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Park and Jhang: Development of an estimating equation for the baseline creatinine level in critically ill pediatric patients



The current diagnostic criteria for acute kidney injury mainly rely on baseline serum creatinine (SCr-base). However, this information is frequently missing or unavailable for a significant number of hospitalized patients. In this study, we developed an estimating equation (EE) for SCr-base and validated its performance in critically ill pediatric patients.


This single-center retrospective study included patients admitted to the pediatric intensive care unit (PICU) at a tertiary care children's hospital between January 2016 and July 2020. These patients had a measured SCr-base (mSCr-base) within 3 months prior to admission and initial SCr value at PICU admission (SCr-adm). The patients were divided by admission date into a derivation cohort and a validation cohort for the development and validation of the EE.


In total, 761 children were included in the study (605 in the derivation cohort and 156 in the validation cohort). We employed linear regression analysis to develop the following EE: eSCr-base=0.159+(–0.031)×sex+(0.355×SCr-adm)+(0.006×weight for height z-score). Compared to other imputation methods for SCr-base, such as SCr-adm and SCr-base determined by back-calculation with an assumed estimated glomerular filtration rate of 75 mL/min/1.73 m2 (SCr-eGFR75), eSCr-base demonstrated higher agreement with mSCr-base, exhibiting less bias (0.005) and narrower limits of agreement (LOA) interval (0.506).


eSCr-base calculated through an EE showed better agreement with mSCr-base, with less bias and a smaller LOA interval than other currently used methods (SCr-adm and SCr-eGFR75). Further large-scale studies are necessary for validation and widespread adoption.


Acute kidney injury (AKI) is characterized by abruptly deteriorating renal function and is a common condition associated with elevated morbidity and mortality in critically ill pediatric patients [1-4]. It is defined and diagnosed using standardized diagnostic criteria, most of which primarily rely on the elevation of serum creatinine (SCr) from baseline serum creatinine (SCr-base) values [5-9]. Therefore, having a reliable and available SCr-base value is essential for accurately evaluating AKI. However, this value is often missing or unavailable in a large number of hospitalized patients, which can hinder the precise evaluation of AKI and related researches [10-12].
To solve this problem, several efforts have been made to identify an ideal imputation method for missing SCr-based values, including the use of initial SCr value at pediatric intensive care unit (PICU) admission (SCr-adm), minimum SCr values during hospitalization, dynamic SCr values during a 48-hour or 7-day time window, or back-calculation of SCr values by assuming an estimated glomerular filtration rate (eGFR) of 75 mL/min/1.73 m2 using the modification of diet in renal disease (MDRD) equation or the Chronic Kidney Disease Epidemiology Collaboration formula [11,13-16]. Furthermore, recent research has adopted and proposed multiple imputation methods as a substitute [17]. However, no consensus-based gold standard method has been established. Additionally, these methods have been primarily studied in adult populations, with few studies focusing on SCr-based imputation in critically ill children.
In this study, we hypothesized that the simple imputation of a uniform value by extrapolating methods used in adults may be unsuitable for critically ill children. Instead, estimating the SCr-base while taking into account individual characteristics and adjusting for relevant clinical parameters could enhance the accuracy of the estimation. Therefore, our objective was to develop an estimating equation (EE) for SCr-base and validate its performance in estimating SCr-base for critically ill pediatric patients.


This retrospective chart review study, which involved human participants, adhered to the ethical standards of both the institutional and national research committees, as well as the 1964 Helsinki Declaration and its subsequent amendments or equivalent ethical guidelines. The Institutional Review Board of Asan Medical Center granted approval for this study (No. 2020-0878). Due to the study's retrospective nature, the requirement for informed consent was waived.

