# Estimated Glomerular Filtration Rate and Prognosis in Heart FailureValue of the Modification of Diet in Renal Disease Study-4, Chronic Kidney Disease Epidemiology Collaboration, and Cockroft-Gault Formulas

## Author + information

- Received September 6, 2011
- Revision received November 26, 2011
- Accepted November 29, 2011
- Published online May 8, 2012.

## Author Information

- Elisabet Zamora, MD, PhD
^{⁎},^{†}, - Josep Lupón, MD, PhD
^{⁎},^{†}, - Joan Vila, MSc
^{‡},^{§}, - Agustín Urrutia, MD, PhD
^{⁎},^{†}, - Marta de Antonio, MD
^{⁎},^{†}, - Hèctor Sanz, BSc
^{‡}, - Maria Grau, MD, PhD
^{‡}, - Jordi Ara, MD
^{∥}and - Antoni Bayés-Genís, MD, PhD
^{⁎},^{†},^{⁎}(abayesgenis{at}gmail.com)

- ↵⁎
**Reprint requests and correspondence:**

Dr. Antoni Bayes-Genis, Cardiology Service, Hospital Universitari Germans Trias i Pujol, Carretera de Canyet s/n 08916, Badalona (Barcelona), Spain

## Abstract

**Objectives** The purpose of this study was to assess the value of estimated glomerular filtration rate (eGFR) calculated by different formulas for predicting the risk of death in heart failure (HF) outpatients.

**Background** Patients with both HF and renal insufficiency have a poor prognosis. Three formulas are mostly used to assess renal function: Cockroft-Gault formula, MDRD-4 (Modification of Diet in Renal Disease Study) formula, and the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation. The prognostic values of these formulas have not been adequately compared in HF patients.

**Methods** A total of 925 patients (72% men; age 69 years; interquartile range: 59 to 75.5 years) with a left ventricular ejection fraction of 31% (interquartile range: 23.5% to 39%) were studied. Follow-up was 1,202 days (interquartile range: 627.5 to 2,156.5 days). Measures of performance were evaluated using continuous data and by dividing patients into 4 subgroups according to the eGFR: ≥90, 89 to 60, <60 to 30, and <30 ml/min/1.73 m^{2}.

**Results** The 3 formulas correlated significantly, with the best correlation found between the MDRD-4 and CKD-EPI formulas. The 3 formulas afforded independent prognostic information over long-term follow-up. However, risk prediction was most accurate using the Cockroft-Gault formula as evaluated by Cox proportional hazards models (hazard ratio: 0.75 vs. 0.81 with the MDRD-4 formula and 0.80 with the CKD-EPI equation), area under the curve (0.67 vs. 0.62 and 0.64, respectively), and Bayesian information criterion (both analyzing eGFR as a continuous or categorical variable). Indeed, net reclassification improvement and integrated discrimination improvement using the Cockroft-Gault formula were 21% and 5.04, respectively, versus the MDRD-4 formula (the most used) and 13.1% and 3.77 respectively versus CKD-EPI equation (the more recent) (all p values <0.001).

**Conclusions** In this ambulatory, real-life cohort of HF patients, the Cockroft-Gault formula was the most accurate of the 3 used eGFR formulas to improve the risk stratification for death.

Renal insufficiency is prevalent in patients with heart failure (HF), and the coexistence of both conditions results in a worse prognosis (1–5). The most precise methods for calculating kidney function, such as the isotopic glomerular filtration rate (GFR) and creatinine clearance in a 24-h urine specimen, are not used in daily clinical practice (6). Instead, several formulas based on creatinine clearance were developed to calculate the estimated GFR (eGFR), the best known of which are the Cockroft-Gault formula (7) and the Modification of Diet in Renal Disease (MDRD) 6 formula (8,9), as well as the simplified MDRD-4 formula (10). A recent formula, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation (11), has been described and validated in population studies. The CKD-EPI equation has been suggested to be more precise than the MDRD formula (11). These formulas have been applied to general populations and to patients with variable degrees of renal insufficiency, although data on the application of these formulas in other contexts or pathological situations is scarce. To the best of our knowledge, the prognostic values of these formulas have not been compared in patients with HF. Our objective was to assess the agreement between the Cockroft-Gault formula, the MDRD-4 formula, and the CKD-EPI equation and evaluate their prognostic role in a population of outpatients with HF during long-term follow-up.

