Estimation of glomerular filtration rates before and after orthotopic liver transplantation: Evaluation of current equations

Authors


Abstract

The ability to estimate rather than measure the glomerular filtration rate (GFR) in patients before and after liver transplantation would be helpful in estimating risk, dosing drugs, and assessing long-term toxicity of calcineurin inhibitors. Currently available equations for estimating the GFR have not been validated in either the pre- or post-liver transplant population. We have evaluated the performance of currently used formulas for the estimation of the GFR in this setting. Data were collected prospectively on patients who underwent liver transplantation between 1984 and 2001. GFR per 1.73 m2 was measured by I125 iothalamate in patients at the pretransplant evaluation and at 3 months, 1 year, and yearly posttransplant thereafter. GFR estimated by the Cockcroft-Gault equation, the Nankivell equation, and the equations from the Modification of Diet in Renal Disease (MDRD) Study (6, 5, and 4 variables) was compared with the measured GFR. Pretransplant GFR was available in 1,447 patients. The mean GFR was 90.7 ± 40.5 mL/min. Values for r and r2 were highest for the MDRD Study 6-variable equation (0.70 and 0.49, respectively). Only 66% of estimates were within 30% of the measured GFR. At 3 months, 1 year, and 5 years posttransplant, the mean GFR was 59.5 ± 27.1 mL/min, 62.7 ± 27.8 mL/min, and 55.3 ± 26.1 mL/min, respectively. Values for r and r2 for the MDRD Study 6-variable equations at 1 and 5 years posttransplant were 0.74 (0.55) and 0.76 (0.58), respectively. At these time points, however, only 67% and 64% of the estimated GFR were within 30% of the measured GFR. MDRD Study equations had greater precision than other equations, but the precision was lower than reported for MDRD estimation of GFR in other populations. Better methods for estimating the GFR are required for evaluation of renal function before and after liver transplantation. (Liver Transpl 2004;10:301–309.)

Assessment of renal function in patients is critical, both before and after liver transplantation. Survival posttransplant can be correlated with pretransplant renal function, and the choice of initial immunosuppression may be dependent on the renal function of the patient.1–5 Furthermore, immunosuppressive drugs can be nephrotoxic, and liver transplant recipients can lose as much as 40% of their renal function posttransplant, presumably from the effect of immunosuppressive drugs.6, 7 Long-term follow-up of patients after liver transplantation demonstrates that as many as 10% to 25% of the total patients undergoing transplantation have severe chronic kidney disease by 10 years posttransplant. As many as 6% to 15% of the total patients undergoing transplantation may reach end-stage renal disease in the same time period.8–10

Numerous studies have documented that simple assessment of renal function in cirrhotic patients by measurement of serum creatinine is inadequate. The “gold standard” for evaluation of renal function is direct measurement of the glomerular filtration rate (GFR) by use of inulin clearance or other validated filtration markers, such as iothalamate. However, these measurements can be time-consuming and costly. Therefore, the estimation of GFR through equations that use commonly available clinical variables would be extremely useful in this patient population. Commonly used equations for the estimation of GFR or creatinine clearance have not been validated in either the cirrhotic or the postliver transplant population. A recently published review of all currently available studies illustrates the problems and pitfalls associated with the use of commonly available equations for estimating the GFR in patients with end-stage liver disease.11 This study evaluates the utility of equations for estimating the GFR before and after liver transplantation. We have used commonly available equations including the Cockcroft-Gault (derived for use in clinical practice for patients without severe renal disease), the Nankivell (derived for use in renal transplant recipients being treated with calcineurin inhibitors), and the Modification of Diet in Renal Disease (MDRD) Study equations (derived for use in patients with moderate renal disease).

Abbreviations

GFR, glomerular filtration rate; MDRD, modification of diet in renal disease; Ccr, creatinine clearance; BUN, blood urea nitrogen; CG, Cockcroft-Gault; Nank, Nankivell; r, correlation coefficient; r2, coefficient of determination; S0I, slope with 0 intercept.

