A New Equation to Estimate the Glomerular Filtration Rate (1)

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Abstract and Introduction

Abstract

Background. A new estimated glomerular filtration rate (eGFR) equation, designed for isotope dilution mass spectrometry-

standardized serum creatinine (Scr), is presented for use in children, adolescent boys and girls and young adults.

Methods. The new equation, eGFR = 107.3/(Scr/Q), is based on the concept of normalized Scr: Q is the normalization value

and is considered as the Scr concentration for the average healthy child, adolescent or young adult of a specific height (L) and

is modeled as a height-dependent polynomial of the fourth degree.

Results. The well-known Schwartz equation [eGFR = kL/Scr, k = 0.413 (Schwartz) or k = 0.373 (SchwartzLyon)] for children

between 1 and 14 years can be seen as a special case of the new equation for which the Q-polynomial is simplified to a linear

equation: Q = 0.0035 L (cm). The new eGFR equation has been validated in a data set of n = 750 children, adolescents and

young adults aged 1025, against the true GFR (inulin method), and outperforms the selected (but most used) creatinine-based

eGFR equations for children, mainly in the healthy GFR region.

Conclusions. The new Q(height)-eGFR equation serves as an excellent screening tool for kidney disease in 125-year-old

children, adolescents and young adults.

Introduction

The glomerular filtration rate (GFR) is widely considered the best overall index of kidney function in health and disease.

Because direct measurements of GFR cannot always be performed in clinical routine settings, formulas have been presented to

estimate the GFR (eGFR).[1] In those formulas, serum creatinine (Scr, expressed in mg/dL) is most commonly used as a

marker for renal function.

In the last decade, new eGFR formulas have been developed for adults and children because of the evolution in laboratory

testing of Scr to iotope dilution mass spectrometry (IDMS)-standardized techniques, but few attempts have been undertaken to

develop new formulas for adolescents. Selistre et al.[2] assessed multiple existing adult and pediatric creatinine-based eGFR

equations in adolescents and young adults, using inulin clearance as the reference method. The adult eGFR formulas

substantially overestimate the GFR, but better prediction performance was found for the pediatric equations.[3, 4] (An overview of

the pediatric equations used in this study is given in ). Selistre et al., therefore, recommend the use of pediatric equations,

especially the updated Schwartz equation to estimate the GFR from childhood to early adulthood.

Table 1. Overview of eGFR equations.

GFR estimating equations Formula

SchwartzLyon equation [2]?dctmLink chronic_id='0901c7918075996a' object_id='0901c7918075996a'

edit_widget_type=graphic??dctmEditor selectedObject='0901c7918075996a'?

Updated Schwartz IDMS equation [3]?dctmLink chronic_id='0901c7918075996b' object_id='0901c7918075996b'

edit_widget_type=graphic??dctmEditor selectedObject='0901c7918075996b'?

A New Equation to Estimate the Glomerular Filtration Ratein Children, Adolescents and Young AdultsLiesbeth Hoste, Laurence Dubourg, Luciano Selistre, Vandrea Carla De Souza, Bruno Ranchin, Aoumeur

Hadj-Assa, Pierre Cochat, Frank Martens, Hans Pottel

Nephrol Dial Transplant. 2014;29(5):1082-1091.



Simple height-independent equation

(Simple) [7]?dctmLink chronic_id='0901c7918075996c' object_id='0901c7918075996c'

edit_widget_type=graphic??dctmEditor selectedObject='0901c7918075996c'?

FM equation [14]?dctmLink chronic_id='0901c7918075996d' object_id='0901c7918075996d'

edit_widget_type=graphic??dctmEditor selectedObject='0901c7918075996d'?

Q(age) equation (this is an extension

of the simple height-independent

equation [7]) ?dctmLink chronic_id='0901c7918075996e' object_id='0901c7918075996e'

edit_widget_type=graphic??dctmEditor selectedObject='0901c7918075996e'?

Q(height) equation?dctmLink chronic_id='0901c7918075996f' object_id='0901c7918075996f'

edit_widget_type=graphic??dctmEditor selectedObject='0901c7918075996f'?

L, height in cm or in Q(height) equation, m; Scr, serum creatinine in mg/dL, age in years.

However, none of the pediatric equations have been developed to be used in the adolescent population. Moreover, these

formulas do not differentiate between boys and girls, although there is an important difference in growth (height) and in Scr

concentration between sexes ever since adolescence. This large variation in body shape and growth determines extreme

variation in muscular mass and may be a dominant factor when developing eGFR formulas for this population.

In this paper, we demonstrate how a new eGFR formula for adolescents is constructed from a particular rationale, based on the

knowledge of Scr for healthy adolescents, combined with the use of metadata.[5, 6] This rationale uses the concept of

population-normalized Scr in which the normalization constant (Q) is the median or the average Scr concentration of a specific

population of healthy people, be it children or adults.[79] It has been shown that for adults between 18 and 65 years of age, the

value of Q is a constant and equals 0.70 mg/dL for Caucasian females and 0.90 mg/dL for Caucasian males.[10] For children, Q

is the median Scr for healthy children and depends linearly on age.[7] We extended this idea of normalized Scr to adolescents.

By modeling Q as a function of age, we experienced different relationships for girls and boys, but when modeling Q as a

function of height, we found a unique relationship between Q and height for both boys and girls. This Q(height) relationship

forms the basis for a promising new eGFR equation suitable for children, adolescents and even young adults.

Materials and Methods

Databases

In order to define Q-values (the median Scr for healthy children and adolescents), we used a data set of 15,978 subjects aged

between 0.1 and 20 years from AZ Groeninge Hospital in Kortrijk, Belgium. This data set contains Scr-values, age and sex of

the patients, which allowed to calculate the Q values as a function of age. To evaluate the height dependency of Q, we used the

national growth curves.[11] Once the new eGFR formulas for children and adolescents were created (one formula with age-

dependent Q-values and one formula with height-dependent Q-values), an independent database was used for the validation.

This database, which contains 750 unique inulin measurements in children, adolescents and young adults aged between 10

and 25, was previously used by Selistre et al..[2] Characteristics of the database can be found in .

Table 2. Characteristics of the validation database.

Characteristic Database

n 750

Male (%) 54

mGFR (mL/min/1.73 m2) 95 (72112)



Age (years) 17 (1221)

Weight (kg) 51.6 (40.061.0)

Height (cm) 161 (148170)

BSA (m2) 1.50 (1.301.70)

CKD classification

Stage I 428 (57.1%)

Stage II 208 (27.7%)

Stage III 102 (13.6%)

Stage IVV 12 (1.6%)

BSA, body surface area; CKD, chronic kidney disease. Values are median (IQR) or n(%) unless otherwise specified.

Scr and GFR Measurements

The Scr data of AZ Groeninge Hospital were obtained with the Roche enzymatic assay, described in Pottel et al..[10] The

enzymatic method was considered IDMS-standardized. In the validation database, Scr was determined with the Roche

compensated Jaffe assay. The Scr measurements obtained by the compensated Jaffe assay were standardized by linear

regression adjustment to concentrations obtained by liquid mass chromatography as described in Selistre et al..[2] Since the

enzymatic method used to design our equations has been calibrated against the IDMS method, and since all compensated

Jaffe Scr results in the validation database were calculated back to the gold standard method, both Scr concentrations in the

design and validation step of our study are considered equivalent.

