023

0.359

?0.315

?2.075

?0.670

?1.187

?0.430

0.335

55.9%

33.6%

12.2%

56.4%

54.6%

32.2%

49.9%

6.6%

——

0.2%

0.5%

0.2%

o0.1%

0.8%

0.3%

0.1%

?0.018

0.041

?0.082

?0.006

0.128

?0.022

0.032

Abbreviations: BMI, body mass index; BSA, body surface area; CKiD, Chronic Kidney

Disease in Children Cohort Study; GFR, glomerular filtration rate; MACS, Multicenter

AIDS Cohort Study.

aAll variables except gender in natural logarithmic scale.

bDependent variable is the natural log of the observed fast area.

cDependent variable is the residual of the regression of fast area on BSA (log scale).

25

20

15

10

5

3

2

1

0.35

1.0

0.5

–0.5

0.0

–1.0

Training data set

CKiD (Δ) n=546

MACS (o) n=350

–1.5

1015

25

50

100300

200600

Slow area (mg min/ml)

0.51.0

BSA (m2)

1.5 2.0 2.5 3.03.5

Training data set

CKiD (Δ) n=546

MACS (o) n=350

Fast area = 6.46*(BSA) –1.023

R2 = 56%

R2 = 0.2%

Fast area

(mg min/ml)

log (fast area) – log (6.46)

–1.023 log (BSA)

a

b

Figure 1|Relationships between fast area, BSA, and slow

area. (a) Regression of fast area (y axis) on body surface area

(BSA; x axis) in the log scale for the combined Multicenter AIDS

Cohort Study (MACS) and Chronic Kidney Disease in Children

(CKiD) training data set. The dashed line represents the

nonparametric spline. (b) Non-relationship of residuals from the

regression of fast area on body surface area presented in a (y axis)

and slow area (x axis) from the training data set.

Kidney International (2011) 80, 423–430

425

DKS Ng et al.: Two-sample iohexol GFR for diverse populations

technical notes

Page 4

Hence,

ðGFR0;2=GFR2;2Þ ? 1 ¼ 0:0012?GFR0;2

which, solving for GFR2,2, yields our proposed equation for

d

GFR2;2¼ GFR0;2=½1 þ 0:12ðGFR0;2=100Þ?

or, in short,

GFR2;2from GFR0,2as follows:

d

d

Solid line=0.12 × (GFR0,2/100)

Dashed line=Nonparametric spline

GFR ¼ slowGFR=½1 þ 0:12ðslowGFR=100Þ?

This equation is of the same form as the one proposed by

Fleming7and simpler than the one proposed by Brochner-

Mortensen and Jodal.9More importantly, the form of the

equation is consonant with the theoretical and physiological

considerations put forward by these authors.

Figure 2 plots the data for (GFR0,2/GFR2,2) –1 (y axis) on

GFR0,2(x axis) and it indicates that the equation including

the simple proportionality factor of 0.12 not only fits the data

well for both cohorts but also explains 75% of the variability

for the combined training data set.

Evaluation of equations to calculated

For the validation data sets of each study population (1/3

random sample), Table 4a and b describes the agreement of

GFR2,2(measured) and the d

included the original Brochner-Mortensen equations for

adult4

and pediatric6

populations; those published by

Brochner-Mortensen and Jodal8and Fleming;7and our

proposed equation.

The original Brochner-Mortensen equations showed

significant underestimation of GFR2,2in the MACS (bias:

?3.3%, 95% confidence interval (CI): ?3.9, ?2.7%) and in

the CKiD (?1.7%, 95% CI: ?2.0%, ?1.4%). The equations

also produced significant underdispersion in both popula-

tions and higher root mean square errors (RMSEs) and lower

percentages ofd

cally significant, the effect size was relatively small. The

equations proposed by Brochner-Mortensen and Jodal9and

GFR2;2and agreement

betweend

GFR2;2and GFR2,2

GFR2;2 (estimated) from four

different GFR0,2-based equations. The equations evaluated

GFR2;2within 5% of GFR2,2than those of our

proposed equation. Although these estimates were statisti-

0.40

0.30

R2=75%

0.20

0.12

0.10

0.05

0.03

(GFR0,2/GFR2,2)– 1

0.01

10 20

GFR0,2 (GFR based on two-point, slow component

only; ml/min per 1.73 m2)

30 5070 100 170

Training data set

CKiD (Δ) n=546

MACS (o) n=350

220

Figure 2|Relationship between GFR0,2(x axis) and (GFR0,2/

GFR2,2) – 1 (y axis) in the log scale, for the combined

Multicenter AIDS Cohort Study (MACS) and Chronic Kidney

Disease in Children (CKiD) training data set. The equation,

(GFR0,2/GFR2,2) – 1¼0.12?(GFR0,2/100), is depicted as the solid

line. GFR, glomerular filtration rate.