Materials and Methods

Starting in 1984, the liver transplant program at Baylor University Medical Center has maintained a prospectively collected database on liver transplant recipients. This has been previously described.6, 7, 9 Part of the pretransplant evaluation and posttransplant follow-up of these patients is the measurement of GFR using I125-iothalamate clearance.12, 13 GFR per 1.73 m2 is measured in patients at the pretransplant evaluation, at 3 months posttransplant, and at yearly evaluations. Other clinical data are also collected at these same time points. This database of 1,447 patients served as the source for this study. Patients were included in the study if they had a GFR determination performed. There were no exclusions. Patients were included in the analysis if they had the data necessary for the calculated GFR to compare with a measured GFR. There were no exclusions. The Institutional Review Board of Baylor University Medical Center approved the study. The database was queried for the GFR of patients pretransplant and at 3 months, 1 year, and 5 years posttransplant. Patients who underwent transplantation between 1984 and 2001 were used for the study. The database was further queried for clinical variables necessary to estimate GFR or creatinine clearance with equations commonly used in clinical practice. The following equations, shown in Table 1, were used: Cockcroft-Gault,14 Nankivell,15 and the equations derived from the MDRD Study.16, 17 From the latter study, we used the 4-, 5-, and 6-variable equations (MDRD 4, MDRD 5, MDRD 6). The calculated GFR or creatinine clearance was then compared with the measured GFR at the following time points: initial evaluation (cirrhotic patient) and 3 months, 1 year, and 5 years posttransplant. All transplant recipients were maintained on calcineurin inhibitors, with more than 70% maintained on cyclosporine. All patients received corticosteroids early in their posttransplant course, but in the later years, steroids were withdrawn after 3 months. Trimethoprim (an inhibitor of tubular secretion of creatinine) and sulfamethoxazole (Bactrim [Roche, USA, Nutley, NJ] 1 single-strength tablet daily) was routinely prescribed for the first 12 months after transplantation. Inhibition of tubular secretion of creatinine would be expected to contribute to systematic error in GFR estimates for all equations at the 3-month and 1-year time point, but not later. Serum creatinine measurements were not recalibrated in the laboratories in which the GFR estimation equations were developed. As reported previously, differences resulting from the calibration of serum creatinine assay between the Baylor University Medical Center clinical laboratory and the laboratories in which the GFR estimation equations were developed would be expected to contribute to systematic error in GFR estimates.18 This latter source of error would vary among equations and be present at all time points before and after transplantation.

Table 1. Equations Utilized in Study
  1. Abbreviations: CCr, creatinine clearance; GFR, glomerular filtration rate; BUN, blood urea nitrogen; MDRD, Modification of Diet in Renal Disease.

1. Cockcroft-Gault:CCr (male) = Ideal body weight ([140 − age)]/72 × serum creatinine mg/dl])
 CCr (female) = 0.85 × Ideal body weight ([140 − age)]/72* serum creatinine mg/dl])
2. Nankivell:GFR = 6.7/serum creatinine (mmol/L) + body weight (kg)/4 − BUN (mmol/L)/2-100/height2 (m) + 35 (male) or 25 (female)
3. MDRD 4:GFR = 186 × creatinine (mg/dl)−1.154 × age−0.203 × 1.212 (if black) × 0.742 (if female)
4. MDRD 5:GFR = 270 × creatinine (mg/dl)−1.007 × age−0.180 × 1.178 (if black) × 0.762 (if female) × serum urea nitrogen−0.169
5. MDRD 6:GFR = 170 × creatinine (mg/dl)−0.999 × age−0.176 × 1.180 (if black) × 0.762 (if female) × serum urea nitrogen−0.170 × albumin0.138

Statistical analysis for bias and precision of the equations included correlation with GFR (r), coefficient of determination (r2, a measurement of precision), and slope with 0 intercept (a measurement of bias). To evaluate the accuracy of the prediction equations, the following were evaluated: average absolute difference between measured and estimated GFR, median absolute difference between measured and estimated GFR, 75th percentile difference, 90th percentile difference, average percent difference between GFR and the predictions with the 50th, 75th, and 90th percentile of percent difference, and the percent of predictions within 30% and 50% of GFR. Measures of bias and accuracy are affected by systematic error that may result from inhibition of creatinine secretion and differences among laboratories in calibration of serum creatinine assay. All analyses were performed both on the linear and log-transformed scales for measured and estimated GFR. All statistical analysis was performed with the SAS statistical package (SAS Institute, Cary, NC) and was similar to that reported previously by one of the authors.17