In the validation database, the GFR was measured by the renal clearance of inulin (polyfructosan, Inutest; Fresenius Kagi,

Graz, Austria).[2] A standard technique was used by trained staff with a continuous infusion after a priming dose of 30 mg/kg

polyfructosan. Water diuresis was induced by oral administration of 5 mL/kg of water followed by 3 mL/kg every 30 min

combined with an intravenous infusion of 0.9% sodium chloride. This enabled the patients to spontaneously empty their bladder

every 30 min. Three to four urine samples were collected and a blood sample was drawn mid-way to each collection period. The

clearance values were calculated from the mean values of the three to four clearance periods. Serum and urine polyfructosan

measurements were performed using the enzymatic method (within-run precision



years as a function of age, separately for boys and girls (Figure 1A and B). Figure 2A shows the median data only, without the

individual subject values. These figures demonstrate that the median Scr for boys and girls evolves equivalently from birth till

~13 years of age and then gradually starts to diverge. In a first attempt to build a new eGFR model for adolescents, the model

eGFR = 107.3/(Scr/Q) with age-dependent Q-values for boys and girls (an extrapolation of the simple height-independent

formula for children[7]) was presented. However, we observed large growth differences between adolescents and young adults of

the same age and therefore we also modeled Q as a function of height and used this Q(height) relationship in the above

presented eGFR formula. The median height of healthy children and adolescents (aged between 0.1 and 20) was obtained from

the national growth curves.[11] The median Scr was fitted against age, resulting in a Q(age) relationship (Figure 2A) which

differs for boys and girls. The median Scr was also fitted against height, resulting in a unique Q(height) relationship (Figure 2B).

In both cases, a fourth-degree polynomial was required to adequately fit the Q data. The fourth-degree polynomials for Q are:



Figure 1.

Scr in mg/dL as a function of age for boys (A) and girls (B). The solid line represents the fitted line for the median values.



Figure 2.

The median Scr (in mg/dL) as a function of age (A) and as function of median height (B) for boys (bullets) and girls (squares).

The first part (for heights between 76 and 166 cm, corresponding to children between 1 and 14 years of age) of the curve in (B)

can be linearly modeled as Q = 0.0035 L.

?dctmLink chronic_id='0901c79180759966' object_id='0901c79180759966' edit_widget_type=graphic??dctmEditor

selectedObject='0901c79180759966'?

with L the height (m).

Piepsz et al.[5, 6] showed that after maturation of the kidneys, the true GFR for healthy children stabilizes to the median value

of 107.3 mL/min/1.73 m2, a value we used previously to present a general form for an eGFR formula for children: eGFR =

107.3/(Scr/Q).[7] Building further on this concept, and using the polynomials for Q, this leads to two new eGFR formulas with

age-dependent [Q(age)-eGFR] or height-dependent Q-values [Q(height)-eGFR].

Validation of the New Equations

To validate our new formulas, we used an independent data set containing measured GFR (mGFR) (inulin method). We present

comparisons between our new equations and mGFR and with four other pediatric equations ( ): the updated Schwartz,[3] the

SchwartzLyon,[4] the simple height-independent (Simple)[7] and the Flanders metadata (FM)[14] equation. The comparisons

were performed in three different age-subgroups: 1014-year-old children, 1418-year-old adolescents and 1825-year-old

young adults.










(Simple) [7] ?dctmLink chronic_id='0901c7918075996c' object_id='0901c7918075996c'











Accuracy expressed as within 10 and 30% of the mGFR and bias calculations in the different age-subgroups for mGFR 90 mL/min/1.73 m2 are summarized in . Differences between mGFR and eGFR for

the whole cohort are visualized in BlandAltman plots in Figure 3.

Table 3. Statistical results for the prediction performance and results of the performance scoring system (results between

brackets) of eGFR equations, in age and mGFR-based subgroups.

Group

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-

independent eGFR FM eGFR

Q(age)-

eGFR

Q(height)-

eGFR

mGFR



Bias SD

(score)

3.2* 10.0

(5)1.9 9.1 (5) 17.5* 14.5 (0)

5.1*

10.2 (3)

15.2*

11.9 (0)

6.7* 9.8

(3)

Within 30%

(score)86.4a,b,c(5) 86.4d,e,f (5) 40.7a,d,g,h (0) 83.1g,i (5) 44.1b,e,i,j (0) 72.9c,f,h,j (3)

Within 10%

(score)25.4a (1) 27.1b (1) 18.6 (0) 25.4c (1) 8.5a,b,c (0) 18.6 (0)

Overall (n = 114)

mGFR = 44.1 10.9

Bias SD 5.8* 10.2 3.1 9.0 13.8* 13.86.5*

10.0

13.7*

11.77.2* 9.5

Within 30% 78.1a,b 82.5c,d,e,f 50.0a,c,g,h,i 76.3d,g,j 49.1b,e,h,j,k 72.8f ,i,k

Within 10% 27.2a 33.3b,c 21.9 b,d 28.1e 12.3a,c,d,e,f 25.4 f

SCORE** 25 35 8 23 3 24

mGFR between 6090 mL/min/1.73 m2

Children (n = 78, 1014 year)

mGFR = 76.4 8.4

Bias SD

(score)

10.2*

13.1 (1)2.4 12.0 (5) 8.8* 13.0 (3)

8.0*

12.8 (3)

11.8*

13.8 (1)

6.4* 13.5

(3)

Within 30%

(score)76.9a,b (3) 97.4a,c,d,e,f (5) 84.6c (5) 83.3 d (5) 82.1e (5) 87.2b,f (5)

Within 10%

(score)41.0 (5) 42.3 (5) 41.0 (5) 48.7 (5) 39.7 (3) 43.6 (5)

Adolescents (n = 46, 1418 year)

mGFR = 75.7 9.0

Bias SD

(score)

5.4* 16.2

(3)0.6 15.2 (5) 12.9* 19.3 (1)

6.2*

16.2 (3)

18.4*

20.2 (0)

6.9* 15.6

(3)

Within 30%

(score)80.4 (5) 87.0a (5) 73.9 (3) 80.4 (5) 71.7a (3) 80.4 (5)

Within 10%

(score)41.3 (5) 39.1 (3) 39.1 (3) 43.5 (5) 30.4 (3) 41.3 (5)

Young adults (n = 94, 1825 year)

mGFR = 75.5 8.9

Bias SD

(score)

4.7* 15.2

(5)7.7* 13.7 (3) 15.9* 21.0 (0)

1.9 15.7

(5)

11.2*

18.9 (1)

1.1 17.6

(5)

Within 30%

(score)84.4a (5) 84.0b (5) 64.9a,b,c,d,e (1) 83.0c (5) 78.7d (3) 85.1e (5)

Within 10%

(score)28.7 (1) 31.9 (3) 30.9 (3) 35.1a (3) 34.0 (3) 23.4a (1)

Overall (n = 218)

mGFR = 75.8 8.7

2.8* 16.13.4* 13.0*

4.2* 16.0



Bias SD 2.4* 14.2 12.7* 18.3 15.5 17.7

Within 30% 80.7a,b 89.5a,c,d,e 73.9b,c,f,g 82.6d,f 78.4e,h 84.9g,h

Within 10% 35.8a 37.2 36.2 41.7a,b 35.3 34.4 b

SCORE** 33 39 24 39 22 37

mGFR >90 mL/min/1.73 m2


mGFR = 115.7 19.7

Bias SD

(score)

1.4 17.8

(5)11.6* 17.7 (1) 4.1* 18.8 (5)

4.2* 17.4

(5)

0.0 19.0

(5)

5.7* 18.0

(3)

Within 30%

(score)95.7 (5) 95.7 (5) 95.7 (5) 96.3 (5) 94.5 (5) 95.7 (5)