## Methods

Patients were consecutively recruited from a multidisciplinary HF unit integrated into a tertiary hospital. Most patients were referred from cardiology (70%) and internal medicine (15%), and the principal referral criterion was HF irrespective of etiology (at least 1 HF hospitalization and/or reduced left ventricular ejection fraction [LVEF]). At the first visit, patients gave us written consent to obtain analytic samples and to use their clinical data for research purposes. Follow-up visits included a minimum of a visit every 3 months with a nurse and every 6 months with the physician (cardiologist, internist, or family physician), and optional visits with specialists in geriatrics, psychiatry, and rehabilitation.

Of the 960 patients who were admitted to our HF unit between August 2001 and December 2008, the eGFR at the first follow-up visit and vital status at the end of follow-up were available for 925 patients (96%) (in addition to other demographic, clinical, echocardiographic, and analytical data).

Three formulas were used: 1) the Cockroft-Gault formula, (140 − age in years) × weight in kg/(72 × serum creatinine level in mg/dl) adjusted by sex (× 0.85 in women) (7) and later adjusted by body surface area; 2) the MDRD-4 formula, 186.3 × creatinine^{−1.154} × age^{−0.203} × 1.212 (if black) × 0.742 (if female) (10); and 3) the CKD-EPI equation, male: 141 × minimum (creatinine/0.9, 1)^{−0.411} × maximum (creatinine/0.9, 1)^{−1.209} × 0.993^{Age} × 1.159 (if black); female: 141 × minimum (creatinine/0.7, 1)^{−0.329} × maximum (creatinine/0.7, 1)^{−1.209} × 0.993^{Age} × 1.018 × 1.159 (if black) (11).

Serum creatinine levels were analyzed using the CREA method with a Dimension Clinical Chemistry System (Siemens, Newark, New Jersey), using a modification of the kinetic Jaffe reaction described by Larsen (8) with picrate as the reactant.

The relationship between the eGFR and survival at the end of follow-up was evaluated. Renal insufficiency was considered if the eGFR was <60 ml/min/1.73 m^{2}. In addition, 4 subgroups of patients were analyzed according to the eGFR following the stages defined in the clinical guidelines of the National Kidney Foundation (6): ≥90 ml/min/1.73 m^{2}; 89 to 60 ml/min/1.73 m^{2}; <60 to 30 ml/min/1.73 m^{2}; and <30 ml/min/1.73 m^{2}. Patients from groups 4 (<30 to 15 ml/min/1.73 m^{2}) and 5 (<15 ml/min/1.73 m^{2} or on dialysis) were merged into 1 group due to the small number of patients in group 5.