Study Population

This was a single-center, retrospective cohort study. We screened all critically ill children who were consecutively admitted to a 14-bed multidisciplinary PICU of a tertiary care academic referral hospital between January 2016 and July 2020 for enrollment. The inclusion criteria were patients aged 1 month to 18 years with a measured SCr-base (mSCr-base), defined as the lowest value within 3 months prior to PICU admission, and a SCr value at PICU admission (SCr-adm). We excluded patients aged under 1 month or over 18 years, those without available mSCr-base or SCr-adm, those with pre-existing chronic renal failure, those on dialysis prior to PICU admission, and those who stayed in the PICU for less than 24 hours. The study population was divided into derivation and validation cohorts based on the admission period. The derivation cohort, which was used to develop the EE for SCr-base, consisted of patients admitted from January 2016 to June 2019. The validation cohort, which was used to evaluate the EE, consisted of patients admitted from July 2019 to July 2020.

Data Collection

We retrospectively reviewed the electronic medical records of all included patients and collected data on baseline demographic characteristics, underlying disorders, reasons for PICU admission, the duration of PICU stay, and laboratory findings. Using body weight (W) and height (H) data, the weight for height (WFH) z-scores were evaluated in accordance with the 2017 growth standards for Korean children. We defined moderate to severe malnutrition as a z-score ≤−2. To evaluate disease severity and organ dysfunction, the Pediatric Risk of Mortality III and the pediatric Sequential Organ Dysfunction Assessment scores were calculated using the worst documented values within the first 24 hours of PICU admission [18,19].

Study Design

Given that mSCr-base values are missing for some patients, we developed an EE for mSCr-base, taking into account the association between various clinical parameters and SCr. This EE was derived from the results of a linear regression analysis conducted on the derivation cohort. Using the EE, we estimated the baseline SCr (eSCr-base) and compared it to mSCr-base. We also evaluated the agreement between mSCr-base and either SCr-adm or SCr-base, which were back-calculated assuming an eGFR of 75 mL/min/1.73 m2 (SCr-eGFR75) using the Schwartz formula for eGFR.

Statistical Analysis

Data were analyzed using IBM SPSS ver. 21.0 (IBM Corp.). Continuous variables are reported as means with standard deviations (SDs) or medians with interquartile ranges. Categorical variables are expressed as numbers and proportions. We performed multiple linear regression analysis to identify clinical parameters associated with mSCr-base. Based on the results, we developed an EE for SCr-base. Correlation analysis was performed, and Pearson correlation coefficients were used to measure the strength of associations between pairs of normally distributed continuous variables. Agreement between two variables was assessed using Bland-Altman plots. Bland-Altman plots were visually described with the bias (the mean difference between two parameters) and limits of agreement (LOA), defined as the bias±1.96×SD. For all analyses, variables with a two-sided p-value of <0.05 were considered statistically significant.


Baseline Characteristics of the Study Population

In accordance with the inclusion and exclusion criteria of this study, 1,228 potentially eligible patients were evaluated, and 761 patients were ultimately included in the study and separated into derivation and validation cohorts (Fig. 1). The derivation cohort comprised 605 patients with 337 boys and 268 girls. The validation cohort included 156 patients, with 83 boys and 73 girls. Comparison between two groups are presented in Table 1.

Development of the EE

Based on the results of multiple linear regression analysis (Table 2), we developed an EE for SCr-base from the derivation cohort as follows:
eSCr-base=0.159+(–0.031)×sex+(0.355×SCr-adm)+(0.006×WFH z-scores)
The Pearson correlation coefficients between mSCr-base and eSCr-base, SCr-adm, and SCr-eGFR75 were 0.753, 0.750, and 0.354, respectively (p<0.001). The agreement between mSCr-base and eSCr-base, SCr-adm, and SCr-eGFR75 was demonstrated graphically using Bland-Altman plots. The arrangement of data points visually indicates the degree of agreement. eSCr-base showed better agreement with mSCr-base than SCr-adm and SCr-eGFR75, with lower bias (0.0004) and narrower LOA (0.760).

Validation of EE

The performance of EE was evaluated in terms of the agreement of eSCr-base with mSCr-base in the validation cohort. The bias and LOA interval of eSCr-base were 0.005 and 0.506, which were lower and narrower, respectively, than the corresponding values of SCr-adm and SCr-eGFR75. The Bland-Altman plots between mSCr-base and eSCr-base, SCr-adm, and SCr-eGFR75 visually showed that eSCr-base had the best agreement with mSCr-base (Fig. 2). The Pearson correlation coefficients between mSCr-base and eSCr-base, SCr-adm, and SCr-eGFR75 were 0.659, 0.654, and 0.642, respectively (p<0.001).