Within 10%

(score)45.1 (5) 42.1a (5) 40.2b (5) 47.0 (5) 43.9 (5) 49.4a,b (5)


mGFR = 111.1 13.9

Bias SD

(score)

9.9* 16.1

(3)13.9* 15.2 (1) 3.3 19.5 (5)

8.8* 16.2

(3)

6.1* 19.6

(3)

2.8 18.8

(5)

Within 30%

(score)92.6 (5) 93.8 (5) 92.6 (5) 92.6 (5) 88.9 (5) 92.6 (5)

Within 10%

(score)44.4a (5) 32.1a,b,c (3) 53.1b (5) 45.7c (5) 49.4 (5) 44.4 (5)


mGFR = 113.4 16.5

Bias SD

(score)

18.2* 17.4

(0)22.4* 15.8 (0) 6.0* 23.8 (3)

14.6*

17.9 (1)

1.2 21.0

(5)

7.7* 21.0

(3)

Within 30%

(score)83.8a (5) 78.0a,b,c,d (3) 82.7e (5) 86.1b (5) 89.0c,e (5) 87.3d (5)

Within 10%

(score)27.8a,b,c (1) 16.8a,d,e,f,g (0) 33.0d,h (3) 31.8e,i,j (3) 45.1b,f,h,i (5) 40.5c,g,j (5)

Overall (n = 418)

mGFR = 113.9 17.4

Bias SD 10.0* 18.8 16.5* 17.2 0.2 21.7 9.4* 17.9 1.7 20.0 5.9* 19.5

Within 30% 90.2 88.0a,b 89.7 91.4 a 91.2 91.6 b

Within 10% 37.8a,b,c 29.7a,d,e,f,g 39.7d,h 40.4 e 45.5b,f,h 44.7c,g

SCORE** 34 23 41 37 43 41

OVERALL

SCORE***92 97 73 99 68 102

mGFR is expressed in mL/min/1.73 m2. Bias is calculated as mGFR eGFR. Equal letters in each row denote statistically

significant differences (P < 0.05, exact McNemar's test).



*Denotes statistically significant difference between eGFR and mGFR (P < 0.05, paired t-test).

**The SCORE is the sum of the scores of the bias, the within 30% and the within 10% of all age subgroups within a specific

mGFR subgroup.

***The OVERALL SCORE is the sum of the SCORES of the three mGFR subgroups.

Figure 3.

BlandAltman plots for the difference between mGFR and eGFR [Schwartz eGFR (A), SchwartzLyon eGFR (B), Simple

height-independent eGFR (Simple) (C), FM eGFR (D), Q(age)-eGFR (E) and Q(height)-eGFR (F)] against the average. Dotted

lines show the mean biases. Solid horizontal upper and lower lines are 95% limits of agreement (LOA).

A performance score for the six different eGFR formulas ( ) in each subgroup (defined by mGFR 90 mL/min/1.73 m2 and by age: 1014, 1418 and >18 years old) and for the

overall cohort was calculated. Results of the scoring system can be found in .







Updated Schwartz IDMS equation [3] ?dctmLink chronic_id='0901c7918075996b' object_id='0901c7918075996b'
















Group

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-


Q(age)-

eGFR

Q(height)-

eGFR

mGFR



Bias SD

(score)

3.2* 10.0

(5)

1.9 9.1 (5) 17.5* 14.5 (0) 5.1*

10.2 (3)

15.2*

11.9 (0)

6.7* 9.8

(3)

Within 30%


Within 10%

(score)25.4a (1) 27.1b (1) 18.6 (0) 25.4c (1) 8.5a,b,c (0) 18.6 (0)

Overall (n = 114)

mGFR = 44.1 10.9

Bias SD 5.8* 10.2 3.1 9.0 13.8* 13.86.5*

10.0

13.7*

11.77.2* 9.5



SCORE** 25 35 8 23 3 24



mGFR = 76.4 8.4

Bias SD

(score)

10.2*

13.1 (1)2.4 12.0 (5) 8.8* 13.0 (3)

8.0*

12.8 (3)

11.8*

13.8 (1)

6.4* 13.5

(3)

Within 30%


Within 10%

(score)41.0 (5) 42.3 (5) 41.0 (5) 48.7 (5) 39.7 (3) 43.6 (5)


mGFR = 75.7 9.0

Bias SD

(score)

5.4* 16.2

(3)0.6 15.2 (5) 12.9* 19.3 (1)

6.2*

16.2 (3)

18.4*

20.2 (0)

6.9* 15.6

(3)

Within 30%

(score)80.4 (5) 87.0a (5) 73.9 (3) 80.4 (5) 71.7a (3) 80.4 (5)

Within 10%

(score)41.3 (5) 39.1 (3) 39.1 (3) 43.5 (5) 30.4 (3) 41.3 (5)


mGFR = 75.5 8.9

Bias SD

(score)

4.7* 15.2

(5)7.7* 13.7 (3) 15.9* 21.0 (0)

1.9 15.7

(5)

11.2*

18.9 (1)

1.1 17.6

(5)

Within 30%


Within 10%

(score)28.7 (1) 31.9 (3) 30.9 (3) 35.1a (3) 34.0 (3) 23.4a (1)

Overall (n = 218)

mGFR = 75.8 8.7

Bias SD2.8* 16.1

2.4* 14.2 12.7* 18.3 3.4* 13.0* 4.2* 16.0



15.5 17.7


Within 10% 35.8a 37.2 36.2 41.7a,b 35.3 34.4 b

SCORE** 33 39 24 39 22 37



mGFR = 115.7 19.7

Bias SD

(score)

1.4 17.8

(5)11.6* 17.7 (1) 4.1* 18.8 (5)

4.2* 17.4

(5)

0.0 19.0

(5)

5.7* 18.0

(3)

Within 30%

(score)95.7 (5) 95.7 (5) 95.7 (5) 96.3 (5) 94.5 (5) 95.7 (5)

Within 10%

(score)45.1 (5) 42.1a (5) 40.2b (5) 47.0 (5) 43.9 (5) 49.4a,b (5)


mGFR = 111.1 13.9

Bias SD

(score)

9.9* 16.1

(3)13.9* 15.2 (1) 3.3 19.5 (5)

8.8* 16.2

(3)

6.1* 19.6

(3)

2.8 18.8

(5)

Within 30%

(score)92.6 (5) 93.8 (5) 92.6 (5) 92.6 (5) 88.9 (5) 92.6 (5)

Within 10%

(score)44.4a (5) 32.1a,b,c (3) 53.1b (5) 45.7c (5) 49.4 (5) 44.4 (5)


mGFR = 113.4 16.5

Bias SD

(score)

18.2* 17.4

(0)22.4* 15.8 (0) 6.0* 23.8 (3)

14.6*

17.9 (1)

1.2 21.0

(5)

7.7* 21.0

(3)

Within 30%


Within 10%


Overall (n = 418)

mGFR = 113.9 17.4

Bias SD 10.0* 18.8 16.5* 17.2 0.2 21.7 9.4* 17.9 1.7 20.0 5.9* 19.5

Within 30% 90.2 88.0a,b 89.7 91.4 a 91.2 91.6 b


SCORE** 34 23 41 37 43 41

OVERALL

SCORE***92 97 73 99 68 102







mGFR subgroup.


In the mGFR subgroup 90 mL/min/1.73 m2, Q(age)-eGFR

(score = 43) gets the highest score, closely followed by Q(height)-eGFR (score = 41) and by the Simple equation (score = 41).