Table 4|Agreement of the estimated GFR (d

GFR2;2) based on two-point GFR from the slow curve only (GFR0,2) and selected

models with the observed four-point GFR (GFR2,2) in the (a) MACS (n=177) and (b) CKiD (n=274) validation data sets

Model ofd

(a) MACS validation data set (n=177)

Original Brochner-Mortensen

C1(GFR0,2/100) + C2(GFR0,2/100)2

C1=98.31; C2=–0.1218

GFR0,2/[1+ B0? (GFR0,2/100)B1? BSAB2]

B0=0.185; B1=1, B2=–0.3

GFR0,2/[1+B0 ? (GFR0,2/100)B1]

B0=0.17; B1=1

MACS and CKiD proposed equation

GFR0,2/[1+B0? (GFR0,2/100)B1]

B0=0.12; B1=1

GFR2;2as a function of GFR0,2and BSASource

Bias ratio

(95% CI)

Ratio of s.d.’s

(95% CI)

Correlation

(95% CI) RMSE

% ofd

GFR2,2

GFR2;2

within 5% of

Brochner-Mortensen4

0.967

(0.961, 0.973)

0.937

(0.909, 0.965)

0.978

(0.971, 0.984)

6.4962.7%

Brochner-Mortensen

and Jodal8,9

Fleming7

0.972

(0.967, 0.978)

0.960

(0.934, 0.986)

0.979

(0.972, 0.984)

5.8066.1%

0.953

(0.947, 0.959)

0.941

(0.916, 0.967)

0.979

(0.972, 0.984)

7.4949.7%

Training set

CKiD + MACS 2/3

random sample (n=896)

1.005

(1.000, 1.011)

0.987

(0.962, 1.013)

0.980

(0.972, 0.985)

4.5979.1%

(b) CKiD validation data set (n=274)

Original Brochner-Mortensen

C1(GFR0,2/100) + C2(GFR0,2/100)2

C1=101.0; C2=–0.17

GFR0,2/[1+ B0? (GFR0,2/100)B1? BSAB2]

B0=0.185; B1=1, B2=–0.3

GFR0,2/[1+B0? (GFR0,2/100)B1]

B0=0.17; B1=1

MACS and CKiD proposed equation

GFR0,2/[1+B0 ? (GFR0,2/100)B1]

B0=0.12; B1=1

Brochner-Mortensen et al.6

0.983

(0.980, 0.986)

0.968

(0.959, 0.976)

0.996

(0.995, 0.997)

2.0491.2%

Brochner-Mortensen

and Jodal8,9

Fleming7

0.978

(0.975, 0.981)

0.984

(0.976, 0.992)

0.996

(0.995, 0.997)

1.9286.5%

0.980

(0.978, 0.983)

0.983

(0.974, 0.991)

0.996

(0.995, 0.997)

1.8790.9%

Training set

CKiD + MACS 2/3

random sample (n=896)

1.004

(1.001, 1.006)

1.005

(0.996, 1.013)

0.996

(0.995, 0.997)

1.4696.0%

Abbreviations: BSA, body surface area; CI, confidence interval; CKiD, Chronic Kidney Disease in Children Cohort Study; GFR, glomerular filtration rate; MACS, Multicenter AIDS

Cohort Study; RMSE, root mean square error.

Bold indicates statistically significantly different from 1 (that is, Po0.05).