In this study, we developed an EE for SCr-base using multiple linear regression analysis as a more accurate and reliable imputation approach for missing SCr-base values. As most AKI diagnostic criteria are heavily dependent on SCr-base, it is crucial to use an appropriate SCr-base value to accurately evaluate AKI. Ideally, SCr-base should reflect the patient’s steady state before admission or development of AKI. However, there have been some debates and inconsistencies in the absence of a definitive, consensus-based method for deriving SCr-base. Furthermore, it has been reported to be missing in up to 40% of cases [12,20-23]. In fact, in this study, 326 patients were excluded due to the unavailability of mSCr-base, which accounted for 26.5% of the screened (evaluated) study population. Considering that AKI is common and significantly associated with short and long-term prognosis in critically ill children, it is crucial not to exclude these patients without an mSCr-base in order to assess the prevalence of AKI accurately and promptly in this population in clinical studies, as well as to provide timely and appropriate interventions to improve clinical outcomes. For patients with an unavailable mSCr-base, there are no universally accepted imputation methods; however, several approaches have been evaluated and suggested for adult populations [11,13,14,16]. Among these methods, we compared eSCr-base to SCr-adm and SCr-eGFR75.
The SCr-eGFR75 method is the most widely used and recommended approach for imputing missing mSCr-base values, as suggested by the Acute Dialysis Quality Initiative and the Kidney Disease: Improving Global Outcomes. This approach involves back-calculating the SCr value using the MDRD equation, assuming an eGFR of 75 mL/min/1.73 m2 [11,14,24]. However, there are numerous formulas for estimating GFR, which are often categorized by population specificity. It is well known that different equations are applied to various age groups, such as pediatric and adult populations. As a result, the choice of EE for eGFR can affect the back-calculated SCr value, leading to a range of possible values.
In this study, we used the Schwartz formula for back-calculating SCr, as it is the most commonly used method for estimating GFR in pediatric populations. However, this may result in a different SCr value compared to that obtained using the MDRD formula. Additionally, this approach assumes a fixed eGFR value of 75 mL/min/1.73 m2, which may not be appropriate for all study participants. Moreover, pediatric patients have a wide range of normal eGFR values, and critically ill children may have unique clinical situations that affect their SCr values. Consequently, the use of a "universal value" may be inaccurate in these cases.
Another widely used approach for imputing missing SCr-base values is to use SCr-adm as a substitute, which offers the advantages of being easily accessible, time-saving, and enabling prompt evaluation of AKI. In fact, the Acute Kidney Injury Network recommends diagnosing and classifying AKI based on SCr-adm. However, as previously noted, this method has limitations in detecting community-acquired AKI. It may fail to diagnose patients whose SCr has already increased above the true baseline at the time of admission, potentially underestimating the actual prevalence and significance of AKI. In line with this, the current study found poor agreement between the two methods, SCr-eGFR75 and SCr-adm, in comparison to mSCr-base.
In order to impute a reliable SCr-base, we aimed to develop an EE that takes various factors into account. It is well-known that SCr value measurements are significantly influenced by methods and laboratory settings, as well as factors such as age, sex, muscle mass, nutritional state, and diet [25-27]. Therefore, we developed an EE for eSCr-base that considers several associated clinical factors based on statistical analysis. While incorporating more parameters can improve the accuracy of estimates, there are existing multiple imputation methods that consider up to 15 parameters in adults [17]. However, increased complexity may reduce the practicality of an estimation method. Considering the importance of prompt, easy, and precise assessment of AKI, as well as the general usefulness of the method, we opted to include only the minimum parameters necessary for estimating SCr-base. These parameters were SCr-adm, sex, and the WFH z-score.
