Article Text

## Abstract

**Background** Several equations for glomerular filtration rate (GFR) estimation based on serum creatinine (SCr) have been proposed for children, but most were developed among patients with kidney disease. The association between SCr and GFR may be distorted by kidney dysfunction and thus not applicable to healthy children. This study aimed to evaluate the applicability of existing SCr-based GFR estimation equations in healthy Chinese children.

**Methods** GFR estimation equations that developed in healthy children were mainly analysed, including the Flanders Metadata (FM), simple height-independent (Simple), full age spectrum (FAS) and FAS-height equations. The FM equation assumed that GFR is proportional to the ratio of height to SCr. The Simple, FAS and FAS-height equations assumed that the ratio of GFR to population mean is equal to the reciprocal ratio of SCr to population mean (denoted by Q). Estimated GFR were calculated using data of SCr, age, sex and height collected from 12 208 healthy Chinese children aged 3 months to <20 years. The performance of GFR estimation equations was evaluated by the sex and age distribution of the estimated GFR and the deviation from the measured GFR reported by other literatures.

**Results** The FM and Simple equations performed well in their applicable age of 1 month to 14 years, but presented undesirable sex difference after adolescence. The FAS and FAS-height equations showed reasonable development trend of estimated GFR throughout childhood, and the FAS equation had higher consistency than the FAS-height equation compared with measured GFR in healthy children. The GFR estimated by the FAS equation increased with age before 2 years, and reached the adult level thereafter without important sex difference.

**Conclusions** The FAS equation is applicable to healthy Chinese children.

- Nephrology

## Data availability statement

Data are available upon reasonable request.

This is an open access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited, appropriate credit is given, any changes made indicated, and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/.

## Statistics from Altmetric.com

#### What is already known on this topic

Several equations for glomerular filtration rate (GFR) estimation based on serum creatinine (SCr) have been proposed for children, but which one is most suitable for Chinese children remains unknown.

#### What this study adds

The full age spectrum (FAS) equation is applicable to healthy Chinese children.

The FAS equation is developed in healthy children, and thus the possibility of distortion of the association between SCr and GFR due to kidney dysfunction is largely reduced.

The study population of the FAS equation covered the entire age range of children, and thus can well present the development trend of kidney function from birth to adulthood.

#### How this study might affect research, practice or policy

The FAS equation is recommended to estimate GFR in Chinese children with normal kidney function.

## Introduction

Glomerular filtration rate (GFR) is defined as the volume of plasma filtered through the glomerulus per unit.1 It is one of the best clinical indicators to evaluate kidney function, and is widely used in the diagnosis of kidney disease, the determination of disease progression and the adjustment drug dosage excreted via kidney.2 3 In healthy children, the value of GFR depends on the maturity of kidney development. Therefore, GFR generally increases after birth, reaches the adult level at about 2 years and remains stable afterwards without sex difference.4–6

GFR cannot be measured directly in the human body, unless with the help of exogenous filtration markers. The gold standard for measuring GFR is the kidney clearance of inulin.1 7 Other exogenous markers include ^{51}Cr-labelled EDTA, ^{99m}Tc-diethylene triamine pentaacetic acid, iohexol and iothalamate, but all of these are complex, expensive, not easily achieved, and some are even radioactive.2 In order to reduce the invasive risk and financial burden of measuring GFR with exogenous markers, especially for children, using endogenous markers to estimate GFR has become a more common approach in clinical practice.

Serum creatinine (SCr) is a typical endogenous kidney biomarker that can filter glomeruli freely.2 Since the concentration of SCr in the human body is affected by muscle mass (and is therefore related to age, sex, height, weight and race),8 SCr alone cannot accurately indicate kidney function. For better assessment of kidney function in children, several GFR estimation equations based on SCr have been developed, such as the Schwartz,9–12 Updated Schwartz,13 Schwartz-Lyon,14 Counahan-Barratt,15 Léger,16 British Columbia’s Children’s Hospital (BCCH),17 Modified BCCH,18 Flanders Metadata (FM),19 and full age spectrum (FAS) equations.20 However, the applicability of these equations to Chinses children remains largely unknown. On one hand, as detected by our previous survey, most equations were not commonly used in China, and were even unrecognised by Chinese paediatricians.21 On the other hand, the measurement of GFR is often available in paediatric patients with kidney disease, while equations based on those with kidney dysfunction might not reflect the real association between SCr and GFR in physiology.

