Validation of the estimated glomerular filtration rate equation for Japanese children younger than 2 years

Background We have developed a simple and easy method of estimating the glomerular filtration rate (eGFR) of serum creatinine in Japanese children (eGFRUemura). The eGFR equation is for children aged 2–18 years. Therefore Uemura et al. developed an equation for children younger than 2 years (eGFRunder 2). The aim of the present study was to validate this new equation. Methods We collected the data of 13 patients from previous studies and compared the results of eGFRunder 2, eGFRUemura, and updated eGFR developed by Schwartz (eGFRSchwartz) with measured GFR using mean error (ME), root mean square error (RMSE), P30 and Bland–Altman analysis. Results The ME of eGFRunder 2, eGFRUemura and eGFRSchwartz were 2.3 ± 15.9, 7.7 ± 14.5, and 16.0 ± 18.2 ml/min/1.73m2, respectively. The RMSEs were 15.5, 15.9, and 49.6, respectively. The P30 values were 76.9%, 76.9%, and 53.8%, respectively. The graph of Bland–Altman bias analysis showed fan-shape. The eGFRunder 2 equation was the most accurate in the three equations. Conclusion The eGFRunder 2 equation was useful for Japanese children younger than 2 years.


Introduction
The gold standard for evaluation of renal function is inulin clearance (Cin). However, the procedure of Cin is complicated and difficult, especially in younger children and/ or patients with bladder dysfunction. Therefore, various simple and easy methods to determine the estimated GFR (eGFR) have been developed. Recently, the most known equation for eGFR used in children is the updated Schwartz (eGFR Schwartz ) equation [1]. However, Uemura et al. reported that the eGFR Schwartz equation is not applicable for Japanese children [2]. Therefore, an original equation for eGFR (eGFR Uemura ) was developed using serum creatinine (Cr) in Japanese children [3], and its accuracy was validated [4]. However, the equation was for children aged 2-18 years. Therefore, an equation for children younger than 2 years was then developed by multiplying eGFR Uemura by a coefficient (0.107 × ln(age[month]) + 0.656) [5]. In this study, we aimed to validate eGFR under 2 equation.

Study population
We extracted the data of patients under 2 years of age from three studies. The first was 7 of 174 patients' data when the eGFR Uemura equation was created [3]. The second was 8 of 140 patients' data when the accuracy of the eGFR Uemura equation was validated [4]. The third was 1 of 59 patients' data validated the safety of Inulide® for Japanese children (in press) ( Table 1). All data were collected from pediatric patients with chronic kidney disease (CKD) in clinical need of Cin. Finally, we used data from 13 patients after excluding patients (Table1).
The measured GFR (mGFR) for each patient was obtained using Cin. The procedure is described in a previous report [6]. Cin values were measured in the same way in three studies.
The calculate method of eGFR under 2 is as follows:

Exclusion criteria and cases excluded
The exclusion criteria were as follows: 1. Primary diseases including severe obstructive uropathy, infection during treatment, inflammatory disease, dehydration, neuromuscular disease, severe cardiac, hepatic, or pancreatic disease, and/or endocrine disease, including thyroid impairment. 2. Cases in which the ratios of inulin excretion and intravenous inulin administration were < 0.5, or > 1.5, during the measurement of Cin. We determined the dose of intravenous inulin by assuming that the blood concentration was constant during testing. Ratios of inulin excretion and intravenous inulin that were not within 0.5 and 1.5 may have been due to failure to collect all urine. 3. Cases in which the measured GFR (mGFR) was > 150 ml/min/1.73m 2 ; pediatric patients with CKD due to a hyperfiltration disease such as diabetic nephropathy are rare. We were only interested in cases in which GFR was < 120 ml/min/1.73m 2 . Therefore, we excluded cases in which mGFR was > 150 ml/min/1.73m 2 .