In the correlation analysis, mSCr-base and SCr-adm demonstrated a significant correlation, which was stronger than that between mSCr-base and SCr-eGFR75. This suggests that the assumption of "normal" may not be appropriate for replacing mSCr-base in these critically ill patients. Although SCr-adm exhibited a strong correlation with mSCr-base, it also displayed a significant bias compared to mSCr-base. We further adjusted this by incorporating several associated clinical factors, such as sex and WFH z-score. Sex is a well-known factor associated with SCr. As for the WFH z-score, we utilized it as an indirect indicator of nutritional status and related muscle mass. Since SCr values are influenced by skeletal muscle mass, a loss of muscle mass alters the amount of creatinine generated in the body. A substantial reduction in creatinine generation has been observed in patients with chronic illness, critical illness, and those with longer hospital stays [28-30]. Therefore, considering these factors may be essential, particularly in critically ill patients.
In this study, the EE performed well in predicting eSCr-base, exhibiting the highest agreement with mSCr-base, the lowest bias, and the narrowest LOA interval in comparison to other currently used imputation methods (SCr-adm and SCr-eGFR75). This finding is consistent with previous results suggesting that taking individual factors into account and adjusting for clinical factors are crucial for achieving a more accurate estimation than general, undifferentiated approaches.
Our study possesses several strengths. To date, few studies have focused on the evaluation of SCr-based measurements in pediatric patients. To the best of our knowledge, this is the first study to develop an EE for SCr-based measurements in children, particularly in critically ill pediatric patients. We developed this EE using multiple linear regression analysis, taking into account associated clinical parameters from a derivation cohort of 605 critically ill children, which is a substantial number. We then validated the EE using eSCr-based measurements in a separate validation cohort, distinct from the derivation cohort. Additionally, we compared the eSCr-based measurements to widely used and evaluated imputation methods in the adult population, which facilitates an understanding of the degree of improvement achieved by using the EE compared to previously employed methods.
Despite the aforementioned advantages, this study has several limitations. It was a single-center retrospective study. Although we divided the enrolled patients by admission date, the characteristics of the derivation and validation cohorts were so similar that there could have been an overfitting issue in the validation of EE. Since we designed this study to include pediatric patients with mSCr-base, 326 patients were excluded due to the absence of mSCr-base, which could have resulted in selection bias. Given the limited number of patients included in this study, it was necessary to selectively include certain parameters in the development of EE, which could have also potentially introduced some bias. In addition, due to the nature of our institution as a tertiary academic referral hospital, the study population is also subject to selection bias, limiting the generalizability of the results.
In conclusion, the accurate evaluation of AKI—encompassing diagnosis, staging, and the prediction of mortality risk—is significantly influenced by SCr-base. Therefore, reliable imputation methods for missing SCr-base values are crucial. To address this need, we developed an EE based on statistical analysis, taking into account associated clinical parameters. This method demonstrated excellent performance for eSCr-base, showing better agreement with mSCr-base than SCr-adm and SCr-eGFR75. It is essential to consider individual characteristics, particularly in critically ill children. Further large-scale studies are needed to validate this EE for widespread use in general practice.