### Statistical analysis

Intraclass correlation coefficients (ICCs) were used for correlations between pairs of continuous variables, and Cohen's kappa index was used for categorical variables. Mean differences between scores and 95% limits of agreement (LoA) were analyzed using the Bland-Altman method (12). To compare ICCs and kappa values between pairing methods, we used bootstrap methods with 500 replicates. Cox proportional hazard regression models were used to model long-term survival as a function of the formulas. Good prediction was determined by discrimination and calibration (measures of performance). The D'Agostino-Nam version of the Hosmer-Lemeshow goodness-of-fit test was used to calculate a chi-square value (calibration describes how closely the predicted probabilities agree numerically with the actual outcomes) (13). A model is well calibrated when predicted and observed values agree for any reasonable grouping of the observation (no significant differences in Hosmer-Lemeshow goodness-of-fit test). The area under the receiver-operating characteristic curve (AUC) summarized the diagnostic discrimination (discrimination refers to a model's ability to correctly distinguish the 2 classes of outcomes). We used the index of rank correlation, Somers' D, which equals 2 × (c − 1/2), where c is the concordance (discrimination) probability (14). This test already incorporates information of censored data. The AUCs between models were compared using the U-statistic test for equality concordance. For each model, the Bayesian information criterion (BIC) was calculated; given any 2 estimated models, the model with the lower BIC value was preferred. No statistical test can be performed between different BIC estimations; the lower BIC is the better model. Reclassification between the Cockroft-Gault formula, MDRD-4 formula, and CKD-EPI equation from the Cox models were tested using net reclassification improvement (NRI) and integrated discrimination improvement (IDI), comparing quartiles of probability at 1,827 days. Analyses were performed with R, a language and environment for statistical computing, version 2.11.1 (R Foundation for Statistical Computing, Vienna, Austria).

## Results

A total of 925 patients (72% men; median age 69 years; interquartile range, 59 to 75.5 years) were studied (Table 1). The etiology of HF was mainly ischemic heart disease (56%). The median LVEF was 31% (interquartile range: 23.5% to 39%). A total of 143 patients (15.5%) in this cohort had LVEF ≥45% and 224 patients (24%) had LVEF ≥40%. Most patients were in New York Heart Association functional class II (55.6%) or III (36.3%). Median follow-up was 1,202 days (interquartile range: 627.5 to 2,156.5 days). The prevalence of renal insufficiency significantly differed according to the different formulas: 58% with the Cockroft-Gault formula, 49% with MDRD-4 formula, and 53% with CKD-EPI equation (p < 0.001 using the McNemar test). The distribution of patients by National Kidney Foundation groups according to the 3 formulas is shown in Table 2.

### Agreement of measurements

Figure 1 shows the correlation between formulas using scatterplot and Bland-Altman analysis. The Cockroft-Gault and MDRD-4 formula values were quite similar when the eGFR was low (<60 ml/min/1.73 m^{2}) (Fig. 1A, left). However, a systematic difference was found, with Cockroft-Gault values 2.96 points (mean) lower than MDRD-4 values (95% LoA, −27.1 to +21.1) (Fig. 1A, right). When the eGFR was high, differences between both formulas were very large, but a specific tendency was not shown. The Cockroft-Gault and CKD-EPI equation values were also quite similar when the eGFR was low (Fig. 1B, left), with Cockroft-Gault formula values 0.81 points (mean) lower than CKD-EPI equation values (95% LoA, −21.8 to +20.2) (Fig. 1B, right). When the Cockroft-Gault formula values were high, the CKD-EPI equation values were systematically lower. The MDRD-4 and CKD-EPI equation values were the most similar among the different formulas, especially at a low eGFR (Fig. 1C, left). MDRD-4 formula values were 2.16 points (95% LoA, −8.1 to +12.4) (Fig. 1C, right) lower than CKD-EPI values. The ICCs for the 3 formulas are shown in Table 3. Differences among the ICCs of the 3 pairings were all statistically significant as assessed by bootstrap methods (all p <0.001).

When patients were classified into 4 subgroups (as defined by the National Kidney Foundation) or only 2 subgroups (≥60 or <60 ml/min/1.73 m^{2}), the best agreement was found between the MDRD-4 and CKD-EPI formulas (kappa = 0.856 and 0.905, respectively) and the least between the Cockroft-Gault and MDRD-4 formulas (kappa = 0.627 and 0.720, respectively) (Table 3). Using the bootstrap method, differences in kappa values were statistically significant among all the combinations of the 3 formulas for the 2 classifications (4 subgroups and 2 subgroups) (all p values <0.001).