When the overall score is calculated, the new Q(height) equation (score = 102) shows the best score, followed by the FM

formula (score = 99), the SchwartzLyon equation (score = 97), the updated Schwartz equation (score = 92), the Simple

formula (score = 73) and Q(age)-eGFR (score = 68). The Q(height) equation is therefore the best generally applicable eGFR

equation for children, adolescents and young adults and outperforms the other height-dependent equations especially in the

GFR >60 mL/min/1.73 m2 region.

Weight categories were defined based on international cut-off points for body mass index (BMI) for thinness grades 1 (very

severely underweight), 2 (severely underweight) and 3 (underweight),[15] overweight and obesity[16] by sex for exact ages

between 10 and 18 years, defined to pass through BMI of 16, 17, and 18.5, 25 and 30 kg/m2 at age 18, obtained by averaging

data from Brazil, Great Britain, Hong Kong, Netherlands, Singapore and USA.

Because the subgroups 'severely underweight' and 'very severely underweight' only contained 6, 9, 7 and 4, 1, 4 children,

adolescents and young adults, respectively, we pooled all underweight patients in the 'underweight' subgroup, corresponding to

one subgroup for thinness grades 1, 2 and 3.

If the bias, the within 10% and the within 30% accuracies in the overweight, the normal weight and the underweight children,

adolescents and young adults are calculated ( ), then an increased bias and lower accuracies in the underweight patients can

be noticed, especially when the age-based eGFR formulas [Simple formula and Q(age) equation] are used. The Q(height)-eGFR

formula still gives good results in the underweight subjects. The SchwartzLyon equation seems to perform better in the

underweight than in the overweight patients.

Table 4. Statistical results for the prediction performance of eGFR equations according to weight subgroups.

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height- independent

eGFR

FM

eGFR

Q(age)-

eGFR

Q(height)-

eGFR

Overweight (n = 108)

Bias

SD7.8 18.1 13.7 17.2 2.8 22.3

7.0

17.70.9 17.6 5.2 19.0

Within

30%88.0 84.3 78.7 88.9 87.0 86.1

Within

10%41.7 28.7 44.4 44.4 41.7 38.0

Normal weight (n = 511)

Bias

SD4.5 18.0 9.9 16.9 4.0 19.9

4.0

17.25.7 18.5 1.2 17.5

Within

30%85.5 88.3 82.4 86.9 83.0 87.7

Within

10%33.7 31.7 36.6 37.8 40.7 38.9

Underweight (n = 131)



Bias

SD1.7 18.6 4.1 18.2 15.9 19.5

2.8

17.9

15.9

20.13.3 19.2

Within

30%84.0 87.8 66.4 83.2 68.7 84.0

Within

10%38.2 38.2 26.7 38.9 21.4 38.9

In the validation cohort, 123 transplant patients are included for which bias, within 10 and within 30% accuracies of the various

eGFR models were calculated ( ). The bias of the Schwartz equation, the FM formula and Q(height)-eGFR are not significantly

different from zero (P > 0.05). The results for the renal graft patients do not differ from the results in the whole cohort, especially

when compared with the overall subgroup mGFR between 60 and 90 mL/min/1.73 m2 ( ).

Table 5. Statistical results for the prediction performance of eGFR equations in transplant patients.

Kidney transplants (n

= 123)

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-

independent eGFR

FM

eGFR

Q(age)-

eGFR

Q(height)-

eGFR

mGFR = 60.9 19.5

Bias SD 1.3 13.2 2.3* 12.1 11.3* 14.72.0

12.7

10.7*

13.71.8 13.4

Within 30% 86.2 86.2 67.5 86.2 72.4 84.6

Within 10% 29.3 36.6 31.7 37.4 23.6 30.9

Within 30%, Simple height-independent eGFR and Q(age)-eGFR are significantly different from the other percentages within the

row.Within 10%, Q(age)-eGFR is significantly different from FM eGFR and from Schwartz-Lyon eGFR.

*Statistically significant difference between eGFR and mGFR (P < 0.05, paired t-test).



Group

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-


Q(age)-

eGFR

Q(height)-

eGFR

mGFR



Within 10%

(score)

25.0 (1) 33.3 (3) 16.7 (0) 25.0 (1) 16.7 (0) 20.8 (1)


mGFR = 43.2 11.6

Bias SD

(score)

3.2* 10.0

(5)1.9 9.1 (5) 17.5* 14.5 (0)

5.1*

10.2 (3)

15.2*

11.9 (0)

6.7* 9.8

(3)

Within 30%


Within 10%

(score)25.4a (1) 27.1b (1) 18.6 (0) 25.4c (1) 8.5a,b,c (0) 18.6 (0)

Overall (n = 114)

mGFR = 44.1 10.9

Bias SD 5.8* 10.2 3.1 9.0 13.8* 13.86.5*

10.0

13.7*

11.77.2* 9.5



SCORE** 25 35 8 23 3 24



mGFR = 76.4 8.4

Bias SD

(score)

10.2*

13.1 (1)2.4 12.0 (5) 8.8* 13.0 (3)

8.0*

12.8 (3)

11.8*

13.8 (1)

6.4* 13.5

(3)

Within 30%


Within 10%

(score)41.0 (5) 42.3 (5) 41.0 (5) 48.7 (5) 39.7 (3) 43.6 (5)


mGFR = 75.7 9.0

Bias SD

(score)

5.4* 16.2

(3)0.6 15.2 (5) 12.9* 19.3 (1)

6.2*

16.2 (3)

18.4*

20.2 (0)

6.9* 15.6

(3)

Within 30%

(score)80.4 (5) 87.0a (5) 73.9 (3) 80.4 (5) 71.7a (3) 80.4 (5)

Within 10%

(score)41.3 (5) 39.1 (3) 39.1 (3) 43.5 (5) 30.4 (3) 41.3 (5)


mGFR = 75.5 8.9

Bias SD

(score)

4.7* 15.2

(5)7.7* 13.7 (3) 15.9* 21.0 (0)

1.9 15.7

(5)

11.2*

18.9 (1)

1.1 17.6

(5)

Within 30%


Within 10%28.7 (1) 31.9 (3) 30.9 (3) 35.1a (3) 34.0 (3) 23.4a (1)



(score)

Overall (n = 218)

mGFR = 75.8 8.7

Bias SD 2.8* 16.1 2.4* 14.2 12.7* 18.33.4*

15.5

13.0*

17.74.2* 16.0


Within 10% 35.8a 37.2 36.2 41.7a,b 35.3 34.4 b

SCORE** 33 39 24 39 22 37



mGFR = 115.7 19.7

Bias SD

(score)

1.4 17.8

(5)11.6* 17.7 (1) 4.1* 18.8 (5)

4.2* 17.4

(5)

0.0 19.0

(5)

5.7* 18.0

(3)

Within 30%

(score)95.7 (5) 95.7 (5) 95.7 (5) 96.3 (5) 94.5 (5) 95.7 (5)

Within 10%

(score)45.1 (5) 42.1a (5) 40.2b (5) 47.0 (5) 43.9 (5) 49.4a,b (5)


mGFR = 111.1 13.9

Bias SD

(score)

9.9* 16.1

(3)13.9* 15.2 (1) 3.3 19.5 (5)

8.8* 16.2

(3)

6.1* 19.6

(3)

2.8 18.8

(5)

Within 30%

(score)92.6 (5) 93.8 (5) 92.6 (5) 92.6 (5) 88.9 (5) 92.6 (5)

Within 10%

(score)44.4a (5) 32.1a,b,c (3) 53.1b (5) 45.7c (5) 49.4 (5) 44.4 (5)


mGFR = 113.4 16.5

Bias SD

(score)

18.2* 17.4

(0)22.4* 15.8 (0) 6.0* 23.8 (3)

14.6*

17.9 (1)

1.2 21.0

(5)

7.7* 21.0

(3)

Within 30%


Within 10%


Overall (n = 418)

mGFR = 113.9 17.4

Bias SD 10.0* 18.8 16.5* 17.2 0.2 21.7 9.4* 17.9 1.7 20.0 5.9* 19.5

Within 30% 90.2 88.0a,b 89.7 91.4 a 91.2 91.6 b


SCORE** 34 23 41 37 43 41

OVERALL



SCORE*** 92 97 73 99 68 102





mGFR subgroup.