426

Kidney International (2011) 80, 423–430

technical notes

DKS Ng et al.: Two-sample iohexol GFR for diverse populations

Page 5

Fleming7each yielded a slight systematic underestimation

and underdispersion in both populations. Our proposed

equation, based upon the MACS and CKiD, showed good

agreement in each validation data set. In the MACS data set,

there was no significant bias or difference in dispersion

associated withd

(bias: þ0.4%, 95% CI: 0.1%, 0.6%) and no significant

overdispersion (ratio of s.d.’s: þ0.5%, 95% CI: ?0.2%,

1.3%), but these effects were small (p1%). The proposed

equation also provided the lowest RMSE and the highest

percentage of d

were high and essentially the same in both the MACS

(r¼0.980) and CKiD (r¼0.996) validation data sets.

Figure 3 depicts agreement ofd

values were essentially identical to GFR2,2 with minimal

bias, a preservation of dispersion, low RMSE, and very high

correlation in these two distinct populations.

GFR2;2compared with GFR2,2. In the CKiD

data set, there was a minor, but significant, overestimation

GFR2;2 being within 5% of GFR2,2 of the

equations tested. The correlations between all four equations

GFR2;2calculated using the

MACS and CKiD proposed equation with GFR2,2. Thed

GFR2;2

DISCUSSION

Current guidelines provide separate equations to calculate

d

populations. The literature often cautions that equations to

calculated

two large studies of different populations, demographically

diverse and with a broad range of renal function, underwent

essentially the same iohexol GFR2,2measurement protocols;

this allowed us to develop an equation suitable for both

GFR2;2 for adults and children, but the present analysis

shows that a universal equation is applicable in diverse

GFR2;2are appropriate only in populations similar

to those in which they were developed. In the present study,

populations. Crucial findings for the proposed universal

equation were that the fast area was inversely proportional

to BSA and that the BSA-adjusted fast area was independent

of the slow area. Thus, BSA was a key consideration when

evaluating the common dynamic between these two popula-

tions, and must routinely be accounted for when measuring

GFR.

The simple relationship between the fast area and BSA

allowed the derivation of a simple equation to calculate

d

analysis was performed on the data in Figure 2. Indeed,

the slope (¼1.025) was not significantly different from 1

(95% CI: 0.987, 1.063), and the intercept (that is, at

GFR0,2¼100ml/min per 1.73m2) was equal to 0.117.

Our proposed equation provides an accurate and reliable

GFR measurement from as few as two blood samples

collected between 120 and 300min after injection of iohexol.

This modification of the iohexol-based protocol represents

an important reduction in study burden for subjects and

personnel, and should facilitate GFR measurements in

large-scale clinical and epidemiological studies.

Our analysis assessed the agreement between GFR2,2and

d

equations showed good agreement, our proposed equation

was even better: RMSEs were 4.59 and 1.46ml/min

per 1.73m2for the MACS and CKiD validation data sets,

respectively. Furthermore, our proposed equation had

the highest proportion ofd

Importantly, the equation

(GFR0,2/100)] is consistent in form with the equations

proposed by Brochner-Mortensen and Jodal8,9and Fleming7

and coheres with the theoretical principles discussed by these

authors. Specifically, using the general expression:

GFR2;2from GFR0,2, as measured by an iohexol-based GFR

protocol. To confirm this derivation, a direct regression

GFR2;2 of our proposed equation as well as of previously

published equations.4,7–9Although the previously published

GFR2;2 within 5% of the GFR2,2

(79% for MACS and 96% of CKiD).

d

GFR2;2¼

GFR0,2/[1þ0.12

GFR0;2=ð1 þ B0? ? GFR0;2=100ÞB1?BSAB2Þ

the Brochner-Mortensen and Jodal8,9equation corresponds

to B0¼0.185, B1¼1, and B2¼–0.3; the Fleming7equation

corresponds to B0¼0.17, B1¼1, and B2¼0; and our

proposed equation corresponds to B0¼0.12, B1¼1, and

B2¼0.

Another feature of our proposed equation is that it is

invariant with respect to the injected amount of iohexol.

Indeed, the relationship describing GFR0,2and the ratio of

GFR0,2to GFR2,2in Figure 2 is not dependent on the dose of

iohexol and the equation with 0.12 provided an excellent fit

to the data. In contrast, the constant of 6.4 relating fast

area to BSA is directly proportional to the dose of iohexol

and in general, if fast area¼c/BSA, c will be equal to

0.00116?1.73?I, where c¼6.4 for I¼3200. Thus, our

proposed equation may be applicable to other iohexol

protocols (with variations in amounts of iohexol injection),

although the estimation of fast area by 6.4/BSA is specific to

this protocol (that is, when I¼3200mg).