### Prediction, discrimination, and calibration

The 3 formulas were effective for the prediction of long-term mortality. However, the Cockroft-Gault formula was the most accurate, as evaluated by Cox proportional hazards models, AUC (Fig. 2,Table 4), and BIC (both analyzing the eGFR as a continuous or categorical variable) (Table 4). All 3 formulas performed correctly in terms of prognosis calibration, as shown by the Hosmer-Lemeshow goodness-of-fit test (Table 4).

Long-term survival Kaplan-Meier curves using the 3 formulas are shown in Figure 3. All of the formulas showed highly significant predictive prognostic values (log-rank test, p < 0.001). However, the 4 eGFR groups diverged in a more pronounced way with the Cockroft-Gault formula: chi-square values were 104.0 for Cockroft-Gault formula versus 70.0 for the CKD-EPI and 69.9 for MDRD-4 formulas. Even after adjustment for other important HF covariates (age, sex, New York Heart Association functional class, LVEF, HF etiology, diabetes, plasma urea levels, recent HF hospital admission, and treatment with beta-blockers and angiotensin-converting enzyme inhibitors), the Cockroft-Gault formula remained the most accurate for predicting mortality.

We analyzed the performance of the 3 formulas for patients with an LVEF ≥40% (n = 224) and those with an LVEF <40% (n = 701). Cockroft-Gault formula remained the most accurate formula for predicting survival in patients with a preserved LVEF and in patients with a reduced LVEF.

Comparing clinical characteristics of patients of the different eGFR subgroups according to the classification obtained with each formula, Cockroft-Gault formula patients with an eGFR ≥90 ml/min/1.73 m^{2} were younger (p = 0.003) and had a higher body mass index (p = 0.002). In contrast, Cockroft-Gault formula patients with an eGFR <30 ml/min/1.73 m^{2} were older (p = 0.004) and had lower body weight (p = 0.026) compared with MDRD and CKD-EPI formula patients, respectively. No differences in the other clinical characteristics were found among the formulas.

Reclassification of patients according to quartiles of the probability of dying at 1,827 days showed an NRI of 21.02% (95% confidence interval [CI]: 12.75 to 29.29; p < 0.001) when comparing the Cockroft-Gault formula with the MDRD-4 formula and an NRI of 13.10% (95% CI: 5.6 to 20.6; p < 0.001) when comparing the Cockroft-Gault formula with the CKD-EPI equation. The comparison of the MDRD-4 and CKD-EPI equations favored the CKD-EPI equation (NRI of 8.58%; 95% CI: 4.27 to 12.89; p < 0.001). In sum, the Cockroft-Gault formula reclassified 1 of 5 patients better compared with the MDRD-4 formula and 1 of 8 patients compared with the CKD-EPI equation. Reclassification using IDI also highly significantly favored the Cockroft-Gault formula (IDI of 5.04 [95% CI: 4.1 to 5.97] vs. the MDRD-4 formula; p < 0.001 and IDI: 3.77 [95% CI: 3.05 to 4.49] vs. the CKD-EPI equation; p < 0.001). On the other hand, the CKD-EPI equation did better than the MDRD-4 formula (IDI of 1.27; 95% CI: 0.099 to 1.55; p < 0.001).

## Discussion

In this ambulatory, real-life cohort of HF patients, the Cockroft-Gault formula performed better for predicting death than the MDRD-4 formula or CKD-EPI equation. The improvement in risk assessment remained strong when it was estimated by means of statistical measures that evaluate model prediction, discrimination, and calibration.