Discussion

There are many creatinine-based formulas to estimate the GFR for children, including the Schwartz formula,[3] the Schwartz

Lyon equation,[4] the FM formula [14], the Simple equation,[7] the LundMalm formula,[17] the Lger equation,[18] the BCCH1

equation[19] and the formula of Zappitelli.[20] However, there is no formula especially designed for adolescents. Recently,

Selistre et al.[2] recommend the use of pediatric formulas, especially the updated Schwartz formula, to estimate the GFR in the

adolescent and young adult population. However, these pediatric formulas have not been designed for use in adolescents or

young adults, but they outperform the MDRD[21] and CKD-EPI[22] equations for adults.

During adolescence, like in children, Scr increases with height (Figure 2B), although no longer in a linear way. This

simultaneous increase in Scr and height might be the reason why the updated Schwartz equation (eGFR = kL/Scr) still gives

reasonable results in adolescents ( ). However, there has never been an adaptation of the constant k = 0.413 in the updated

Schwartz equation for adolescents, although Schwartz made the adaptation in the original equation from 0.55 to 0.70 for

adolescent boys, showing the need for adjustments in the formulas for adolescents.[23, 24]



Group

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-


Q(age)-

eGFR

Q(height)-

eGFR

mGFR




mGFR = 43.2 11.6

Bias SD

(score)

3.2* 10.0

(5)1.9 9.1 (5) 17.5* 14.5 (0)

5.1*

10.2 (3)

15.2*

11.9 (0)

6.7* 9.8

(3)

Within 30%


Within 10%

(score)25.4a (1) 27.1b (1) 18.6 (0) 25.4c (1) 8.5a,b,c (0) 18.6 (0)

Overall (n = 114)

mGFR = 44.1 10.9

Bias SD 5.8* 10.2 3.1 9.0 13.8* 13.86.5*

10.0

13.7*

11.77.2* 9.5



SCORE** 25 35 8 23 3 24



mGFR = 76.4 8.4

Bias SD

(score)

10.2*

13.1 (1)2.4 12.0 (5) 8.8* 13.0 (3)

8.0*

12.8 (3)

11.8*

13.8 (1)

6.4* 13.5

(3)

Within 30%


Within 10%

(score)41.0 (5) 42.3 (5) 41.0 (5) 48.7 (5) 39.7 (3) 43.6 (5)


mGFR = 75.7 9.0

Bias SD

(score)

5.4* 16.2

(3)0.6 15.2 (5) 12.9* 19.3 (1)

6.2*

16.2 (3)

18.4*

20.2 (0)

6.9* 15.6

(3)

Within 30%

(score)80.4 (5) 87.0a (5) 73.9 (3) 80.4 (5) 71.7a (3) 80.4 (5)

Within 10%

(score)41.3 (5) 39.1 (3) 39.1 (3) 43.5 (5) 30.4 (3) 41.3 (5)


mGFR = 75.5 8.9

Bias SD

(score)

4.7* 15.2

(5)7.7* 13.7 (3) 15.9* 21.0 (0)

1.9 15.7

(5)

11.2*

18.9 (1)

1.1 17.6

(5)

Within 30%


Within 10%

(score)28.7 (1) 31.9 (3) 30.9 (3) 35.1a (3) 34.0 (3) 23.4a (1)

Overall (n = 218)



mGFR = 75.8 8.7

Bias SD 2.8* 16.1 2.4* 14.2 12.7* 18.33.4*

15.5

13.0*

17.74.2* 16.0


Within 10% 35.8a 37.2 36.2 41.7a,b 35.3 34.4 b

SCORE** 33 39 24 39 22 37



mGFR = 115.7 19.7

Bias SD

(score)

1.4 17.8

(5)11.6* 17.7 (1) 4.1* 18.8 (5)

4.2* 17.4

(5)

0.0 19.0

(5)

5.7* 18.0

(3)

Within 30%

(score)95.7 (5) 95.7 (5) 95.7 (5) 96.3 (5) 94.5 (5) 95.7 (5)

Within 10%

(score)45.1 (5) 42.1a (5) 40.2b (5) 47.0 (5) 43.9 (5) 49.4a,b (5)


mGFR = 111.1 13.9

Bias SD

(score)

9.9* 16.1

(3)13.9* 15.2 (1) 3.3 19.5 (5)

8.8* 16.2

(3)

6.1* 19.6

(3)

2.8 18.8

(5)

Within 30%

(score)92.6 (5) 93.8 (5) 92.6 (5) 92.6 (5) 88.9 (5) 92.6 (5)

Within 10%

(score)44.4a (5) 32.1a,b,c (3) 53.1b (5) 45.7c (5) 49.4 (5) 44.4 (5)


mGFR = 113.4 16.5

Bias SD

(score)

18.2* 17.4

(0)22.4* 15.8 (0) 6.0* 23.8 (3)

14.6*

17.9 (1)

1.2 21.0

(5)

7.7* 21.0

(3)

Within 30%


Within 10%


Overall (n = 418)

mGFR = 113.9 17.4

Bias SD 10.0* 18.8 16.5* 17.2 0.2 21.7 9.4* 17.9 1.7 20.0 5.9* 19.5

Within 30% 90.2 88.0a,b 89.7 91.4 a 91.2 91.6 b


SCORE** 34 23 41 37 43 41

OVERALL

SCORE***92 97 73 99 68 102







mGFR subgroup.


In this study, we developed a new eGFR formula for children and adolescents based on the concept of population-normalized

Scr where the normalization constant (Q) may be seen as the Scr concentration of the average healthy person in a specific

population, equivalent to what has been described previously for children and adults.[79] For adults between 18 and 65 years of

age, a CKD-EPI-like equation with a constant value Q (0.70 mg/dL for Caucasian females and 0.90 mg/dL for Caucasian males)

has been proposed.[8, 9] Recently, the Simple eGFR equation for children, based on the same concept, was published.[7] For

children, Q depends linearly on age (Q = 0.0270 Age + 0.2329). In the current study, we extended the use of Scr/Q to

adolescents in two possible ways: with Q the Scr for the average healthy child or adolescent of a specific age or with Q as the

Scr of the average healthy child or adolescent of a specific height. The Scr/Q concept can now be used for different age

classes: for children,[7] adolescents and adults.[8] For adults, race and sex information is included in the value of Q. By

normalizing Scr by Q, Scr/Q becomes independent of age, race and sex.[8, 25]

After the development of the two new formulas, they were compared with the mGFR and with the updated Schwartz, the

SchwartzLyon, the Simple and the FM equation ( ). The SchwartzLyon equation is a locally adapted form of the original

Schwartz formula.[24] With a small age-dependent modification of the updated Schwartz constant, the FM equation was

developed, which can be used to estimate the GFR in infants (aged >1 month) and children up to 14 years of age. The Simple

equation is valid for children between 1 and 14 years. All these pediatric equations were applied to subgroups of children,

adolescents and young adults.


