175

CKiD, n=274 (validation data set) MACS, n=177 (validation data set)

150

125

100

75

GFR (ml/min per 1.73 m2)

25

50

0

Bias ratio=1.005

Ratio of s.d.’s=0.987

Correlation=0.980

RMSE=4.59

Bias ratio=1.004

Ratio of s.d.’s=1.005

Correlation=0.996

RMSE=1.46

GFR2,2

GFR2,2

GFR2,2

GFR2,2

Figure 3|Comparison ofd

Multicenter AIDS Cohort Study (MACS; n¼177) and Chronic

Kidney Disease in Children (CKiD; n¼274). Percentile (2.5th,

5th, 10th, 25th, 50th, 75th, 90th, 95th, and 97.5th) box plots

showing a high agreement within each study validation data set.

GFR, glomerular filtration rate; RMSE, root mean square error.

GFR2;2based on GFR0,2and proposed

equation with four-point GFR2,2in the validation data sets for

Kidney International (2011) 80, 423–430

427

DKS Ng et al.: Two-sample iohexol GFR for diverse populations

technical notes

Page 6

The difference between the Fleming equation and our

equation was meaningful: the Fleming equation had relatively

high RMSE in our study populations and it systematically

underestimatedGFR2,2,although

was modest (B2% in the CKiD and 5% in the MACS). This

slight discrepancy may be because of differences in the

exogenous clearance markers used (that is, iohexol versus

51Cr-EDTA); however, previous studies have shown compar-

able GFR measurement performance with either marker.10–12

It is also possible that this discrepancy may be because of

other factors altogether (that is, study design or model

development).

The relationship between fast area and BSA determined in

Table 3 and depicted in Figure 1a (R2¼56%) may be re-

expressed to form the basis of our proposed equation whose fit

to the data is depicted in Figure 2 (R2¼75%). Given that the

fast area depends solely on BSA, we compared our proposed

equation with the agreement in an equation that directly

imputes the fast area as inversely proportional to BSA:

thisunderestimation

d

GFR2;2¼ ½I=ðð6:4=BSAÞ þ slowareaÞ??1:73=BSA

This equation yielded RMSEs of 5.81 and 1.48ml/min per

1.73m2in the MACS and CKiD, respectively; which, for the

MACS, was 27% higher than the RMSE of 4.59 of our

proposed equation (d

only on BSA, the proposed equation does not take into account

the between-subject variability in the fast area among those

with the same BSA. Despite this limitation, the assumption

works well because the fast area does not contribute much to

the overall GFR2,2.

As a secondary analysis, we also investigated how a

previously published Brochner-Mortensen-like equation that

was developed exclusively in the CKiD population2per-

formed when applied separately to the validation data sets in

the two studies. In the CKiD validation data set, there was no

significant bias or difference in dispersion, and a very high

correlation (r¼0.998, 95% CI: 0.995, 0.997) betweend

the same clinical population. However, when the equation

was applied to the MACS validation data set, the measures of

agreement were much poorer: there was significant under-

estimation (bias¼?2.6%, Po0.01), shrinking of dispersion

(ratio of s.d.’s¼0.932, Po0.01), and lower correlation

(r¼0.978, 95% CI: 0.971, 0.984) than had been observed

in the CKiD validation data set. This finding highlights a

limitation of developing an equation within a specific

population and then applying it to a different one. As such,

a limitation of our study is the lack of adult female subjects

studied, with whose data we could have assessed the validity

of the proposed equation. Nevertheless, ours is the only study

that has developed an accurate iohexold

underwent essentially identical GFR protocols.

Although the fast area can be estimated from the body

surface area, it should be noted that the intercept and slope of

GFR2;2 as a function of GFR0,2). As the

main assumption from the analysis is that the fast area depends

GFR2;2

and GFR2,2. This was expected as the equation was derived in

GFR2;2equation using

two disparate, large-scale cohorts (total n¼1347) that

the fast curve cannot be determined with our method.