Results

Pretransplant GFR determinations were available for 1,447 patients. The mean age at the time of initial evaluation for transplant was 48.69 ± 10.65 years with a range of 13 to 72 years. The population was comprised of African American (6.72%) and male (53.78%) patients. Variables necessary to determine the Cockcroft-Gault, Nank, and MDRD equations were available in 1,437, 1,419, and 1,447 patients, respectively. The mean (SD) serum creatinine of the entire group at the initial pretransplant evaluation was 1.14 (0.88) mg/dL with a median value of 0.90 mg/dL. Table 2 lists the actual GFR per 1.73 m2 determinations in these patients and the predicted values obtained by the Cockcroft-Gault, Nankivell, MDRD 4, MDRD 5, and MDRD 6 equations. Presented are the correlation coefficient (r), the coefficient of determination (r2) between the measured and estimated GFR, and the slope of the 0 intercept line. These 3 analyses evaluate bias and precision. The coefficient of determination measures the proportion of the variation in the response that is attributable to the model rather than random error. Values range from 0 to 1. A value of 1 indicates that that the variable can be predicted exactly from the model. The closer the value is to 1, the closer the determinations cluster along the correlation line. The slope of the 0 intercept is used to compare the correlation to the ideal correlation of 1. The greater the slope is more than 1, the more the formula underestimates the true value. Conversely, the more this value is less than 1, the more the formula overestimates the true value. Bias includes systematic error that may result from inhibition of tubular secretion of creatinine in patients taking sulfamethoxazole and systematic error that may result from differences in calibration of serum creatinine assays. Also shown are the median absolute difference between predicted and measured GFR, the percent of estimations that were within 30% of the actual value, and the percent of estimations within 50% of the actual value. These 3 analyses are a measure of the accuracy of the predictions and are affected by both precision and bias. As can be seen in Table 2, the MDRD Study equations were associated with the greatest precision (r and r2 of 0.672–0.698 and 0.452–0.488, respectively), but limited accuracy (percent of estimates within 30% of measured GFR of 66.32–68.90) because of greater bias. The Nank equation overestimated the true GFR, whereas the other 4 equations underestimated the true GFR.

Table 2. GFR and Predictive Equations at Time of Initial Evaluation
Method (n)GFR ± SD (ml/min)Bias and PrecisionAccuracy
rr2S0IMAD*% 30% 50
  • Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r2, coefficient of determination; S0I, slope with 0 intercept; MAD, median absolute difference; CG, Cockcroft-Gault; Nank, Nankivell; MDRD, Modification of Diet in Renal Disease.

  • *

    MAD between prediction and GFR.

  • % of predictions within 30% of GFR.

  • % of predictions within 50% GFR.

GFR (1,447)90.7 ± 40.51.0001.0001.00000.00100100
CG (1,437)82.2 ± 34.10.6470.4191.056419.5960.8283.58
Nank (1,419)95.2 ± 30.10.6530.4270.948218.4763.5780.13
MDRD 4 (1,447)83.8 ± 34.50.6720.4521.040517.5166.6986.39
MDRD 5 (1,447)85.9 ± 35.70.6920.4801.017115.8068.9085.63
MDRD 6 (1,447)78.1 ± 32.90.6980.4881.115917.4466.3287.63

Previous investigators have demonstrated that equations to estimate GFR tend to overestimate the true GFR in cirrhotic patients.11 This, however, was usually in the setting of renal dysfunction. We therefore reanalyzed the data by dividing the patients into 2 groups: those with a measured GFR less than 40 mL/min and those with a measured GFR greater than 40 mL/min. The results of this analysis are shown in Table 3. As would be expected, the equations consistently overestimated the GFR in the setting of decreased renal function. Also demonstrated is that the elimination of these patients from the analysis did nothing to improve the precision of the equations.

Table 3. Comparison of Predictive Equations in Patients With GFR Above and Below 40 cc/min at Initial Evaluation
MethodGFR < 40 ml/minGFR > 40 ml/min
(n)GFR ± SDrr2(n)GFR ± SDRR2
  1. Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r2, coefficient of determination; CG, Cockcroft-Gault; Nank, Nankivell; MDRD, Modification of Diet in Renal Disease.