Q(height) equation

?dctmLink chronic_id='0901c7918075996f' object_id='0901c7918075996f'



The SchwartzLyon equation performs better than all other equations in the mGFR 90 mL/min/1.73 m2 subgroup, very closely followed by the Q(height)-eGFR

method, for all age-categories. The good performance of the Q(height)-eGFR equation in healthy subjects is not surprising, as

this equation has been designed with data of healthy children and adolescents. Note also that the SchwartzLyon equation is

the worst performer in this mGFR subgroup. Although making a ranking of performance of the different eGFR is not

straightforward, we tried to do so by calculating a performance score using three specific but rather arbitrary criteria as

described in the 'Materials and methods' section. When the overall performance score of the six pediatric equations is

calculated, the Q(height)-eGFR gives the highest overall score ( ).



Group

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-


Q(age)-

eGFR

Q(height)-

eGFR

mGFR



Within 10%

(score)25.4a (1) 27.1b (1) 18.6 (0) 25.4c (1) 8.5a,b,c (0) 18.6 (0)

Overall (n = 114)

mGFR = 44.1 10.9

Bias SD 5.8* 10.2 3.1 9.0 13.8* 13.86.5*

10.0

13.7*

11.77.2* 9.5



SCORE** 25 35 8 23 3 24



mGFR = 76.4 8.4

Bias SD

(score)

10.2*

13.1 (1)2.4 12.0 (5) 8.8* 13.0 (3)

8.0*

12.8 (3)

11.8*

13.8 (1)

6.4* 13.5

(3)

Within 30%


Within 10%

(score)41.0 (5) 42.3 (5) 41.0 (5) 48.7 (5) 39.7 (3) 43.6 (5)


mGFR = 75.7 9.0

Bias SD

(score)

5.4* 16.2

(3)0.6 15.2 (5) 12.9* 19.3 (1)

6.2*

16.2 (3)

18.4*

20.2 (0)

6.9* 15.6

(3)

Within 30%

(score)80.4 (5) 87.0a (5) 73.9 (3) 80.4 (5) 71.7a (3) 80.4 (5)

Within 10%

(score)41.3 (5) 39.1 (3) 39.1 (3) 43.5 (5) 30.4 (3) 41.3 (5)


mGFR = 75.5 8.9

Bias SD

(score)

4.7* 15.2

(5)7.7* 13.7 (3) 15.9* 21.0 (0)

1.9 15.7

(5)

11.2*

18.9 (1)

1.1 17.6

(5)

Within 30%


Within 10%

(score)28.7 (1) 31.9 (3) 30.9 (3) 35.1a (3) 34.0 (3) 23.4a (1)

Overall (n = 218)

mGFR = 75.8 8.7

Bias SD 2.8* 16.1 2.4* 14.2 12.7* 18.33.4*

15.5

13.0*

17.74.2* 16.0


Within 10% 35.8a 37.2 36.2 41.7a,b 35.3 34.4 b



SCORE** 33 39 24 39 22 37



mGFR = 115.7 19.7

Bias SD

(score)

1.4 17.8

(5)11.6* 17.7 (1) 4.1* 18.8 (5)

4.2* 17.4

(5)

0.0 19.0

(5)

5.7* 18.0

(3)

Within 30%

(score)95.7 (5) 95.7 (5) 95.7 (5) 96.3 (5) 94.5 (5) 95.7 (5)

Within 10%

(score)45.1 (5) 42.1a (5) 40.2b (5) 47.0 (5) 43.9 (5) 49.4a,b (5)


mGFR = 111.1 13.9

Bias SD

(score)

9.9* 16.1

(3)13.9* 15.2 (1) 3.3 19.5 (5)

8.8* 16.2

(3)

6.1* 19.6

(3)

2.8 18.8

(5)

Within 30%

(score)92.6 (5) 93.8 (5) 92.6 (5) 92.6 (5) 88.9 (5) 92.6 (5)

Within 10%

(score)44.4a (5) 32.1a,b,c (3) 53.1b (5) 45.7c (5) 49.4 (5) 44.4 (5)


mGFR = 113.4 16.5

Bias SD

(score)

18.2* 17.4

(0)22.4* 15.8 (0) 6.0* 23.8 (3)

14.6*

17.9 (1)

1.2 21.0

(5)

7.7* 21.0

(3)

Within 30%


Within 10%


Overall (n = 418)

mGFR = 113.9 17.4

Bias SD 10.0* 18.8 16.5* 17.2 0.2 21.7 9.4* 17.9 1.7 20.0 5.9* 19.5

Within 30% 90.2 88.0a,b 89.7 91.4 a 91.2 91.6 b


SCORE** 34 23 41 37 43 41

OVERALL

SCORE***92 97 73 99 68 102





mGFR subgroup.






Group

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-


Q(age)-

eGFR

Q(height)-

eGFR

mGFR



Within 30%


Within 10%

(score)41.0 (5) 42.3 (5) 41.0 (5) 48.7 (5) 39.7 (3) 43.6 (5)


mGFR = 75.7 9.0

Bias SD

(score)

5.4* 16.2

(3)0.6 15.2 (5) 12.9* 19.3 (1)

6.2*

16.2 (3)

18.4*

20.2 (0)

6.9* 15.6

(3)

Within 30%

(score)80.4 (5) 87.0a (5) 73.9 (3) 80.4 (5) 71.7a (3) 80.4 (5)

Within 10%

(score)41.3 (5) 39.1 (3) 39.1 (3) 43.5 (5) 30.4 (3) 41.3 (5)


mGFR = 75.5 8.9

Bias SD

(score)

4.7* 15.2

(5)7.7* 13.7 (3) 15.9* 21.0 (0)

1.9 15.7

(5)

11.2*

18.9 (1)

1.1 17.6

(5)

Within 30%


Within 10%

(score)28.7 (1) 31.9 (3) 30.9 (3) 35.1a (3) 34.0 (3) 23.4a (1)

Overall (n = 218)

mGFR = 75.8 8.7

Bias SD 2.8* 16.1 2.4* 14.2 12.7* 18.33.4*

15.5

13.0*

17.74.2* 16.0


Within 10% 35.8a 37.2 36.2 41.7a,b 35.3 34.4 b

SCORE** 33 39 24 39 22 37



mGFR = 115.7 19.7

Bias SD

(score)

1.4 17.8

(5)11.6* 17.7 (1) 4.1* 18.8 (5)

4.2* 17.4

(5)

0.0 19.0

(5)

5.7* 18.0

(3)

Within 30%

(score)95.7 (5) 95.7 (5) 95.7 (5) 96.3 (5) 94.5 (5) 95.7 (5)

Within 10%

(score)45.1 (5) 42.1a (5) 40.2b (5) 47.0 (5) 43.9 (5) 49.4a,b (5)


mGFR = 111.1 13.9

Bias SD

(score)

9.9* 16.1

(3)13.9* 15.2 (1) 3.3 19.5 (5)

8.8* 16.2

(3)

6.1* 19.6

(3)

2.8 18.8

(5)

Within 30% 92.6 (5) 93.8 (5) 92.6 (5) 92.6 (5) 88.9 (5) 92.6 (5)



(score)

Within 10%

(score)44.4a (5) 32.1a,b,c (3) 53.1b (5) 45.7c (5) 49.4 (5) 44.4 (5)


mGFR = 113.4 16.5

Bias SD

(score)

18.2* 17.4

(0)22.4* 15.8 (0) 6.0* 23.8 (3)

14.6*

17.9 (1)

1.2 21.0

(5)

7.7* 21.0

(3)

Within 30%


Within 10%


Overall (n = 418)

mGFR = 113.9 17.4

Bias SD 10.0* 18.8 16.5* 17.2 0.2 21.7 9.4* 17.9 1.7 20.0 5.9* 19.5

Within 30% 90.2 88.0a,b 89.7 91.4 a 91.2 91.6 b


SCORE** 34 23 41 37 43 41

OVERALL

SCORE***92 97 73 99 68 102





mGFR subgroup.


