### Results

#### Whole Group of Patients

Among the 126 patients, inulin clearance values at the start of follow-up were distributed as follows: 24% (n = 31) in stage I, 40% (n = 50) in stage II, 30% (n = 38) in stage III and 6% (n = 7) in stage IV of CKD, as defined by K-DOQI.^{[7]} Analytical data on the whole group and subgroups are summarized in Table 1 .

Repeated-measured ANOVA showed that the differences among the five GFR methods at baseline were not due to chance (p < 0.0001). The Dunnett multiple comparison post-test showed a significant difference between inulin clearance and the standard Cockcroft and Gault estimate (t = 3.65; p < 0.01), the abbreviated MDRD equation (t = 5.59; p < 0.01), the Mayo Quadratic Equation (t = 11.83; p < 0.01), but not the BSA-modified Cockcroft and Gault estimate (t = 1.70; p > 0.05). These results are similar to those previously published for an entire cohort of 269 European adults with chronic renal disease.^{[4]}

Pearson's coefficient showed that inulin clearance correlated better with the BSA-modified Cockcroft and Gault formula (r = 0.89; 95% confidence interval: 0.84–0.92; r squared = 0.79), the Mayo Quadratic equation (r = 0.88; 95% confidence interval: 0.83–0.91; r squared = 0.77) and the abbreviated MDRD equation (r = 0.87; 95% confidence interval: 0.82–0.90; r squared = 0.75) than with the standard Cockcroft and Gault equation (r = 0.83; 95% confidence interval: 0.76–0.87; r squared = 0.69).

In the whole population the BSA-modified Cockcroft and Gault formula, the abbreviated MDRD equation and the original Cockcroft and Gault estimate were significantly more accurate than the Mayo Quadratic equation: more than 92.8% of the GFR values predicted by the BSA-modified Cockcroft and Gault formula fell within 30% of the corresponding inulin clearance values, as compared to 89.7% with the abbreviated MDRD equation, 85% with the standard Cockcroft and Gault estimate but only 67.4% with the Mayo Quadratic equation (p < 0.01 in the X^{2} test). Accuracy is reported in Table 2 .

Inulin clearance and creatinine values did not differ in the whole group at the end of follow-up as compared to the basal values (p > 0.05 in the t test and Wilcoxon test respectively) ( Table 1 ). The GFR slope determined by inulin clearance for the whole group was low (−0.3 ml/min/year; range: −72 – +99) and did not differed significantly from that calculated with the GFR estimates (p > 0.05 in the Friedman test) (Cockcroft equation: – 0.12 ml/min/year; range: −60 – +102) (Cockcroft-BSA equation:

−0.18 ml/min/year; range: −60 – +109) (MDRD abbreviated equation: – 0.12 ml/min/year; range: −64 – +138) (Mayo Quadratic Equation: – 0.55 ml/min/year; range: −78 – +52). These results are explained by the fact that about half of the patients were progressors for renal failure whereas renal function improved symmetrically in the other half.

The accuracy of the prediction equations expressed as the GFR slope (ml/min/1.73 m2/year) in each of the two groups of patients (patients with a deterioration in renal function and patients with an improvement) is summarized in Tables 3 and Table 4 .

#### Patients whose Renal Function Deteriorated

During a mean follow-up of 42.86 months (+/− 29.47; range: 6–117), 256 determinations of GFR by inulin clearance were performed in these 65 patients and the median number of GFR per patient was 3 (range 2–11). The mean baseline GFR determined by inulin clearance was 75.30 ml/min/1.73 m2 (+/− 26.15; range: 20–138) and the mean baseline serum creatinine was 123 micromol/L (+/− 57.85; range: 49–316). In this group the median GFR slope determined by inulin clearance was – 3.72 ml/min/1.73 m2/year (range −0.48 to −72) ( Tables 1 and Table 3 ).

Seventeen (26%), fifteen (23%) and sixteen (25%) of these 65 patients were wrongly classified as having no deterioration in renal function by the original Cockcroft-Gault formula and the Mayo Quadratic equation, the BSA-modified Cockcroft and the abbreviated MDRD equation respectively ( Table 4 ). The predictive performance of the three GFR estimates for detecting a deterioration in renal function did not differ significantly (p > 0.05 in the X^{2} test).