GFR(155)22.6 ± 11.11.0001.000(1,218)99.4 + 34.51.0001.000
CG(151)46.1 ± 27.10.2420.059(1,213)85.8 + 31.80.5880.345
Nank(148)58.0 ± 28.30.3000.090(1,198)99.0 + 26.80.5710.327
MDRD 4(155)44.5 ± 28.80.2290.052(1,218)87.8 + 31.60.6100.372
MDRD 5(155)43.9 ± 29.30.2270.052(1,218)90.5 + 32.50.6290.396
MDRD 6(155)39.0 ± 26.20.2240.050(1,218)82.4 + 30.10.6340.402

We next evaluated the value of these equations in estimating the GFR in the posttransplant setting. Posttransplant, many of the metabolic abnormalities of liver disease and cirrhosis have cleared. Results at 3 months, 1 year, and 5 years posttransplant are demonstrated in Tables 4–6. The mean (SD) serum creatinine at these time points was 1.46 (0.77) (median 1.30) mg/dL, 1.56 (0.58) (median 1.50) mg/dL, and 1.73 (0.70) (median 1.60) mg/dL, respectively. As can be seen, there was no improvement of the predictive value of the equations at 3 months. Serum creatinine and measured GFR at 3 months were both lower than at 1 year. This probably reflects a combination of improvement in renal function and gain in muscle mass. The effect of discontinuing sulfamethoxazole would be to decrease serum creatinine for each level of GFR, therefore obscuring the effect of gain in muscle mass. Perhaps because of these factors, values for r and r2 are lowest for the estimates at 3 months.

Table 4. GFR and Predictive Equations 3 Months Posttransplant
MethodGFR ± SD (ml/min)Bias and PrecisionAccuracy
rr2S0IMAD*% 30% 50
  • Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r2, coefficient of determination; S0I, slope with 0 intercept; MAD, median absolute difference; CG, Cockcroft-Gault; Nank, Nankivell; MDRD, Modification of Diet in Renal Disease.

  • *

    MAD between prediction and GFR.

  • % of predictions within 30% of GFR.

  • % of predictions within 50% GFR.

GFR (997)59.5 ± 27.11.0001.0001.00000.00100100
CG (837)61.4 ± 26.70.5690.3240.915414.4156.6378.85
Nank (698)70.3 ± 23.90.6070.3680.840416.8354.7372.49
MDRD 4 (887)59.6 ± 27.00.6140.3760.932812.5061.5684.55
MDRD 5 (887)56.7 ± 25.00.6410.4100.990512.5662.4685.34
MDRD 6 (887)55.3 ± 24.30.6580.4331.020112.2063.1387.15
Table 5. GFR and Predictive Equations 1 Year Posttransplant
MethodGFR ± SD (ml/min)Bias and PrecisionAccuracy
rr2S0IMAD*% 30% 50
  • Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r2, coefficient of determination; S0I, slope with 0 intercept; MAD, median absolute difference; CG, Cockcroft-Gault; Nank, Nankivell; MDRD, Modification of Diet in Renal Disease.

  • *

    MAD between prediction and GFR.

  • % of predictions within 30% of GFR.

  • % of predictions within 50% GFR.

GFR (1,297)62.7 ± 27.81.0001.0001.00000.00100100
CG (1,220)55.1 ± 22.90.6710.4511.095012.7263.7789.92
Nank (555)64.1 ± 20.30.6610.4370.966913.2662.8881.98
MDRD 4 (1,297)52.8 ± 21.40.7220.5221.151411.2268.3192.21
MDRD 5 (1,297)51.1 ± 20.80.7340.5391.192011.9667.0092.52
MDRD 6 (1,297)50.8 ± 20.50.7420.5511.203711.7767.3193.14
Table 6. GFR and Predictive Equations 5 Years Posttransplant
MethodGFR ± SD (ml/min)Bias and PrecisionAccuracy
rr2S0IMAD*% 30% 50
  • Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r2, coefficient of determination; S0I, slope with 0 intercept; MAD, median absolute difference; CG, Cockcroft-Gault; Nank, Nankivell; MDRD, Modification of Diet in Renal Disease.

  • *

    MAD between prediction and GFR.

  • % of predictions within 30% of GFR.

  • % of predictions within 50% GFR.