In this study, we hypothesised that the ability of the glomeruli to filter SCr in children with normal kidney function would more accurately estimate GFR. Therefore, it is necessary to validate the existing GFR estimation equations in China, especially those developed for healthy children. The aim of the study is to evaluate the SCr-based GFR estimation equations in healthy Chinese children and adolescents.

## Materials and methods

### Data sources

Data of SCr, age, sex, height and weight that were required for estimating GFR were obtained from the Pediatric Reference Intervals in China (PRINCE) study.22 A total of 15 150 healthy children aged 0–<20 years were recruited from the north (Beijing Municipality and Hebei Province), northeast (Liaoning Province), northwest (Shanxi Province), middle (Hubei and Henan Provinces), south (Guangdong Province), southwest (Sichuan Province and Chongqing Municipality) and east (Jiangsu Province and Shanghai Municipality) regions of China from January 2017 to August 2018. All participants went through a questionnaire screening and a physical examination to ensure their eligibility. Children with history of chronic illness or congenital disease, operation, blood transfusion, or massive haemorrhage within 1 month, acute illness or fever within 2 weeks, or taking any medicines within 1 week would be excluded in the screening process.

Venous blood samples were then collected for participants after overnight fasting (children aged ≥1 year) or before their next feeding (newborns and infants aged <1 year). Specimens were centrifuged for 10 min after clotting with a relative centrifugal force at 1200×g, followed by an approximately 30 min’ quiescence at room temperature (22–25°C). Subsequently, serum samples were separated and stored in well-sealed freezing containers at −80°C within 8 hours after collection, and were transported to the central laboratory at Beijing Children’s Hospital by cold chain. SCr was measured by the enzymatic method using Cobas C702 automated biochemistry analyzer (Roche Diagnostics GmbH, Mannheim, Germany).

### Data cleaning

Data cleaning was performed according to the predesigned steps (figure 1). First, participants who did not meet the eligibility criteria were excluded. Second, participants with unqualified blood samples such as jaundice, haemolysis, chylous and contamination (impurities in the sample) were excluded. Third, participants with missing values in SCr, age, sex, height, or weight, or with outliers in SCr were excluded. Outliers were detected by the Tukey’s method as less than (Q1−1.5×IQR) or more than (Q3+1.5×IQR) in each year age-period due to the age dependency of SCr, where Q1 is the 25th percentile, Q3 is the 75th percentile and IQR is the IQR (Q3–Q1). The exclusion of outliers was further confirmed by the adjudication committee of the PRINCE study. Finally, participants aged less than 3 months were excluded because of the potential maternal effect on SCr.23 24

### GFR estimation

The following four GFR estimation equations developed for healthy children based on SCr were identified from literature research, including the FM,19 simple height-independent (Simple),25 FAS20 and FAS-height equations.20 The formulas of these equations are presented in table 1.

The FM equation assumed that GFR is inversely proportional to SCr and directly proportional to height (eGFR=kHt/SCr), where the parameter k is associated with children’s age (k=0.0414×ln(Age)+0.3018). Different from the most widely used Schwartz equations that treated k as a constant varying with age and sex,9–13 the FM equation directly set k as an age-dependent coefficient.

The Simple, FAS and FAS-height equations all had the following form: eGFR=107.3×(1−e^{-Age/0.5})/(SCr/Q). They were generated according to a same principle, that is, the departure of SCr from the population mean (denoted by Q) reflects the departure of GFR from 107.3 mL/min/1.73 m^{2} (the mean GFR of healthy people aged 2 years or above, adjusted by the product term of (1−e^{-Age/0.5}) when age was less than 2 years). The Q value of the Simple equation is a linear function of age (Q=0.027Age+0.2329). As an improved version of the Simple equation, the FAS equation gave sperate Q values for boys and girls and included polynomials of age with more powers. The Q value of the FAS equation is dependent on age. In a similar way, the Q value of the FAS-height equation is dependent on height.