Won Kyoung Jhang is an Editor-in-Chief, and Seong Jong Park is an editorial board member of the journal, but they were not involved in the peer reviewer selection, evaluation, or decision process of this article. No other potential conflicts of interest relevant to this article were reported.
Conceptualization: WKJ, SJP. Data curation: WKJ. Formal analysis: WKJ. Investigation: WKJ. Methodology: WKJ, SJP. Validation: SJP. Writing - original draft: WKJ. Writing - review & editing: WKJ, SJP.

Fig. 1.
Flowchart of the study population. PICU, pediatric intensive care unit; SCr, serum creatinine; mSCr-base, measured SCr-base within 3 months prior to admission; SCr-adm, initial SCr value at PICU admission.
Fig. 2.
Agreement of various indices with mSCr-base. The Bland-Altman plots between mSCr-base and (A) eSCr-base, (B) SCr-adm, and (C) SCr-eGFR75. The extent of bias is denoted by the solid horizontal line. Semi-dashed lines denote the limits of agreement. mSCr-base, measured SCr-base within 3 months prior to admission; eSCr-base, estimated SCr-base; SCr-adm, initial SCr value at pediatric intensive care unit admission; SCr-eGFR75, back-calculation of Scr assuming an estimated glomerular filtration rate (eGFR) of 75 mL/min/1.73 m2.
Table 1.
Baseline characteristics of the study population
Variable Derivation cohort (n=605) Validation cohort (n=156) p-value
Male 337 (55.7) 83 (53.2) 0.576
Age (mo) 22.3 (7.2 to 81.3) 27.1 (8.8 to 104.6) 0.477
Weight (kg) 9.8 (5.8 to 19.3) 10.5 (5.6 to 25.2) 0.316
Height (cm) 80.0 (62.5 to 115.3) 82.0 (65.0 to 123.8) 0.595
WFH z-score –1 (–3 to 1) –1 (–2 to 2) 0.192
Duration of PICU stay (day) 7 (3.0 to 16.5) 5 (3.0 to 9.0) 0.005
Underlying disease 0.386
 Cardiac 173 (28.6) 45 (28.8)
 Hematologic-oncologic 130 (21.5) 36 (23.1)
 Gastrointestinal/hepatic 109 (18.0) 25 (16.0)
 Respiratory 69 (11.4) 23 (14.7)
 Neurologic 41 (6.8) 10 (6.4)
 Genetic 39 (6.4) 5 (3.2)
 Endocrinologic 17 (2.8) 7 (4.5)
 Nephrologic 9 (1.5) 4 (2.6)
 None 18 (3.0) 1 (0.6)
Cause of PICU admission 0.541
 Respiratory problems 243 (40.2) 57 (36.5)
 Gastrointestinal/hepatic problems 117 (19.3) 25 (16.0)
 Cardiac problems 91 (15.0) 24 (15.4)
 Shock 47 (7.8) 20 (12.8)
 Neurological problems 38 (6.3) 14 (9.0)
 Hematologic-oncologic problems 24 (4.0) 6 (3.8)
 Nephrologic problems 22 (3.6) 4 (2.6)
 Post-cardiopulmonary arrest 10 (1.7) 2 (1.3)
 Others 13 (2.1) 4 (2.6)
CRRT within 7 days of PICU admission 44 (7.3) 6 (3.8) 0.121
Moderate to severe malnutrition state 279 (46.1) 62 (39.7) 0.497
28-Day mortality 56 (9.6) 13 (8.3) 0.628
mSCr-base 0.29±0.29 0.28±0.16 0.520
SCr-adm 0.52±0.62 0.45±0.44 0.159
SCr-eGFR75 0.66±0.34 0.69±0.36 0.481
PRISM III score 10.0±6.3 9.7±6.0 0.650
pSOFA score 6.3±3.5 7.0±3.5 0.023

Values are presented as number (%), median (interquartile range), or mean±standard deviation.

WFH, weight for height; PICU, pediatric intensive care unit; CRRT, continuous renal replacement therapy; SCr, serum creatinine; mSCr-base, measured SCr-base within 3 months prior to admission; SCr-adm, initial SCr value at PICU admission; SCr-eGFR75, back-calculation of SCr assuming an estimated glomerular filtration rate of 75 mL/min/1.73m2; PRISM, Pediatric Risk of Mortality; pSOFA, pediatric Sequential Organ Failure Assessment.

Table 2.
Multiple linear regression analysis of several clinical factors used in the estimating equation
Model B coefficient 95% CI p-value
SCr-adm 0.355 0.330 to 0.380 <0.001
WFH z-score 0.006 –0.001 to 0.014 0.110
Sex –0.031 –0.062 to 0.0001 0.053
Constant 0.159 0.109 to 0.209 <0.001

R2=0.567, adjusted R2=0.565, MSE=0.038, RMSE=0.195, F score=262.76 (p<0.001). Sex: 1=male, 2=female.

CI, confidence interval; SCr-adm, initial serum creatinine value at pediatric intensive care unit admission; WFH, weight for height.


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