A total of 298 subjects aged ≥ 60 years were recruited for the study, comprising 44 subjects with mGFR < 30 ml/min/1.73 m2, 163 subjects with mGFR 30–59 ml/min/1.73 m2, and 91 subjects with mGFR ≥ 60 ml/min/1.73 m2. Of the participants, 43.96% were female. The age, Scr, and CysC were 71 (65, 77) years, 116.00 (91.53, 168.83) μmol/L, and 1.48 (1.14, 2.01) mg/L, respectively. The mGFR was 48.77 (36.50, 62.45) ml/min/1.73 m2. Detailed characteristics and eGFR values estimated by different equations are provided in Table 2.

The results of these analyses revealed that, except for the MDRD and MDRDc equations, the other five equations were more likely to underestimate mGFR (bias < 0) (Table 3). The bias of the MDRDc equation significantly differed from all other equations except the MDRD equation (P < 0.05), and the bias of the MDRD equation differed from the other four equations except the MDRD and CKD-EPI-Scr equations (P < 0.01). The bias of the FAS equation was apparently different from the other equations except the MDRD and MDRDc equations (P < 0.01). There was no significant difference in the bias of other equations (P > 0.05).

Regarding IQR results, the MDRDc equation had the highest IQR value, followed by the MDRD equation. The IQR values of the remaining equations were arranged in descending order as the CKD-EPI-Scr-Cysc, CKD-EPI-Scr, FAS, BIS1, and CKD-EPI-Cysc equations. The MDRDc and FAS equations showed accuracies (P30) lower than 60% (57.7% and 59.7%, respectively) and were significantly lower than other equations (P < 0.05). The accuracy (P30) of the BIS1 Eq. (72.1%) was significantly higher than all other tested equations (P < 0.05), while the accuracy (P30) of the remaining four equations (CKD-EPI-Scr 62.4%, CKD-EPI-Cysc 67.1%, CKD-EPI-Scr-Cysc 66.4%, MDRD 64.1%) did not differ significantly from each other (P > 0.05).

The RMSE of the BIS1 equation was the smallest, while the RMSE of the MDRD equation was the largest, with the RMSE of the other equations fluctuating around 15–18. The Bland–Altman plots analysis demonstrated that the BIS1 equation exhibited the highest accuracy, with 95% confidence interval (CI) widths of 52.37. Meanwhile, FAS, CKD-EPI-Scr-Cysc, CKD-EPI-Cysc, and CKD-EPI-Scr equations exhibited slightly lower accuracies with 95% CI widths of 55.99, 59.53, 61.68, and 66.73, respectively. The MDRD and MDRDc equations exhibited the lowest accuracy with 95% CI widths of 70.12 and 80.71 (Fig. 2, Table 4).

Comparisons of mGFR and eGFR. a CKD-EPI-Scr equation; b CKD-EPI-Cysc equation; c CKD-EPI-Scr-Cysc equation; d MDRD equation; e MDRDc equation; f FAS equation; g BIS1 equation. Solid and dashed lines in the Bland–Altman plot represent the mean and 95% limits of agreement (LoA) of difference, respectively. CKD-EPI chronic kidney disease epidemiology collaboration, MDRD modification of diet in renal disease, MDRDc MDRD-China, FAS full age spectrum, BIS1 Berlin Initiative Study 1

All subjects were divided into three groups based on their mGFR levels: the mGFR < 30 ml/min/1.73 m2 group, the mGFR 30 ~ 59 ml/min/1.73 m2 group, and the mGFR ≥ 60 ml/min/1.73 m2 group.

For the mGFR < 30 ml/min/1.73 m2 group, there was no significant difference in bias among the seven equations (P > 0.05). IQR results revealed that the CKD-EPI-Cysc equation had the lowest IQR value (6.77), while the MDRDc equation had the highest IQR value (15.29). The accuracy (P30) of the CKD-EPI-Cysc and BIS1 equations was the highest (59.0% and 47.7%, respectively) but did not significantly differ from the rest of the equations (CKD-EPI-Scr 38.6%, CKD-EPI-Scr-Cysc 43.6%, MDRD 43.2%, MDRDc 40.9%, FAS 38.6%, P > 0.05). In this group, the accuracy of all equations was below 60%. The RMSE results showed that the CKD-EPI-Cysc and CKD-EPI-Scr-Cysc equations had the lowest values, followed by the FAS and BIS1 equations, while the remaining three equations had values greater than 12 (Table 3).

In the mGFR 30 ~ 59 ml/min/1.73 m2 group, the bias of the FAS equation was significantly lower than the bias of the other tested equations (P < 0.05), except for the CKD-EPI-Cysc equation (P > 0.05). The bias of the MDRD and MDRDc equations was positive and significantly different from the CKD-EPI-Cysc and CKD-EPI-Scr-Cysc equations (P < 0.05). The bias of the other equations did not significantly differ (P > 0.05). IQR results indicated that the BIS1 and FAS equations had the lowest values (12.85 and 14.38, respectively), while the MDRDc and MDRD equations had the highest values (22.07 and 18.02, respectively). The MDRDc equation also showed the lowest accuracy (P30 60.7%), while the BIS1 equation showed the highest accuracy (P30 74.8%). However, the accuracy of the equations did not significantly differ (P30 CKD-EPI-Scr 63.2%, CKD-EPI-Cysc 69.4%, CKD-EPI-Scr- Cysc 68.8%, MDRD 63.8%, FAS 63.8%, P > 0.05). Similar results were obtained for RMSE, with the BIS1 equation exhibiting the lowest RMSE and the MDRDc equation having the highest RMSE (Table 2).

In the mGFR ≥ 60 ml/min/1.73 m2 group, the bias of the FAS equation was significantly smaller than the other examined equations (P < 0.05), except for the BIS1 equation. The bias of the MDRD and MDRDc equations was the highest; the bias of the MDRD equation was significantly higher than the BIS1 equation (P < 0.05), and the bias of the MDRDc equation was notably higher than the CKD-EPI-Cysc, CKD-EPI-Scr-Cysc, and BIS1 equations (P < 0.05). The bias of the remaining equations did not differ significantly (P > 0.05). The BIS1 equation had the lowest IQR value, followed by the FAS, CKD-EPI-Scr, MDRD, CKD-EPI-Scr-Cysc, and MDRDc equations, while the CKD-EPI-Cysc equation had the highest IQR value. Among the tested equations, the accuracy (P30) of the BIS1 equation was as high as 79. 1%, the accuracy of the MDRD, CKD-EPI-Scr, and CKD-EPI-Scr-Cysc equations was also above 70% (MDRD 74.7%, CKD-EPI-Scr 72.5%, CKD-EPI-Scr-Cysc 72.2%), and the accuracy of the remaining three equations fluctuated between 60 and 70% (CKD-EPI-Cysc 66.7%, MDRDc 60.4%, FAS 62.6%). However, the differences in accuracy between these equations were not significant (P > 0.05). The RMSE results revealed that BIS1, CKD-EPI-Scr-Cysc, and CKD-EPI-Scr equations had RMSE values lower than 20, the CKD-EPI-Cysc and MDRD equations had slightly increased RMSE values, and the FAS and MDRDc equations had the highest RMSE values.