All the above equations were developed in healthy children, so that the possibility of distortion of the association between SCr and GFR due to kidney dysfunction could be largely reduced. In addition, 13 equations developed for children with kidney diseases were also considered. Details of the equations are shown in online supplemental table S1.

### Supplemental material

Estimated GFR (eGFR) were calculated according to each equation and plotted by age. Although the applicable age ranges of some equations did not perfectly cover 3 months to <20 years (the age range of participants in this study), they were extrapolated to all age groups for GFR estimation.

### Statistical analyses

In the absence of measured GFR (mGFR) in the PRINCE study, the performance of the equations was evaluated by the sex and age dependencies of eGFR, that is, whether in line with the normal development trend of kidney function, and whether consistent with the level of healthy children at the same age. An applicable GFR estimation equation should at least satisfy the following three conditions: first, in accordance with the growth and development pattern of children, eGFR should increase gradually from birth to 2 years of age, and after maturation of the kidney, eGFR should stabilise at a certain level. In addition, there should be no important difference in eGFR between boys and girls.4–6 Second, eGFR should be close to mGFR of healthy Chinese children reported by other literatures.26 27 Mean deviation was calculated by mean eGFR minus mean mGFR in each age group. Third, eGFR should be evenly distributed within the reference intervals (RIs) of mGFR. Since there are no paediatric RIs of mGFR in China till now, and the Chinese studies26 27 only reported the average levels of mGFR without percentile ranges and were only available for children <14 years of age, RIs of mGFR established in Belgian children were used as the reference.28 The proportions of eGFR that were lower or higher than RIs were calculated. All statistical analyses were performed with SAS V.9.4 (SAS Institute).

## Results

A total of 12 208 children aged from 3 months to <20 years were included in the analysis (figure 1). Age and sex distributions of SCr, height and weight are shown in table 2. Age and sex distributions of eGFR are shown in figure 2 and table 3. The mean deviations of eGFR from mGFR of healthy Chinese children are provided in online supplemental table S2. To better interpret the above deviations, distributions of SCr, height and weight in the mGFR studies are provided in online supplemental table S3. The proportions of eGFR below or above the RIs of mGFR for Belgian children are shown in online supplemental table S4.

The FM and Simple equations well display the changes in kidney function across the applicable age of 1 month to 14 years (figure 2A and B). However, since the two equations did not incorporate sex to address the sex difference in GFR after puberty, they might underestimate eGFR in children over 14 years of age, especially for boys (online supplemental table S4). On the other hand, the FAS and FAS-height equations were developed for children aged 1 month to 20 years, and the eGFR fitted the expected developmental pattern of kidney function from birth to adulthood (figure 2C and D). Considering the significance of Q value, which should be as close as possible to the mean SCr of healthy children, Q_{age} showed higher adaptability than Q_{height} to Chinese population (figure 3). Coupled with that the FAS-height equation tended to overestimate in early ages (online supplemental table S4), the FAS equation was considered as the most appropriate equation. The distribution of eGFR as well as the comparison with percentiles curves of mGFR is shown in figure 4.

Among the remaining 13 equations that developed in patients with kidney disease, the Counahan-Barratt (online supplemental figure S1), Schwartz (online supplemental figure S2) and Léger (online supplemental figure S3) equations that used Jaffe-assayed SCr were outside our scope at first due to the systematic error in measurement. The BCCH1 (online supplemental figure S4), Updated Schwartz (online supplemental figure S6), Modified BCCH (online supplemental figure S7) and CKiD U25 constant (online supplemental figure S12) equations estimated that eGFR declined from the onset of puberty, usually more rapidly in boys than girls. The BCCH2 equation revealed a downtrend of eGFR before 6 years of age (online supplemental figure S5). All above equations were not suitable to describe the sex and age dependency of eGFR in healthy Chinese children. The Schwartz-Lyon (online supplemental figure S8), Quadratic (online supplemental figure S9), Uemura (online supplemental figure S10), EKFC (online supplemental figure S11) and CKiD U25 age-dependent (online supplemental figure S12) equations were developed in children more than 1 or 2 years of age, and thus had less ability to identify the uptrend of GFR in younger participants. Based on the above considerations, all these equations were inappropriate.