According to the National Kidney Foundation practice guidelines (6), glomerular filtration is the best measurement to assess renal function, although it depends on various factors, including age, sex, and body surface area. In daily clinical practice, different formulas are used to estimate glomerular filtration from serum creatinine, age, sex, race, and weight. The Cockroft-Gault formula (7) was developed in a population study and shown to determine more precisely creatinine clearance in situations in which renal function is only slightly altered. The formula tends to overestimate glomerular filtration when the grade of renal dysfunction is greater, partly because it was developed to estimate creatinine clearance and not the GFR. However, an abundance of literature compares the formula with other measurements or estimations of the GFR. On the other hand, the MDRD-6 and MDRD-4 formulas (8–10) were studied in patients already diagnosed with renal insufficiency; as such, these formulas have less precision in patients with slight alterations in kidney function. The predictive values of both formulas for the estimation of the GFR were previously compared in the general population. Froissart et al. (15) observed that both formulas are much more precise with lower filtration rates, and the MDRD-4 formula appears to be more precise in the majority of categories analyzed with respect to isotopic filtration. However, the Cockroft-Gault formula seemed to fit better in studies of mild alterations in renal function, and it appeared to be better than the MDRD-4 formula in women 65 years of age and older with an eGFR <60 ml/min/1.73 m^{2}. Despite these differences, Froissart et al. concluded that both formulas have little precision and may inappropriately classify approximately 30% of the population. In 2009, Levey et al. (11) reported a new way to calculate glomerular filtration, the CKD-EPI equation, which they developed in a population of >16,000 participants. In addition to validating the formula, which takes into account serum creatinine, age, sex, and race, the study compared the formula with a variant of the MDRD formula (8) and found it to be more precise for classifying individuals with an eGFR >60 ml/min/1.73 m^{2}, but it still remained suboptimal. In our study of patients with HF, the best correlation among the formulas was between the MDRD-4 and CKD-EPI formulas. As with all formulas based on serum creatinine, these formulas are subject to the same bias as creatinine values, especially in overweight and underweight patients in whom muscle mass can influence the serum creatinine level. Small studies have been published in the past that compare the different methods of calculating the eGFR. Eastwood et al. (16) compared creatinine clearance in 24-h urine and the eGFR using the MDRD-4, CKD-EPI, and Cockroft-Gault formulas in a population of individuals from sub-Saharan Africa between the ages of 40 and 75 years who had low body mass index values and weight and a mean filtration rate of 84 ml/min/1.73 m^{2}. The filtration rate that was most similar to the rate calculated with the 24-h urine specimen was that calculated with the CKD-EPI equation, although surprisingly only when it was used without adjusting for the black race. The CKD-EPI equation and MDRD-4 formula were also compared in a study of Australian adults (17) in which the CKD-EPI equation determined a lower prevalence of renal insufficiency than the MDRD-4 formula. In contrast, the lower prevalence of renal insufficiency in our study was determined using the MDRD-4 formula.

Interest in analyzing the association between renal insufficiency and HF has grown over the past few years; as such, different methods and formulas to estimate renal function in these patients have been described. However, the eGFR formulas have not been exhaustively evaluated in patients with important comorbidities, such as HF itself. O'Meara et al. (18) analyzed 45 patients with advanced HF who were undergoing a pre-transplantation assessment and concluded that the MDRD formula, especially MDRD-1, is the most adequate for predicting renal function in these patients, finding it to have better precision than the Cockroft-Gault formula with respect to isotopic filtration. Subsequently, Smilde et al. (19) not only compared the precision of the different formulas for estimating renal function in 110 patients with different grades of HF and systolic dysfunction, but they were also the first investigators to analyze the prognostic values of the MDRD-6, MDRD-4, and Cockroft-Gault formulas with respect to isotopic filtration. In this study, the investigators concluded that the MDRD-6 formula was more accurate, despite a greater deviation, although all of the formulas tended to overestimate lower filtration rates and underestimate more elevated filtration rates, a finding that had also been reported in a healthy population.