The overall performance of the Q(height)-eGFR method is such that it can be used as a first screening tool which is reliable

when the obtained eGFR is higher than 60 mL/min/1.73 m2. In case the eGFR result is below 60 mL/min/1.73 m2, a better

estimation would be obtained from the SchwartzLyon equation and probably it would be advisable to do a direct measurement

in that case.

The new Q(height) equation [eGFR = 107.3/(Scr/Q)] is not a revolution and still lacks precision, the problem with all eGFR

equations, but this equation is not just based on pure statistical modeling, but on a specific rationale, emphasizing the relation

between GFR and Scr. Departure of Scr/Q from '1', the situation for the average healthy child, also leads to the departure of

eGFR from 107.3 mL/min/1.73 m2.

The new Q(height)-eGFR equation is also more broadly applicable than the other pediatric formulas, since the Q(height) formula

can be used to estimate the GFR in children, adolescents and even in young adults up to 25 years of age ( ). Selistre et al.[2]

has shown that the Schwartz or the SchwartzLyon equation already performs better in young adults than adult eGFR

equations like the MDRD[21] or the CKD-EPI[22] equation. This study shows that in young adults with an mGFR >60

mL/min/1.73 m2, the Q(height)-eGFR performs even better than the Schwartz or the SchwartzLyon equation. Moreover, the

updated Schwartz equation for children between 1 and 14 years of age can be seen as a special case of the Q(height)

equation, for which the normalization value Q is linearly dependent on the height of the child (Q = 0.0035 L, R 2 = 0.975, with

76 cm < L < 166 cm). By introducing the result Q = 0.0035 L in our equation eGFR = 107.3/(Scr/Q), this becomes eGFR =

107.3 0.0035 L/Scr = 0.376 L/Scr. The value of 0.376 is also the average in the age region [114 years] of 0.0414



ln(age) + 0.3018, the age-dependent k -value in the FM equation,[14] and is also very close to the value of 0.373 determined by

the research group in Lyon (k = 0.373) for children aged 13 years[4] and only a little smaller than k = 0.413 of the Schwartz

equation.[3] This shows that the Q(height) equation is mathematically equivalent to the Schwartz and/or SchwartzLyon and/or

the FM equation for children between 1 and 14 years of age. Therefore, the alternative Q(height)-eGFR equation [eGFR

=107.3/(Scr/Q)] can be considered as validated for children between 1 and 14 years of age as well.



Group

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-


Q(age)-

eGFR

Q(height)-

eGFR

mGFR





mGFR = 76.4 8.4

Bias SD

(score)

10.2*

13.1 (1)2.4 12.0 (5) 8.8* 13.0 (3)

8.0*

12.8 (3)

11.8*

13.8 (1)

6.4* 13.5

(3)

Within 30%


Within 10%

(score)41.0 (5) 42.3 (5) 41.0 (5) 48.7 (5) 39.7 (3) 43.6 (5)


mGFR = 75.7 9.0

Bias SD

(score)

5.4* 16.2

(3)0.6 15.2 (5) 12.9* 19.3 (1)

6.2*

16.2 (3)

18.4*

20.2 (0)

6.9* 15.6

(3)

Within 30%

(score)80.4 (5) 87.0a (5) 73.9 (3) 80.4 (5) 71.7a (3) 80.4 (5)

Within 10%

(score)41.3 (5) 39.1 (3) 39.1 (3) 43.5 (5) 30.4 (3) 41.3 (5)


mGFR = 75.5 8.9

Bias SD

(score)

4.7* 15.2

(5)7.7* 13.7 (3) 15.9* 21.0 (0)

1.9 15.7

(5)

11.2*

18.9 (1)

1.1 17.6

(5)

Within 30%


Within 10%

(score)28.7 (1) 31.9 (3) 30.9 (3) 35.1a (3) 34.0 (3) 23.4a (1)

Overall (n = 218)

mGFR = 75.8 8.7

Bias SD 2.8* 16.1 2.4* 14.2 12.7* 18.33.4*

15.5

13.0*

17.74.2* 16.0


Within 10% 35.8a 37.2 36.2 41.7a,b 35.3 34.4 b

SCORE** 33 39 24 39 22 37



mGFR = 115.7 19.7

Bias SD

(score)

1.4 17.8

(5)11.6* 17.7 (1) 4.1* 18.8 (5)

4.2* 17.4

(5)

0.0 19.0

(5)

5.7* 18.0

(3)

Within 30%

(score)95.7 (5) 95.7 (5) 95.7 (5) 96.3 (5) 94.5 (5) 95.7 (5)

Within 10%

(score)45.1 (5) 42.1a (5) 40.2b (5) 47.0 (5) 43.9 (5) 49.4a,b (5)




mGFR = 111.1 13.9

Bias SD

(score)

9.9* 16.1

(3)13.9* 15.2 (1) 3.3 19.5 (5)

8.8* 16.2

(3)

6.1* 19.6

(3)

2.8 18.8

(5)

Within 30%

(score)92.6 (5) 93.8 (5) 92.6 (5) 92.6 (5) 88.9 (5) 92.6 (5)

Within 10%

(score)44.4a (5) 32.1a,b,c (3) 53.1b (5) 45.7c (5) 49.4 (5) 44.4 (5)


mGFR = 113.4 16.5

Bias SD

(score)

18.2* 17.4

(0)22.4* 15.8 (0) 6.0* 23.8 (3)

14.6*

17.9 (1)

1.2 21.0

(5)

7.7* 21.0

(3)

Within 30%


Within 10%


Overall (n = 418)

mGFR = 113.9 17.4

Bias SD 10.0* 18.8 16.5* 17.2 0.2 21.7 9.4* 17.9 1.7 20.0 5.9* 19.5

Within 30% 90.2 88.0a,b 89.7 91.4 a 91.2 91.6 b


SCORE** 34 23 41 37 43 41

OVERALL

SCORE***92 97 73 99 68 102





mGFR subgroup.


The database of n = 750 children, adolescents and young adults contained a considerable subgroup of underweighted patients.

The increased bias in the underweight patients, especially when using the age-based eGFR formulas, can be seen in . On the

other hand, the new Q(height)-eGFR formula still gives reasonable results in the underweight patients, probably because weight

and height are highly correlated and underweight mostly goes together with retarded growth. Based on this study, height is a

good indicator for 'muscle mass' and related to that for growth and age.

Table 4. Statistical results for the prediction performance of eGFR equations according to weight subgroups.