## Discussion

In this study, we screened the existing GFR estimation equations based on SCr, and found the FAS equation to be potentially applicable to Chinese children. It was developed in healthy population, and thus the possibility of distortion of the association between SCr and GFR due to kidney dysfunction is largely reduced. Moreover, the study population of the FAS equation covered almost the entire age range of children (1 month to 20 years). Hence, it can well present the development trend of kidney function from birth to adulthood. The performance of the FAS equation was further validated by the sex and age distribution of eGFR and the deviation from mGFR. In accordance with the kidney development pattern of healthy children, the eGFR estimated by the FAS equation increased with age before 2 years, and reached the adult level between 2 and 18 years. No important difference was between boys and girls.

There are many equations to estimate GFR for children, but mainly for those with kidney disease and conducted in North America and Europe. Only one equation was carried out in Japan, which was based on patients with chronic kidney disease over 2 years of age.29 No GFR estimation equation has been developed among healthy Chinese children that covered the whole age span. Our research team has conducted a survey for Chinese paediatricians and found that few paediatricians had experienced the evaluation of GFR in children.21 Among them, 36.5% used the Schwartz equation to estimate GFR, 13.1% used the Updated Schwartz equation, and less than 10% used other equations. More than half of the paediatricians did not know the equations except for the Schwartz.21 Since the Schwartz equation was proposed in 1976, and used the Jaffe method to assay SCr, which has been proved to be biased from the isotope dilution mass spectrometry gold standard method,30 the national guidelines of USA recommended to estimate GFR by the Updated Schwartz equation based on enzymatically determined SCr.1 However, the Updated Schwartz equation was developed for children with chronic kidney disease whose GFR were between 15 and 75 mL/min/1.73 m^{2}, and thus validation studies should be done before the application to other populations such as children without chronic kidney disease or with higher GFR.13 31 Furthermore, the Updated Schwartz equation might overestimate GFR in children of low age and underestimate GFR in adolescents approaching the age of 18 years,32 33 which has also been confirmed by our study (online supplemental figure S6). It is necessary to understand what GFR estimation equations are currently available, compare their applicable populations and performances, and select a suitable equation for Chinese children.

The eGFR estimated by the FAS equation were comparable with the mGFR reported by previous researches.26 27 Although the distributions of SCr, height and weight were not very similar among the studies (online supplemental table S3), it is partly attributed to the systematic errors in measuring SCr by different biochemical analysers, and the different age distributions in each age group due to the small sample sizes of mGFR studies. However, these did not necessarily affect the measurement results of mGFR, especially for children >2 years of age, because mGFR has been proved to be age-independent after 2 years.4–6 Thus, the mGFR reported by previous researches26 27 could still provide important information to determine the applicability of GFR estimation equations in this study.

Similar age-related trend was found between eGFR in our study and mGFR in healthy children.5 28 Moreover, eGFR well linked to mGFR of healthy young adults.28 34–38 On the other hand, the Kidney Disease: Improving Global Outcomes guideline defined <60 mL/min/1.73 m^{2} as a criterion of decreased GFR that might indicate chronic kidney disease in both children and adults.39 None of the eGFR of healthy children aged ≥2 years in our study met that criterion (the minimum value was 62.3 mL/min/1.73 m^{2}), indicating that the FAS equation had practical significance in evaluating kidney function for Chinese children.