The Friedman test showed no difference among the five GFR methods for the determination of the GFR slope (p = 0.29) ( Table 3 ). The Spearman rank correlation showed that inulin clearance correlated similarly with the standard Cockcroft and Gault equation (r = 0.64; 95% confidence interval: 0.43–0.78), the BSA-modified Cockcroft and Gault formula (r = 0.67; 95%; confidence interval: 0.46–0.80) and the abbreviated MDRD equation (r = 0.63; 95% confidence interval: 0.41–0.78) but less with the Mayo Quadratic equation (r = 0.49; 95% confidence interval: 0.23–0.69) ( Table 4 ). Concordance studies with the Bland and Altman test showed a similar bias with the standard Cockcroft-Gault estimate (versus inulin clearance: mean bias = 0.98 ml/min/1.73 m2/year), the BSA-modified Cockcroft-Gault estimate (versus inulin clearance: mean bias = 1.37 ml/min/1.73 m2/year), the Abbreviated MDRD (versus inulin clearance mean bias = 1.30 ml/min/1.73 m2/year) and the Mayo Quadratic equation (versus inulin clearance mean bias = 1.32 ml/min/1.73 m2/year) ( Table 4 ). The precision of the GFR estimates was similar with the standard Cockcroft and Gault equation (SD of bias: 6.08 ml/min/1.73 m^{2}/year), the BSA-modified Cockcroft and Gault formula (SD of bias: 6.88 ml/min/1.73 m^{2}/year) and the abbreviated MDRD (SD of bias: 5.95 ml/min/1.73 m^{2}/year) and larger with the Mayo Quadratic equation (SD of bias: 13.61 ml/min/1.73 m2/year) ( Table 4 ).

Forty-two of these progressor patients had 3 or more repeated GFR measures (median 5; range 3–10) and were followed-up for a median of 60 months (range: 6–117). In these patients, the Friedman test also showed no difference among the five GFR methods for the determination of the GFR slope (p > 0.05). The Spearman rank correlation showed that inulin clearance correlated better with the GFR estimates in these patients with longer follow-up: standard Cockcroft and Gault equation (r = 0.67; 95% confidence interval: 0.41–0.83); BSA-modified Cockcroft and Gault formula (r = 0.74; 95%; confidence interval: 0.52–0.87); abbreviated MDRD equation (r = 0.79; 95% confidence interval: 0.60–0.89); Mayo Quadratic equation (r = 0.71; 95% confidence interval: 0.46–0.85). Similarly, concordance studies with the Bland and Altman test showed a smaller bias with the standard Cockcroft-Gault estimate (versus inulin clearance: mean bias = 0.47 ml/min/1.73 m^{2}/year), the Mayo Quadratic equation (versus inulin clearance mean bias = 0.45 ml/min/1.73 m^{2}/year), and the BSA-modified Cockcroft-Gault estimate (versus inulin clearance: mean bias = 1.19 ml/min/1.73 m^{2}/year), and a similar bias with the Abbreviated MDRD (versus inulin clearance mean bias = 1.43 ml/min/1.73 m^{2}/year). The precision of the GFR estimates was also improved in the standard Cockcroft and Gault equation (SD of bias: 4.45 ml/min/1.73 m^{2}/year) but similar in the BSA-modified Cockcroft and Gault formula (SD of bias: 6.65 ml/min/1.73 m^{2}/year), the abbreviated MDRD (SD of bias: 5.98 ml/min/1.73 m^{2}/year) and the Mayo Quadratic equation (SD of bias: 11.57 ml/min/1.73 m^{2}/year). The improvement in the performance of these equations in patients followed-up for a longer period and having more GFR measurements strongly suggests regression toward the mean, a well-known statistical phenomenon where extreme scores regress toward the mean when remeasured.^{[14]}

#### Patients with an Improvement in Renal Function

During a mean follow-up of 31.91 months (+/− 23.11; range: 6–93) these 61 patients had 196 determinations of GFR by inulin clearance and the median number of GFR per patient was 2 (range 2–10). The mean baseline GFR determined by inulin clearance was 66.47 ml/min/1.73 m2 (+/− 20.78; range: 24–124) and the mean baseline serum creatinine was 114.81 micromol/L (+/− 42.21; range: 53–285) (Table 1). In this group, the median GFR slope determined by inulin clearance was + 6 ml/min/1.73 m^{2}/year (range +0.36 to +99) (Table 1). Sixteen of these 61 patients (26%) were wrongly classified as having no improvement in renal function by the original and BSA-adjusted Cockcroft-Gault formulas; respectively 20 patients (32%) and 21 patients (34%) were wrongly classified by the Mayo Quadratic equation and the abbreviated MDRD equation (Table 4). The predictive performance of the three GFR estimates for detecting an improvement in renal function did not differ significantly (p > 0.05 in the X^{2} test).