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height- independent

eGFR

FM

eGFR

Q(age)-

eGFR

Q(height)-

eGFR

Overweight (n = 108)



Bias

SD

7.8 18.1 13.7 17.2 2.8 22.3 7.0

17.7

0.9 17.6 5.2 19.0

Within

30%88.0 84.3 78.7 88.9 87.0 86.1

Within

10%41.7 28.7 44.4 44.4 41.7 38.0

Normal weight (n = 511)

Bias

SD4.5 18.0 9.9 16.9 4.0 19.9

4.0

17.25.7 18.5 1.2 17.5

Within

30%85.5 88.3 82.4 86.9 83.0 87.7

Within

10%33.7 31.7 36.6 37.8 40.7 38.9

Underweight (n = 131)

Bias

SD1.7 18.6 4.1 18.2 15.9 19.5

2.8

17.9

15.9

20.13.3 19.2

Within

30%84.0 87.8 66.4 83.2 68.7 84.0

Within

10%38.2 38.2 26.7 38.9 21.4 38.9

De Souza et al.[26] previously evaluated if the Schwartz and the SchwartzLyon equation are applicable to kidney transplant

patients. They reported results that were similar to those found in non-transplanted patients. Our study confirms that all

pediatric equations studied here, give results in transplant patients ( ) that are comparable with the overall 750 patients ( ).

Table 5. Statistical results for the prediction performance of eGFR equations in transplant patients.

Kidney transplants (n

= 123)

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-

independent eGFR

FM

eGFR

Q(age)-

eGFR

Q(height)-

eGFR

mGFR = 60.9 19.5

Bias SD 1.3 13.2 2.3* 12.1 11.3* 14.72.0

12.7

10.7*

13.71.8 13.4

Within 30% 86.2 86.2 67.5 86.2 72.4 84.6

Within 10% 29.3 36.6 31.7 37.4 23.6 30.9

Within 30%, Simple height-independent eGFR and Q(age)-eGFR are significantly different from the other percentages within the

row.Within 10%, Q(age)-eGFR is significantly different from FM eGFR and from Schwartz-Lyon eGFR.

*Statistically significant difference between eGFR and mGFR (P < 0.05, paired t-test).



Group

Schwartz

eGFR

SchwartzLyon

eGFR

Simple height-


Q(age)-

eGFR

Q(height)-

eGFR

mGFR



mGFR = 45.7 10.6

Bias SD

(score)

9.9* 9.2

(3)4.7 8.7 (5) 8.7* 11.5 (3)

8.5* 8.9

(3)

10.5*

11.7 (1)

7.6* 8.2

(3)

Within 30%

(score)64.5 (1) 77.4 (3) 64.5 (1) 67.7 (1) 61.3 (1) 71.0 (3)

Within 10%

(score)32.3 (3) 45.2a (5) 32.3 (3) 35.5 (3) 16.1a,b (0) 41.9b (5)


mGFR = 44.4 9.6

Bias SD

(score)

6.8* 10.5

(3)3.8 8.9 (5) 11.4* 12.5 (1)

7.3*

10.6 (3)

14.4*

10.7 (1)

7.6* 10.7

(3)

Within 30%

(score)75.0a (3) 79.2b,c (3) 54.2b (0) 70.8d (3)

45.8a,c,d,e

(0)75.0e (3)

Within 10%

(score)25.0 (1) 33.3 (3) 16.7 (0) 25.0 (1) 16.7 (0) 20.8 (1)


mGFR = 43.2 11.6

Bias SD

(score)

3.2* 10.0

(5)1.9 9.1 (5) 17.5* 14.5 (0)

5.1*

10.2 (3)

15.2*

11.9 (0)

6.7* 9.8

(3)

Within 30%


Within 10%

(score)25.4a (1) 27.1b (1) 18.6 (0) 25.4c (1) 8.5a,b,c (0) 18.6 (0)

Overall (n = 114)

mGFR = 44.1 10.9

Bias SD 5.8* 10.2 3.1 9.0 13.8* 13.86.5*

10.0

13.7*

11.77.2* 9.5



SCORE** 25 35 8 23 3 24



mGFR = 76.4 8.4

Bias SD

(score)

10.2*

13.1 (1)2.4 12.0 (5) 8.8* 13.0 (3)

8.0*

12.8 (3)

11.8*

13.8 (1)

6.4* 13.5

(3)

Within 30%


Within 10%

(score)41.0 (5) 42.3 (5) 41.0 (5) 48.7 (5) 39.7 (3) 43.6 (5)


mGFR = 75.7 9.0



Bias SD

(score)

5.4* 16.2

(3)0.6 15.2 (5) 12.9* 19.3 (1)

6.2*

16.2 (3)

18.4*

20.2 (0)

6.9* 15.6

(3)

Within 30%

(score)80.4 (5) 87.0a (5) 73.9 (3) 80.4 (5) 71.7a (3) 80.4 (5)

Within 10%

(score)41.3 (5) 39.1 (3) 39.1 (3) 43.5 (5) 30.4 (3) 41.3 (5)


mGFR = 75.5 8.9

Bias SD

(score)

4.7* 15.2

(5)7.7* 13.7 (3) 15.9* 21.0 (0)

1.9 15.7

(5)

11.2*

18.9 (1)

1.1 17.6

(5)

Within 30%


Within 10%

(score)28.7 (1) 31.9 (3) 30.9 (3) 35.1a (3) 34.0 (3) 23.4a (1)

Overall (n = 218)

mGFR = 75.8 8.7

Bias SD 2.8* 16.1 2.4* 14.2 12.7* 18.33.4*

15.5

13.0*

17.74.2* 16.0


Within 10% 35.8a 37.2 36.2 41.7a,b 35.3 34.4 b

SCORE** 33 39 24 39 22 37



mGFR = 115.7 19.7

Bias SD

(score)

1.4 17.8

(5)11.6* 17.7 (1) 4.1* 18.8 (5)

4.2* 17.4

(5)

0.0 19.0

(5)

5.7* 18.0

(3)

Within 30%

(score)95.7 (5) 95.7 (5) 95.7 (5) 96.3 (5) 94.5 (5) 95.7 (5)

Within 10%

(score)45.1 (5) 42.1a (5) 40.2b (5) 47.0 (5) 43.9 (5) 49.4a,b (5)


mGFR = 111.1 13.9

Bias SD

(score)

9.9* 16.1

(3)13.9* 15.2 (1) 3.3 19.5 (5)

8.8* 16.2

(3)

6.1* 19.6

(3)

2.8 18.8

(5)

Within 30%

(score)92.6 (5) 93.8 (5) 92.6 (5) 92.6 (5) 88.9 (5) 92.6 (5)

Within 10%

(score)44.4a (5) 32.1a,b,c (3) 53.1b (5) 45.7c (5) 49.4 (5) 44.4 (5)


mGFR = 113.4 16.5

Bias SD 18.2* 17.4 14.6* 1.2 21.0 7.7* 21.0



(score) (0) 22.4* 15.8 (0) 6.0* 23.8 (3) 17.9 (1) (5) (3)

Within 30%


Within 10%


Overall (n = 418)

mGFR = 113.9 17.4

Bias SD 10.0* 18.8 16.5* 17.2 0.2 21.7 9.4* 17.9 1.7 20.0 5.9* 19.5

Within 30% 90.2 88.0a,b 89.7 91.4 a 91.2 91.6 b


SCORE** 34 23 41 37 43 41

OVERALL

SCORE***92 97 73 99 68 102





mGFR subgroup.


In summary, the new Q(height)-eGFR equation is applicable to estimate the GFR in children (114 years), in adolescents (14

18 years) and even in young adults up to 25 years of age. The Q(height)-eGFR formula performs best in healthy patients, but a

low predicted Q(height)-eGFR result may serve as a warning sign for kidney disease. The new Q(height)-eGFR equation can

thus be considered as an excellent screening tool for kidney disease in patients from 1 to 25 years of age.

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We would like to thank Maan Zrein for bringing the research groups in Lyon and in Kortrijk in contact with each other.

Nephrol Dial Transplant. 2014;29(5):1082-1091. 2014 Oxford University Press

Documents

A New Equation to Estimate the Glomerular Filtration Rate (1)