However, the FAS equation seemed to have a certain underestimation for children aged 3–<6 months (online supplemental tables S2,S4). This is because the FAS equation assumed a mean mGFR of 107.3 mL/min/1.73 m^{2} for children over 2 years of age, and used a product term of (1−e^{−Age/0.5}) to adjust the immature kidney function in early life. As a result, the mean mGFR for newborns would be set to 0, and that for 3-month infants would be set to 42.2 mL/min/1.73 m^{2} according to the FAS equation, which was slightly lower than the actual measurement results in healthy Chinese children.26 27 Nevertheless, after 6 months (where the mean mGFR was set to 67.8 mL/min/1.73 m^{2}), the underestimation was almost disappeared.

As stated by a previous review, which discussed over 70 GFR estimation equations based on SCr and/or cystatin C developed for adults, eGFR often differed from mGFR by ±30% or more, so that the authors recommended to use mGFR in clinical settings rather than eGFR.40 Different views have been debated on this issue.41 42 In our opinion, the careful monitoring of kidney function via mGFR may be necessary for patients with kidney disease, but for healthy individuals or those with mild kidney dysfunction, eGFR based on age, sex and SCr can be easily calculated for disease screening and early warning. Under such clinical needs, it is important to find an appropriate GFR estimation equation for Chinese children. In addition, compared with adults, measurement of GFR in children is often more difficult and harmful. eGFR remains a useful indicator to support clinical decision-making; paediatricians will certainly consider other factors in diagnosis and treatment, while using mGFR to give more precise assessment if necessary.

The strengths of our study are as follows. First, our study included a large sample of 12 208 healthy volunteers aged from 3 months to <20 years from 11 provinces or municipalities across China, which was a good representation of healthy Chinese children. Second, our study made a comprehensive comparison of existing equations for paediatric GFR estimation based on SCr, and thus could help understand the similarities and differences among different equations. Third, the selected FAS equation showed good correspondence with the developmental trend of kidney function in children, and the eGFR level was close to that of healthy children at the same age.

There was an important limitation of our study, that is, mGFR, as a gold standard for equation evaluation, was not available. Therefore, we could only visually examine the sex and age distribution of eGFR, and compare with the reported values of mGFR. It is practically impossible to measure GFR with ideal exogenous filtration markers in healthy children, and to provide the age-dependent distribution of mGFR in a large representative population. Besides, although much of the literature suggested that equations based on both SCr and cystatin C provide more accurate estimates of GFR,2 43 cystatin C is not a routine biochemical test and was not collected in the PRINCE study. Because the aim of the PRINCE study is to establish paediatric reference intervals in China for health screening, if the SCr-based eGFR indicates pathology, cystatin C can be further measured in clinical settings.44

In conclusion, the age and sex distribution of eGFR estimated by the FAS equation is consistent with that of mGFR of healthy children with the same age. Hence, the FAS equation can be used to estimate GFR for healthy Chinese children.

## Data availability statement

Data are available upon reasonable request.

## Ethics statements

### Patient consent for publication

### Ethics approval

This study was performed in line with the principles of the Declaration of Helsinki. Approval was granted by the Ethics Committee of Beijing Children’s Hospital (No. 2016-53).

## Acknowledgments

We are grateful to Prof. Hans Pottel for his help in framing the article.

## References

## Supplementary materials

## Supplementary Data

This web only file has been produced by the BMJ Publishing Group from an electronic file supplied by the author(s) and has not been edited for content.

## Footnotes

Contributors XP designed the study. CZ and CW collected the data. RY and ZS analysed the data. RY interpreted the data. RY and ZS drafted the manuscript. XP, CZ and CW revised the manuscript for important intellectual content. All authors read and approved the final manuscript. XP accepts full responsibility for the work and/or the conduct of the study, had access to the data, and controlled the decision to publish.

Funding This study was supported by the Medical Hospital Authority, National Health Commission of the People’s Republic of China (Grant No. 2017374); National Natural Science Foundation of China (Grant No. 72174128); and Beijing Nova Program (Grant No. Z211100002121053).

Competing interests None declared.

Patient and public involvement Patients and/or the public were not involved in the design, or conduct, or reporting, or dissemination plans of this research.

Provenance and peer review Not commissioned; externally peer reviewed.

Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.