The Friedman test showed that the differences among the five GFR methods for the determination of the GFR slope were not due to chance (p < 0.0005) (Table 3). Dunn's multiple comparison post-test showed a significant difference between inulin clearance and the standard Cockcroft and Gault estimate (p < 0.05), the BSA-modified Cockcroft and Gault estimate (p < 0.05), the Abbreviated MDRD equation (p < 0.05) and the Mayo Quadratic Equation (p < 0.05) (Table 3). The Spearman rank correlation showed that inulin clearance correlated similarly with the standard Cockcroft and Gault equation (r = 0.75; 95% confidence interval: 0.58–0.86), the BSA-modified Cockcroft and Gault formula (r = 0.75; 95% confidence interval: 0.58–0.86), the Abbreviated MDRD equation (r = 0.72; 95% confidence interval: 0.54–0.84), but less with the Mayo Quadratic equation (r = 0.46; 95% confidence interval: 0.19–0.67) (Table 4). Concordance studies with the Bland and Altman test showed similar bias with the standard Cockcroft-Gault estimate (versus inulin clearance: mean bias = 3.08 ml/min/1.73 m^{2}/year), the BSA-modified Cockcroft-Gault estimate (versus inulin clearance: mean bias = 2.98 ml/min/1.73 m^{2}/year), the Mayo Quadratic equation (versus inulin clearance: mean bias = 3.02 ml/min/1.73 m^{2}/year) but a smaller bias with the abbreviated MDRD (versus inulin clearance: mean bias = 1.27 ml/min/1.73 m^{2}/year) (Table 4). The precision of the GFR estimates was similar with the standard Cockcroft and Gault equation (SD of bias: 7.98 ml/min/1.73 m^{2}/year), the BSA-modified Cockcroft and Gault formula (SD of bias: 7.63 ml/min/1.73 m^{2}/year), the abbreviated MDRD (SD of bias: 8.87 ml/min/1.73 m^{2}/year) and larger for the Mayo Quadratic equation (SD of bias: 15.46 ml/min/1.73 m^{2}/year) (Table 4).

Twenty-one of these patients had 3 or more repeated measures (median 5; range: 3–10) and were followed-up for a median of 65 months (range: 16–107). Interestingly, in these patients, the Friedman test also showed no difference among the five GFR methods for the determination of the GFR slope (p = 0.10). The Spearman rank correlation showed that inulin clearance also correlated better with the GFR estimates in these patients with longer follow-up; standard Cockcroft and Gault equation (r = 0.86; 95% confidence interval: 0.67–0.94); BSA-modified Cockcroft and Gault formula (r = 0.88; 95%; confidence interval: 0.72–0.95); abbreviated MDRD equation (r = 0.80; 95% confidence interval: 0.54–0.92); the Mayo Quadratic equation (r = 0.72; 95% confidence interval: 0.40–0.88). Similarly, concordance studies with the Bland and Altman test showed a smaller bias with the Abbreviated MDRD (versus inulin clearance mean bias = 0.61 ml/min/1.73 m^{2}/year), the standard Cockcroft-Gault estimate (versus inulin clearance: mean bias = 2.06 ml/min/1.73 m^{2}/year), and the BSA-modified Cockcroft-Gault estimate (versus inulin clearance: mean bias = 2.04 ml/min/1.73 m^{2}/year) and a similar bias with the Mayo Quadratic equation (versus inulin clearance mean bias = 3.28 ml/min/1.73 m^{2}/year).

The precision of the GFR estimates was also improved in the standard Cockcroft and Gault equation (SD of bias: 6.88 ml/min/1.73 m^{2}/year) and the BSA-modified Cockcroft and Gault formula (SD of bias: 6.87 ml/min/1.73 m^{2}/year) and similar with the abbreviated MDRD (SD of bias: 10.94 ml/min/1.73 m^{2}/year) and the Mayo Quadratic equation (SD of bias: 15.98 ml/min/1.73 m^{2}/year). The improvement in the performance of these equations in these improved patients followed-up for a longer period also strongly suggests a regression toward the mean.^{[14]}

#### Characteristics of the Patients

Progressors differed from improvers by higher proteinuria at the outset of the study (p < 0.005 Kruskal-Wallis test with Dunn's multiple comparisons test; Progressors: 1.17 g/24 h (range: 0.32–20); Improvers: 0.5 g/24 h (range: 0.10–19.70)). The percentages of patients receiving immunological treatment and drugs acting on the renin-angiotensin system were similar in the group of progressors and in the group of improvers (p > 0.05 in the X^{2} test).

The inaccuracy of the formulae for classifying patients as improvers or progressors was not related to any of the following clinical features: age (p > 0.05 in the t test), weight (p > 0.05 in the t test), sex (p > 0.05 in the X^{2} test), histological type of the renal disease (p > 0.05 in the X^{2} test).

The area under the ROC curves for discriminating between progressors and improvers were very close for the 4 GFR estimates: 0.79 (95% confidence interval: 0.70–0.87) for the original Cockcroft and Gault Equation; 0.79 (95% confidence interval: 0.71–0.87) for the BSA-modified Cockcroft and Gault formula; 0.78 (95% confidence interval: 0.70–0.86) for the abbreviated MDRD equation and 0.77 (95% confidence interval: 0.68–0.85) for the Mayo Quadratic equation.

BMC Nephrology © 2009

Cite this: Accuracy and Limitations of Equations for Predicting the Glomerular Filtration Rate during Follow-up of Patients with Non-diabetic Nephropathies - *Medscape* - Jun 25, 2009.

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