Determination of these parameters (needed for measures like

the extracellular volume13) would require collecting samples

within 60min of iohexol injection. Another limitation to our

method is that our data did not take into account obese or

edematous subjects, populations for which it is unclear

whether our approach will work. However, in spite of the

substantial differences in weight and body mass index

between the two study populations (that is, MACS men with

a median body mass index of 26kg/m2versus CKiD children

being overweight relative to their height), the analysis showed

excellent agreement in each population.

In conclusion, because of the fast area being dependent on

BSA but not on the slow area, determination of GFR using

only the slow component showed a remarkable consistency

between the MACS and CKiD populations. A simple

equation was derived from a training data set that included

both cohorts and showed excellent agreement when applied

to validation sets from both studies. Using this validated

equation, GFR can be accurately measured across popula-

tions with diverse demographics and renal function using

only the slow iohexol plasma disappearance curve with as few

as two time points.

MATERIALS AND METHODS

Variables

GFRx,y denotes the glomerular filtration rate calculated from

disappearance curves of iohexol-based studies. The subscript x,y

refers to the number of time points sampled in the first (fast) and

second (slow) compartments, respectively. Specifically, GFR2,2

denotes the GFR derived from sampling times of 10 and 30min

(that is, two time points in the fast compartment), and 120 and

240min (or 300min; that is, two time points in the slow

compartment) after iohexol injection; and GFR0,2denotes the GFR

based only on the slow compartment. The area under the curve of

the second compartment is derived from the plasma iohexol

concentrations at 120 and 240min for the MACS and 120 and

300min for the CKiD, and is referred to as the slow area. Likewise,

based on concentrations at 10 and 30min after injection, we derived

the disappearance curve of the first compartment, whose area under

the curve is hereafter referred as the fast area. GFR2,2was calculated

as the ratio of the amount of iohexol injected (I) to the total area

under the iohexol disappearance curve and calibrated to a BSA of

1.73m2. That is, GFR2,2¼(I/(fast areaþslow area))?(1.73/BSA).

If the fast area in the above expression is omitted, it yields GFR0,2¼

(I/slow area)?(1.73/BSA), which always overestimates GFR2,2.

d

the fast compartment are not taken into account. A central aim of

this study was to determine the agreement between d

GFR2;2(with circumflex) denotes the estimate of GFR2,2from an

equation based on GFR0,2in studies where the two time points in

GFR2;2 and

GFR2,2.

Study participants

The MACS is a prospective observational cohort study of the natural

and treated histories of HIV infection among homosexual/bisexual

men over the age of 18 in four sites in the United States. To

investigate the natural history of renal function as it relates

to HIV infection and use of highly active antiretroviral therapy, a

428

Kidney International (2011) 80, 423–430

technical notes

DKS Ng et al.: Two-sample iohexol GFR for diverse populations

Page 7

subgroup of the cohort (n¼565) participated in an iohexol-based

GFR measurement between August 2008 and May 2010. Of

these, 527 (94%) had a successful GFR2,2 study; we excluded

individual patient studies if there were problems with any plasma

concentration measurements (n¼32), if an incorrect amount

of iohexol was administered (n¼3), or if the study indicated an

extremely high GFR2,2(that is, GFR2,24180ml/min per 1.73m2;

n¼3).

The CKiD study enrolled 586 children between 1 and 16 years of

age with mild to moderate chronic kidney disease in 47 sites in

the United States and Canada. Enrollment criteria included an

estimated GFR range of 30 to 90ml/min per 1.73m2, based on the

original Schwartz formula.14From these subjects, there were 915

subject visits at which an iohexol injection for a GFR2,2protocol

occurred. For our analysis, 514 subjects (88% of 586) contributed a

total of 820 GFR2,2studies (90%); we excluded studies if there

were problems with plasma concentration measurements or

blood sampling time values for any of the four samples (n¼38),

the wrong amount of iohexol was administered (o2000 or

44500mg; n¼5), if the GFR2,2 was significantly different

(450%) from the corresponding estimated GFR15(n¼45), or if

the BSA calculation was based on only one measurement of height

and weight instead of the average of three measurements (n¼7).

BSA for both populations was calculated from the Haycock et al.16

formula.

The two studies used nearly identical iohexol GFR protocols: the

only difference was that the last blood sample after injection of iohexol

was collected at 240min in the MACS and at 300min in the CKiD.

This difference in the protocol was justified by the expectation of

relatively normal kidney function among the MACS men.