GFR (521)55.3 + 26.11.0001.0001.00000.00100100
CG (491)46.4 + 20.40.6720.4521.134210.9463.7587.37
Nank (177)58.7 + 19.40.6920.4790.969712.4558.1981.36
MDRD 4 (521)45.9 + 18.90.7470.5581.17969.9265.6491.55
MDRD 5 (521)44.6 + 18.50.7570.5741.213810.7563.3491.94
MDRD 6 (521)44.1 + 18.30.7630.5811.228610.4763.5392.13

At 1 year posttransplant, the MDRD equations had improved in bias, precision, and accuracy. The correlation between measured and estimated GFR in all 3 MDRD equations had increased to more than 0.70 and the r2 had increased to more than 0.50. Furthermore, the median and absolute difference was lower and the percent of predictions within 50% increased to more than 90%. Despite this, the MDRD equations tended to underestimate the true GFR, as did the Cockcroft-Gault. The average Nankivell estimate was numerically closest to the true GFR, but the bias, precision, and accuracy measurements were poor.

We performed an analysis at these 3 time points for those patients with a GFR greater than and less than 40 mL/min. Similar to the results at the initial evaluation, the equations overestimated GFR in patients with a GFR less than 40 mL/min and underestimated the GFR in patients with a GFR greater than 40 mL/min. This improved with time after transplantation, but the correlation was poor. Data from 1 year and 5 years posttransplant are shown in Table 7.

Table 7. Comparison of Predictive Equations in Patients With GFR Above and Below 40 cc/min at 1 and 5 Years Posttransplant
1 Year Posttransplant
MethodGFR < 40 ml/minGFR > 40 ml/min
(n)GFR ± SDrr2(n)GFR ± SDrr2
GFR(270)30.1 ± 7.51.0001.000(913)71.4 ± 23.91.0001.000
CG(242)35.0 ± 10.70.2550.065(867)58.8 ± 21.20.5770.333
Nank(119)46.0 ± 13.10.3460.119(416)68.8 ± 18.60.5220.305
MDRD 6(270)31.4 ± 9.00.4500.202(913)54.7 ± 18.40.6570.432
5 Years Posttransplant
MethodGFR < 40 ml/minGFR > 40 ml/min
(n)GFR ± SDrr2(n)GFR ± SDrr2
  1. Abbreviations: GFR, glomerular filtration rate; R, correlation coefficient; R2, coefficient of determination; CG, Cockcroft-Gault; Nank, Nankivell; MDRD, Modification of Diet in Renal Disease; n, number of determinations.

GFR(146)28.8 ± 9.21.0001.000(324)66.6 ± 20.61.0001.000
CG(140)29.8 ± 9.80.3400.116(303)50.8 ± 19.20.5380.29
Nank(55)42.7 ± 15.50.5960.355(117)65.9 ± 16.10.5590.312
MDRD 6(146)28.1 ± 9.20.5640.318(324)49.6 ± 16.10.6470.419

The scatter plots comparing the measured GFR to the estimated GFR for selected equations are presented in Figs. 1 to 3. Figure 1 compares the Cockcroft-Gault equation at pretransplant evaluation and at 3 months, 1 year, and 5 years posttransplant. All r values are less than 0.7. Note that the regression line intercepts the y-axis above 0. Examination of the plots illustrates the data from Tables 3 and 7, that is, the equations overestimate at the lower GFR values and underestimate at the higher GFR values. Results for the 6-variable MDRD equation and the Nankivell equation are presented in Figs. 2 and 3. The results are similar to those for the Cockcroft-Gault. The regression equations for all of the plots are presented in Table 8.

Figure 1.

Creatinine clearance predicted by the Cockcroft-Gault equation compared with the glomerular filtration rate (GFR) per 1.73 m2 measured by I125-iothalamate at the pretransplant evaluation and at 3 months, 1 year, and 5 years posttransplant.

Figure 2.

GFR predicted by the 6-variable Modification of Diet in Renal Disease (MDRD) equation compared with GFR per 1.73 m2 measured by I125-iothalamate at the pretransplant evaluation and at 3 months, 1 year, and 5 years posttransplant.

Figure 3.

GFR predicted by the Nankivell equation compared with GFR per 1.73 m2 measured by I125-iothalamate at the pretransplant evaluation and at 3 months, 1 year, and 5 years posttransplant.