Statistical analysis
To validate eGFR under 2 equation, we used four methods as follows: 1. Mean error (ME): to evaluate the mean difference between each value for eGFR and mGFR values 2. Root mean square error (RMSE): to evaluate the precision of eGFR and mGFR values. 3. P 30 (the percentage of eGFR value within 30% of mGFR): to evaluate the accuracy of eGFR and mGFR values. 4. Bland-Altman analysis (difference versus average): to determine agreement with the estimation.
We also compared these statistical results of eGFR under 2 equations, with the results of eGFR Uemura , and eGFR Schwartz .
The formula for eGFR Uemura equation is mentioned above in the calculation method of eGFR under 2 from (1) to (2). First, calculate the reference Cr level as described (1), and then the eGFR Uemura from reference Cr and patient's serum Cr using the method described in (2).
The updated Schwartz equation is as follows: eGFR (ml/ min/1.73 m 2 ) = 0.413 × body length (cm)/serum Cr value (mg/dL) by enzymatic Cr determination in children aged 1-16 years [1]. Therefore, in the second analysis, the data of three patients under 1 year of age were excluded. Finally,  (Table 1) Data of 6 patients were extracted from the three studies. Data of three patients were excluded because the ratios of urinary inulin excretion to intravenous inulin administration were < 0.5 or > 1.5. None of the patients were included in the 1 or 3 exclusion criteria. Finally, 13 patients' data (2 female, median 17.0 months of age [interquartile range (IQR) 10.0-20.5 months, range 1-23 months]) were used for analysis (Fig. 1). The number of chronic kidney disease (CKD) stages 1, 2, 3, 4, and 5 were 2, 4, 6, 1, and 0, respectively. The number of renal abnormalities, congenital anomalies of the kidney and urinary tract (CAKUT), solitary kidney, reflux nephropathy, hydronephrosis, and small kidney were 6, 3, 2, 1, and 1, respectively.  Figure 3 shows the Bland-Altman plot of the difference versus the average for both mGFR and each 3 eGFR equations.    Figure 3 shows a scatter plot of the Bland-Altman analysis. In all three equations, the spread of the graph of the Bland-Altman analysis was fan-like shaped, with systematic error.

Result of statistical analysis
In the three equations, the values using eGFR under 2 equation showed the lowest value for ME and Bland-Altman analysis, and showed the larger values for P 30 than that for eGFR Schwartz .

Discussion
We evaluated a new eGFR equation for children under 2 years of age. Using several statistical techniques, we confirmed that the eGFR under 2 equation could be useful.
For Japanese children, there are several eGFR equations with surrogate markers, serum Cr [3], cystatin C [7], and β2 microglobulin [8]. The Cr-based eGFR Uemura equation is the most commonly used method for children aged 2-18 years. Cystatin C and β2 microgrobulin based eGFR are not always available for retrospective epidemiologic studies or common clinical practice. Therefore, we developed  Cr-based eGFR for children younger than 2 years using eGFR Uemura using a coefficient. The method reported in a previous article [5] is based on the following idea. Physiologically, kidney function gradually increases from birth and reaches adult stage at the age of 2 years. Using the median normal reference values of GFR for each age (months) up to 2 years examined previously, we estimated the percentage of the normal adult GFR that corresponds to and calculated a regression curve using a logarithmic function. As a result, the coefficient was calculated as 0.  Schwartz .
In the analysis of 13 patients, the ME value of eGFR under 2 was the smallest among the three equations. The RMSE value and percent of P 30 of eGFR under 2 and eGFR Uemura were similar. On the other hand, the ME and RMSE values of eGFR Schwartz were the highest, and the percentage of P 30 was the lowest among the three eGFR equations. In the analysis of 10 patients, the ME and RMSE values of eGFR under 2 were lower than that of eGFR Schwartz . The percentage of P 30 of eGFR under 2 was higher than that of eGFR Schwartz . This study has several limitations. First, the sampling data was small particular under 1 year of age. Although we collected patients' data from our three previous studies, there were only 13 among 373 patients (3.5%) under 2 years of age. Further, it is very rare to perform inulin clearance in patients under 2 years of age, thus limiting data collection. In addition to that, there were only two patients of a female under the age of two. However, since there was no gender difference in normal Cr values at younger ages [9], we believed that this result was not affected. Second, to add to the data as much as possible, we also used the patient data when creating the equation of eGFR Uemura . Third, we did not exclude preterm infants and low birth weight infant because we had no information for them. We don't know whether the eGFR under 2 equation can be applied to such cases or not.

Conclusion
We evaluated the eGFR under 2 equation for Japanese children aged 2 years or less. The results suggest that eGFR under 2 equation could be a useful parameter.