Both the MACS and CKiD studies were approved by Research

Review Boards at all participating sites in the United States and

Canada.

Statistical analysis

To overcome the limitation of studies that do not measure

concentrations of iohexol at time points in the fast compartment,

formulas to predict the fast area are needed. We used standard

linear regression methods with the log of the fast area as the

dependent variable and we examined the predictive power of the

following independent variables: BSA, slow area, GFR0,2, height,

weight, body mass index, age, and male gender. The prediction

formulas can be used to directly impute the missing fast area and

also to derive formulas to estimate GFR2,2as a function of GFR0,2,

as this is the form that numerous investigators have previously

used.7–9In order to develop a formula to predict the fast area, we

randomly selected a 2/3 sample of each cohort and combined these

two subgroups into a training data set in which the models were

developed. Once the predicted formula for the fast area was

developed, and in order to independently test the agreement

between GFR2,2andd

data set).

In all regression analyses, a generalized estimating equation was

used to account for correlation between repeated measurements and

to obtain correct standard errors.17Results were unchanged when

we performed the same analysis using only the first GFR2,2study

contributed by each CKiD subject (n¼514; training data set

n¼343, validation data set n¼171). To maximize the use of all

available GFR studies, the results from the generalized estimating

equation analyses using all the studies are reported.

GFR2;2 we applied the equation ford

GFR2;2

to the remaining 1/3 random sample from each study (validation

Agreement betweend

described by Bland and Altman18and extended by regressing the

difference on the average of the two measurements centered around

the overall mean.1Absence of bias corresponds to the intercept of

the regression being equal to zero and equal dispersion corresponds

to the slope being equal to zero.1Robust methods were used to

account for repeated measurements. The 95% CIs for correlations

were determined by Fisher’s method. Agreement plots were used to

visually depict each data point and the box-percentile plots for

d

calculated from the published population-specific Brochner-Mor-

tensen-equations,4,6the equations by Brochner-Mortensen and

Jodal9and Fleming,7and our proposed equation derived from the

training data set. The calculatedd

both fast and slow compartments in the validation data set.

GFR2;2and GFR2,2

Agreement was assessed in the validation data set using methods

GFR2;2 and GFR2,2 in each cohort.19To compare with other

published equations, in each MACS and CKiD data set,d

GFR2;2was

GFR2;2values based on these four

equations were then compared with the observed GFR2,2based on

DISCLOSURE

All the authors declared no competing interests.

ACKNOWLEDGMENTS

Data in this article were collected by the Chronic Kidney Disease in

Children prospective cohort study (CKiD) with clinical coordinating

centers (principal investigators) at Children’s Mercy Hospital and the

University of Missouri–Kansas City (BAW), The Children’s Hospital of

Philadelphia (SLF), data coordinating center at the Johns Hopkins

Bloomberg School of Public Health (AM), and the Central

Biochemistry Laboratory at the University of Rochester (GJS). The

CKiD is funded by the National Institute of Diabetes and Digestive

and Kidney Diseases, with additional funding from the National

Institute of Neurological Disorders and Stroke, the National Institute

of Child Health and Human Development, and the National Heart,

Lung, and Blood Institute (U01 DK82194, U01-DK-66143, U01-DK-

66174, and U01-DK-66116). The CKiD website is located at http://

www.statepi.jhsph.edu/ckid. Data in this manuscript were also

collected by the Multicenter AIDS Cohort Study (MACS) with centers

(principal investigators) at The Johns Hopkins Bloomberg School of

Public Health (JBM, LPJ), Howard Brown Health Center, Feinberg

School of Medicine, Northwestern University, and Cook County

Bureau of Health Services (John P. Phair, Steven M. Wolinsky),

University of California, Los Angeles (Roger Detels), University of

Pittsburgh (Charles R. Rinaldo), and the Central Biochemistry

Laboratory at the University of Rochester (GJS). The MACS is funded

by the National Institute of Allergy and Infectious Diseases, with

additional supplemental funding from the National Cancer Institute

(UO1-AI-35042, UL1-RR025005 (GCRC), UO1-AI-35043, UO1-AI-35039,

UO1-AI-35040, and UO1-AI-35041). Website located at http://

www.statepi.jhsph.edu/macs/macs.html. We are grateful to GE

Healthcare, Amersham Division, for providing the CKiD and MACS

studies with ioxehol (Omnipaque) for the GFR measurements.