Table 8. Regression Equations for Comparing Calculated GFR to Measured GFR
Cockcroft-Gault
PretransplantGFR = 27.66071 + 0.776781 × CG
3 months postGFR = 25.64229 + 0.569141 × CG
1 year postGFR = 17.07224 + 0.842556 × CG
5 years postGFR = 16.82167 + 0.85794 × CG
MDRD 6 Variable
PretransplantGFR = 23.68275 + 0.864908 × MDRD
3 months postGFR = 17.41549 + 0.771961 × MDRD
1 year postGFR = 9.417705 + 1.065179 × MDRD
5 years postGFR = 7.080935 + 1.112458 × MDRD
Nankivell
  1. Abbreviations: GFR, glomerular filtration rate; CG, Cockcroft-Gault; MDRD, Modification of Diet in Renal Disease; Nank, Nankivell.

PretransplantGFR = 7.160441 + 0.885988 × Nank
3 months postGFR = 10.16776 + 0.726897 × Nank
1 year postGFR = 4.372697 + 0.905875 × Nank
5 years postGFR = −1.959625 + 0.990234 × Nank

We next performed log transformations of the GFR and the estimated GFR as described in the derivation of the MDRD equations16 (data not shown). This model uses the log of the model to predict log (GFR). The average calculated r2 was compared across time points for the untransformed data and log calculations. In every case, calculating r2 for log (GFR) versus log (model) gave higher r2 values compared with the transformed data. This was true whether or not the models were derived using logs (as the MDRD equations were). The average increases ranged from 0 for Nankivell to 0.051 for MDRD. For models including the 3 MDRD models, these increases were statistically significant (P < .05), whereas they were not for the remaining models. The average increase ranged from 0.038 to 0.051 for the MDRD group and from 0 to 0.029 for the other models. Calculating r2 on the basis of logs may give a relatively small advantage to the MDRD equations that were developed using logs. In any case, the magnitudes of the r2 values are similar and rarely exceeded 0.6.

Discussion

Patients presenting for liver transplantation have varying degrees of renal dysfunction. Much of this may be attributable to the changes in renal circulation associated with liver disease and some of it to fixed renal disease.19 Before making decisions on suitability for transplant, need for combined kidney liver transplant, or the best immunosuppression for each patient, accurate knowledge of the patient's true GFR is necessary.1–5 Furthermore, because of the known nephrotoxicity of immunosuppressive drugs, particularly calcineurin inhibitors, careful assessment of the patient's renal function postoperatively is needed.6–10 In the pretransplant cirrhotic patient, the estimation of GFR with the Cockcroft-Gault equation and other older equations has been shown to be inaccurate.11 It is generally accepted that these equations overestimate GFR. Furthermore, there are no data available in the literature as to the validity of equations in estimating GFR in the postliver transplant population. We therefore undertook the current study to evaluate the performance of known equations in these 2 populations.

In addition to the equations described here, we also used other lesser-known equations such as the 1/serum creatinine, Jeliffe, Sanaka, and Walser-Drew-Guldan equations. These proved no better or worse than the ones presented here (data not shown). We chose to concentrate on commonly used equations. The Cockcroft-Gault equation was chosen because of its widespread use in clinical practice. The Nankivell equation was originally derived to estimate GFR in renal transplant recipients being treated with cyclosporine.15 We chose this equation for evaluation because our patients were also receiving calcineurin inhibitors. The equations derived from the MDRD study are well known and accepted as reasonably accurate. In the MDRD Study, r and r2 for the 6-variable equation were 0.95 and 0.903, respectively, and the percent of estimates within 30% and 50% of measured GFR were 91% and 98%, respectively. However, the MDRD Study equations were derived from nontransplant patients with a lower mean GFR (40 mL/min/1.73 m2), consistent with moderate-to-advanced renal insufficiency.16, 17 We chose to evaluate all 3 variations of these equations because of the high incidence of renal insufficiency in the postliver transplant population.

The results of these analyses are interesting. Precision (r and r2) was substantially less than previously reported for all equations. The MDRD Study equations were the most precise but were also associated with higher estimates of bias (S01) than other equations. Despite this, the MDRD Study equations had higher accuracy than other equations. In general, approximately 65% to 70% of estimates were within 30% of the measured GFR.