In our study, the 3 eGFR formulas were shown to be valuable prognostic predictors, but the Cockroft-Gault formula had significantly better results. However, we did not compare the efficacy of the 3 eGFR formulas with respect to the actual filtration rate, as done in previous studies. Our objective was to assess the prognostic values of the mostly used formulas in clinical practice in HF patients. Smilde et al. (19) also looked at the prognostic value of isotopic filtration, which was the best predictor, as well as the value of the other formulas, finding MDRD and the simplified MDRD to have better predictive abilities and the Cockroft-Gault formula to have the worst predictive prognosis among the analyzed formulas. They looked at a composite end point of death, heart transplantation, myocardial infarction, primary percutaneous transluminal coronary angioplasty, or an admission because HF within 12 months, comparing their AUCs. In contrast, our larger study population (925 patients vs. 110 patients) and longer follow-up found the Cockroft-Gault formula to be the best prognostic predictor of mortality on long-term follow-up. The comparison made in our study is more comprehensive, incorporating new reclassification criteria. The Cockroft-Gault formula has demonstrated better prognostication because of the greatest value of AUC, the lowest BIC, the absence of statistical significance on the Hosmer-Lemeshow goodness-of-fit test, and the better results in the 2 reclassification tests used. Remarkably, the Cockroft-Gault formula better classified 1 of 5 patients compared with the MDRD-4 formula and 1 of 8 patients compared with the CKD-EPI equation. We do not have a clear explanation for the observed differences in the prognostic ability of the Cockroft-Gault formula. A possible explanation for the better predictive value of the Cockroft-Gault formula over the MDRD-4 and CKD-EPI formulas is that the patient's weight is included in the formula. This fact may be key because body mass index is known to be significantly associated with survival in HF patients (20).

The better predictive value of the Cockroft-Gault formula over the MDRD-4 formula was also observed in a short follow-up (1 year) study after acute myocardial infarction (21). Similar to our results, the investigators found that the Cockroft-Gault formula tends to calculate a lower eGFR than the MDRD-4 formula in the elderly and those with low body weight and a higher eGFR in young patients and those with high body weight. The investigators concluded that this fact largely explains why the Cockroft-Gault formula is better for predicting mortality. As in our case, the investigators found that the Cockroft-Gault formula classified a greater number of patients as having moderate and severe renal dysfunction than the MDRD-4 formula. This may partly be explained by HF patients being older, having impaired hemodynamics and renal perfusion, and being treated with angiotensin-converting enzyme inhibitors, angiotensin II receptor blockers, and other drugs that may influence eGFR estimation using these formulas.

### Study limitations

The study only compares the 3 formulas, and no gold standard study of GFR, such as an isotopic measurement, has been performed. We did not have data for the cystatin C levels of our patients or microalbuminuria. We cannot disregard the fact that, in a small number of patients, the reference weight during the first visit that was used for the Cockroft-Gault formula may not have been the true dry weight and could have been overestimated. Our population was a general HF population treated at a specific and multidisciplinary HF unit in a tertiary hospital, and most patients were referred from the cardiology department, resulting in relatively young men with HF of ischemic etiology and reduced LVEF. As such, the results that we obtained cannot necessarily be extrapolated to a global HF population. In addition, the almost exclusively white population limits the generalization of the findings.

## Conclusions

Of the 3 eGFR formulas used, the Cockroft-Gault formula was the most accurate for predicting death in ambulatory patients with HF.

## Acknowledgments

The authors acknowledge Beatriz González, Lucía Cano, and Roser Cabanes, nurses on the HF Unit, for data collection and their invaluable work on the HF Unit.

## Footnotes

All authors have reported that they have no relationships relevant to the contents of this paper to disclose.

- Abbreviations and Acronyms
- AUC
- area under the receiver-operating characteristic curve
- BIC
- Bayesian information criterion
- CI
- confidence interval
- CKD-EPI
- Chronic Kidney Disease Epidemiology Collaboration
- eGFR
- estimated glomerular filtration rate
- GFR
- glomerular filtration rate
- HF
- heart failure
- ICC
- intraclass correlation coefficient
- IDI
- integrated discrimination improvement
- LoA
- limits of agreement
- LVEF
- left ventricular ejection fraction
- MDRD
- Modification of Diet in Renal Disease
- NRI
- net reclassification improvement

- Received September 6, 2011.
- Revision received November 26, 2011.
- Accepted November 29, 2011.

- American College of Cardiology Foundation

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