REFERENCES

1.Schwartz GJ, Furth SL, Cole SR et al. Glomerular filtration rate via plasma

iohexol disappearance: pilot study for chronic kidney disease in children.

Kidney Int 2006; 69: 2070–2077.

2. Schwartz GJ, Abraham AG, Furth SL et al. Optimizing iohexol plasma

disappearance curves to measure the glomerular filtration rate in children

with chronic kidney disease. Kidney Int 2010; 77: 65–71.

3. Work DF, Schwartz GJ. Estimating and measuring glomerular filtration

rate in children. Curr Opin Nephrol Hypertens 2008; 17: 320–325.

4.Brochner-Mortensen JA. A simple method for the determination of

glomerular filtration rate. Scand J Clin Lab Invest 1972; 30:

271–274.

Kidney International (2011) 80, 423–430

429

DKS Ng et al.: Two-sample iohexol GFR for diverse populations

technical notes

Page 8

5.Fleming JS, Zivanovic MA, Blake GM et al. Guidelines for the

measurement of glomerular filtration rate using plasma sampling.

Nucl Med Commun 2004; 25: 759–769.

Brochner-Mortensen JA, Haahr J, Christoffersen J. A simple method

for accurate assessment of the glomerular filtration rate in children.

Scand J Clin Lab Invest 1974; 33: 139–143.

Fleming JS. An improved equation for correcting slope-intercept

measurements of glomerular filtration rate for the single

exponential approximation. Nucl Med Commun 2007; 28:

315–320.

Jodal L, Brochner-Mortensen J. Reassessment of a classical single

injection n51Cr-EDTA clearance method for determination of renal

function in children and adults. Part I: Analytically correct relationship

between total and one-pool clearance. Scand J Clin Lab Invest 2009;

69: 305–313.

Brochner-Mortensen J, Jodal L. Reassessment of a classical single

injection n51Cr-EDTA clearance method for determination of renal

function in children and adults. Part II: Empirically determined

relationships between total and one-pool clearance. Scand J Clin Lab

Invest 2009; 69: 314–322.

Rydstrom M, Tengstrom B, Cederquist I et al. Measurement of

glomerular filtration rate by single-injection, single-sample

techniques, using51Cr-EDTA or iohexol. Scand J Urol Nephrol 1995;

29: 135–139.

6.

7.

8.

9.

10.

11.Brandstrom E, Grzegorczyk A, Jacobsson L et al. GFR measurement with

iohexol and51Cr-EDTA. A comparison of the two favoured GFR markers in

Europe. Nephrol Dial Transplant 1998; 13: 1176–1182.

Bird NJ, Peters C, Michell AR et al. Comparison of GFR measurements

assessed from single versus multiple samples. Am J Kid Dis 2009; 54:

278–288.

Abraham AG, Mun ˜oz A, Furth SL et al. Extracellular volume and disease

progression in children with chronic kidney disease. Clin J Am Soc Nephrol

2011; 6: 741–747.

Schwartz GJ, Haycock GB, Edelmann Jr CM et al. A simple estimate of

glomerular filtration rate in children derived from body length and

plasma creatinine. Pediatrics 1976; 58: 259–263.

Schwartz GJ, Mun ˜oz A, Schneider MF et al. New equations to

estimate GFR in children with CKD. J Am Soc Nephrol 2009; 20:

629–637.

Haycock GB, Schwartz GJ, Wisotsky DH. Geometric method for measuring

body surface area: a height-weight formula validated in infants, children,

and adults. J Pediatr 1978; 93: 62–66.

Liang KY, Zeger SL. Longitudinal data analysis using generalized linear

models. Biometrika 1986; 73: 13–22.

Bland JM, Altman DG. Statistical methods for assessing agreement

between two methods of clinical measurement. Lancet 1986; 1: 307–310.

Esty W, Banfield J. The box-percentile plot. J Stat Software 2008;

8: 1–14.

12.

13.

14.

15.

16.

17.

18.

19.

430

Kidney International (2011) 80, 423–430

technical notes

DKS Ng et al.: Two-sample iohexol GFR for diverse populations