Greater precision of the MDRD Study equations compared with other equations is consistent with observations in other clinical populations.20 We suspect that reduced precision of the MDRD Study equation in this study reflects differences in muscle mass compared with that found in patients without liver disease or requiring liver transplantation. Differences in bias among equations likely reflect differences in calibration of serum creatinine assays.18 Because of differences in calibration of serum creatinine assay, it is difficult to make definitive conclusions about the utility of equations based on estimates of accuracy.

As shown in Table 2, the equations seemed to underestimate GFR in the general cirrhotic population presenting for liver transplant evaluation. Previous reports11 clearly showed that predictive equations tended to overestimate the true GFR in cirrhotic patients. Most of those studies were evaluating the patient with severe cirrhosis including ascites. These patients tend to have decreased GFR, in part because of the liver disease and malnourishment, which would artificially lower creatinine out of proportion to the GFR. Our overall population may have been better nourished or not as ill as in previous studies. However, the mean serum albumin of patients presenting for evaluation in our center was 3.04 ± 0.63 gm/L. When we divided the patients into 2 groups based on GFR, an interesting split was seen (Table 3). The patients with poor function (GFR < 40 mL/min) had their GFR overestimated by all the equations. This is consistent with published studies. The patients with reasonable renal function (GFR > 40 mL/min) had their GFR underestimated by the equations. This may be accounted for by the fact that these equations, particularly the MDRD, were derived in patients with chronic kidney disease and may not be useful in patients with a relatively normal GFR. Given the poor correlation and accuracy demonstrated in Table 2, direct measurement of the GFR is preferable to the use of these equations in the cirrhotic patient undergoing pretransplant evaluation.

Posttransplant, the equations did not perform at a higher level. At 3 months, many of the metabolic abnormalities of liver disease had cleared. However, the patients' true GFRs were not accurately estimated by any of the equations (Table 4). Although the mean GFR estimates were close to the mean GFR, the accuracy and precision was poor as manifested by all of the parameters tested. This may have been because of the routine use of sulfamethoxazole and higher dose of immunosuppressive agents at 3 months compared with later time periods. All of these may have effects on the equations (e.g., raising blood urea nitrogen) that are independent of the GFR. Accuracy of GFR estimates was lowest at this time point.

At 1 and 5 years posttransplant, the patients are generally stable, and as a population resemble a patient with chronic kidney disease. This may be the reason that the MDRD equations have the best precision and accuracy, because they were derived in a population of patients with chronic kidney disease. However, despite a higher precision, they do not accurately estimate the true GFR in this population of patients. This is true even if one compares the log-transformed equations to the log-transformed GFR (data not shown). Furthermore, the MDRD equations actually underestimate the GFR. In addition to the effects of bias caused by differences in calibration of serum creatinine assay, this may be secondary to the effect of calcineurin inhibitors on creatinine and blood urea nitrogen that may be independent of GFR.21 The water loading that is part of the iothalamate method of GFR measurement may partially reverse the renal vasoconstriction present in calcineurin-treated patients and increase the GFR. Conversely, cyclosporine-treated patients have an increased tubular reabsorption of urea that may lead the MDRD equations to underestimate the true GFR.21 Regardless of the cause, accuracy of the equations remained limited (∼65% of estimates within 30% of measured GFR).

This study demonstrates that care should be taken when attempting to estimate the GFR. Current equations were derived in specific populations and may not be applicable in other populations of patients. Serum creatinine needs to be calibrated similar to the way it was calibrated in the laboratory in which the prediction equation was developed. If an accurate measurement of GFR is needed, one should perform a clearance study using a validated filtration marker, such as iothalamate, iohexol, or inulin. Newer filtration markers for estimating GFR, such as cystatin C measurement,22–24 need to be verified in large populations. In using equations that were derived in large populations, it is difficult to determine if there are subgroups of patients in whom the equations may be more useful. This is illustrated in our attempt to determine whether there were better correlations based on the true GFR (Table 3). It is unlikely that models, which are not precise enough to predict GFR well, are precise enough to reliably identify subgroups of patients in whom the models will work. However, further analysis of this question is ongoing, and perhaps we will be able to identify subgroups of patients in whom the equations are useful. This could be based on physiologic, biopsy, or disease subgroups. Furthermore, new disease-specific equations for estimating the GFR in the cirrhotic patient and the posttransplant patient are needed. We are attempting to determine which variables can be included to modify the existing equations to make them more reliable.

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