### Introduction

### Methods

### Study subjects

^{2}; random urine albumin to creatinine (Cr) ratio ≥ 30 mg/g; Cr measured more than twice with ≥ 1-week interval in the last 6 months. These patients fulfilled the KDIGO criteria for the diagnosis of CKD [3]. Participants using diuretics were instructed to discontinue its use two months prior to the start of the study. Exclusion criteria included: uncontrolled HTN (BP > 160/100 mmHg); pregnant women; active malignancy; a diagnosis of cardiovascular disease within the previous 6 months; hyperkalemia (serum potassium > 5.5 mEq/L); and diabetes mellitus. In the ESPECIAL cohort, intensive LSD education was supported by a dietary consultant and telephone feedback for 30 minutes once a week during the study period. Conventional LSD education was defined by routine LSD instructions given at an outpatient clinic. The study protocol was approved by the institutional review boards at the seven study centers (representative site: Kyung Hee University Hospital). Written informed consent was obtained from each patient prior to study inclusion.

### Data collection

### Generation of ESPECIAL formula

### Statistical analysis

*t*test was used to compare the USE between measured and estimated values. Correlation analysis was used to assess the relationship between measured and estimated values. The Bland-Altman plot was used to estimate the difference and limits of agreement between the measurements and estimations (obtained using each respective formula). The receiver-operating characteristic (ROC) curve was used to analyze the sensitivity and specificity of the rate of reduction of the estimated USE with regard to the measured USE.

### Results

^{2}. None of the 228 patients had significant hyponatremia or hypernatremia.

*P*< 0.001).

### Comparing previously reported formulas for the prediction of USE in CKD patients

*r*= 0.340). The Nerbass formula had the best correlation (

*r*= 0.469). However, the Nerbass formula also produced the largest difference (mean bias = 33.7 mEq/day) from the measured USE (Table 2).

### Development of the ESPECIAL formula

*P*< 0.001). Bland-Alt-man plots using the ESPECIAL formula showed minimal bias and few outliers (Fig. 2B).

### Comparing the efficacy of the ESPECIAL formula and other formulas to estimate the measured USE after 8 weeks of treatment with olmesartan

*r*= 0.571) to the measured USE, which was comparable to that of the baseline data (week 0) (Table 3). Bland-Altman plots showed that outlier biases in the Kawasaki, Tanaka, and ESPECIAL formulas had smaller ranges than those noted using the INTERSALT and Nerbass formulas (Fig. 3).

### Comparison between the efficacy of the ESPECIAL formula and other formulas to predict the measured USE after 8 weeks of randomized LSD education (Table 4)

*P*< 0.001). In the conventional education group, the mean estimated USE obtained using the Tanaka formula (mean, 151.3 mEq/day) was the closest to the measured USE compared to those of the other formulas. However, the Tanaka formula had a poor correlation (

*r*= 0.226). In the intensive education group, the mean estimated USE based on the INTERSALT formula (mean, 120.3 mEq/day) was the closest to/most accurately matched to the measured USE. All of the estimated USEs significantly differed from the measured USE, including those based on the Kawasaki (mean, 174.7 mEq/day), Tanaka (mean, 139.2 mEq/day), Nerbass (mean, 97.0 mEq/day), and ESPECIAL formulas (mean, 149.9 mEq/day). The INTERSALT formula showed the weakest correlation with the measured USE (

*r*= 0.448).

### Prediction of the estimated USE for reduction of the measured USE (> 30%) after LSD education

### Discussion

*r*= 0.57,

*P*< 0.001). In order to evaluate the performance of our formula compared to those of others, we applied our new formula and prior formulas to the second samples obtained from patients after 8 weeks of treatment with olmesartan. The measured sodium excretion (156.6 ± 70.6 mEq/day) was not significantly changed from that observed at baseline (154.1 ± 69.6 mEq/day). All of the equations demonstrated perfect reproducibility in the estimation of the USE with a similar bias and correlation coefficient when applied to the same population after ARB treatment. Our new formula also demonstrated negligible bias (1.2 mEq/day), and a good correlation when compared to the measured 24-hour USE.

*P*< 0.001; mean, 1,302.2 ± 300.5 mg/day) and Kawasaki (

*P*= 0.001; mean, 1,305.3 ± 376.8 mg/day) formulas. Therefore, both the Tanaka and Kawasaki formulas seem to be unreliable because they tend to systemically overestimate the 24-hour urine Cr excretion in CKD patients.

^{2}. Of note, however, neither the MDRD nor CKD EPI, which are representative eGFR formulas, consider the CKD stage.