From the 1 Department of Transplantation, Mayo Clinic, Jacksonville, FL; 2 Baylor Regional Transplant Institute, Dallas, TX; 3 Division of

Estimation of Glomerular Filtration Rates Before and After Orthotopic Liver Transplantation: Evaluation of Current Equations Thomas A. Gonwa, 1 Linda Jennings, 2 Martin L. Mai, 1 Paul C. Stark, 3 Andrew S. Levey, 4 and Goran B. Klintmalm 2 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 m 2 was measured by I 125 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 r 2 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 r 2 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 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; r 2, coefficient of determination; S0I, slope with 0 intercept. From the 1 Department of Transplantation, Mayo Clinic, Jacksonville, FL; 2 Baylor Regional Transplant Institute, Dallas, TX; 3 Division of Clinical Care Research, Tufts-New England Medical Center, Boston, MA; and 4 Division of Nephrology, Tufts-New England Medical Center, Boston, MA. This work was presented in part at the annual meeting of the American Society of Nephrology, November 2002, Philadelphia, Pennsylvania. Address reprints to Thomas A Gonwa, MD, FACP, Department of Transplantation, Mayo Clinic Jacksonville, 4205 Belfort Road, Suite 1100, Jacksonville, FL 32216. Telephone: 904-296-9075; FAX: 904-296-5874; E-mail: Gonwa.Thomas@mayo.edu Copyright 2004 by the American Association for the Study of Liver Diseases Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/lt.20017 Liver Transplantation, Vol 10, No 2 (February), 2004: pp 301 309 301

302 Gonwa et al. Table 1. Equations Utilized in Study 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/height 2 (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 albumin 0.138 Abbreviations: CCr, creatinine clearance; GFR, glomerular filtration rate; BUN, blood urea nitrogen; MDRD, Modification of Diet in Renal Disease. 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). 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 I 125 -iothalamate clearance. 12,13 GFR per 1.73 m 2 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. Statistical analysis for bias and precision of the equations included correlation with GFR (r), coefficient of determination (r 2, 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

Estimation of GFR Before and After OLT 303 Table 2. GFR and Predictive Equations at Time of Initial Evaluation Bias and Precision Accuracy Method (n) GFR SD (ml/min) r r 2 S0I MAD* % 30 % 50 GFR (1,447) 90.7 40.5 1.000 1.000 1.0000 0.00 100 100 CG (1,437) 82.2 34.1 0.647 0.419 1.0564 19.59 60.82 83.58 Nank (1,419) 95.2 30.1 0.653 0.427 0.9482 18.47 63.57 80.13 MDRD 4 (1,447) 83.8 34.5 0.672 0.452 1.0405 17.51 66.69 86.39 MDRD 5 (1,447) 85.9 35.7 0.692 0.480 1.0171 15.80 68.90 85.63 MDRD 6 (1,447) 78.1 32.9 0.698 0.488 1.1159 17.44 66.32 87.63 Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r 2, 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. 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 m 2 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 (r 2 ) 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 r 2 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. 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. 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

304 Gonwa et al. Table 3. Comparison of Predictive Equations in Patients With GFR Above and Below 40 cc/min at Initial Evaluation Method (n) GFR SD r r 2 (n) GFR SD R R 2 GFR (155) 22.6 11.1 1.000 1.000 (1,218) 99.4 34.5 1.000 1.000 CG (151) 46.1 27.1 0.242 0.059 (1,213) 85.8 31.8 0.588 0.345 Nank (148) 58.0 28.3 0.300 0.090 (1,198) 99.0 26.8 0.571 0.327 MDRD 4 (155) 44.5 28.8 0.229 0.052 (1,218) 87.8 31.6 0.610 0.372 MDRD 5 (155) 43.9 29.3 0.227 0.052 (1,218) 90.5 32.5 0.629 0.396 MDRD 6 (155) 39.0 26.2 0.224 0.050 (1,218) 82.4 30.1 0.634 0.402 Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r 2, coefficient of determination; CG, Cockcroft-Gault; Nank, Nankivell; MDRD, Modification of Diet in Renal Disease. 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 r 2 are lowest for the estimates at 3 months. 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 r 2 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. 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 Table 4. GFR and Predictive Equations 3 Months Posttransplant Bias and Precision Accuracy Method GFR SD (ml/min) r r 2 S0I MAD* % 30 % 50 GFR (997) 59.5 27.1 1.000 1.000 1.0000 0.00 100 100 CG (837) 61.4 26.7 0.569 0.324 0.9154 14.41 56.63 78.85 Nank (698) 70.3 23.9 0.607 0.368 0.8404 16.83 54.73 72.49 MDRD 4 (887) 59.6 27.0 0.614 0.376 0.9328 12.50 61.56 84.55 MDRD 5 (887) 56.7 25.0 0.641 0.410 0.9905 12.56 62.46 85.34 MDRD 6 (887) 55.3 24.3 0.658 0.433 1.0201 12.20 63.13 87.15 Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r 2, 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.

Estimation of GFR Before and After OLT 305 Table 5. GFR and Predictive Equations 1 Year Posttransplant Bias and Precision Accuracy Method GFR SD (ml/min) r r 2 S0I MAD* % 30 % 50 GFR (1,297) 62.7 27.8 1.000 1.000 1.0000 0.00 100 100 CG (1,220) 55.1 22.9 0.671 0.451 1.0950 12.72 63.77 89.92 Nank (555) 64.1 20.3 0.661 0.437 0.9669 13.26 62.88 81.98 MDRD 4 (1,297) 52.8 21.4 0.722 0.522 1.1514 11.22 68.31 92.21 MDRD 5 (1,297) 51.1 20.8 0.734 0.539 1.1920 11.96 67.00 92.52 MDRD 6 (1,297) 50.8 20.5 0.742 0.551 1.2037 11.77 67.31 93.14 Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r 2, 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. 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. We next performed log transformations of the GFR and the estimated GFR as described in the derivation of the MDRD equations 16 (data not shown). This model uses the log of the model to predict log (GFR). The average calculated r 2 was compared across time points for the untransformed data and log calculations. In every case, calculating r 2 for log (GFR) versus log (model) gave higher r 2 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 r 2 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 r 2 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 Table 6. GFR and Predictive Equations 5 Years Posttransplant Bias and Precision Accuracy Method GFR SD (ml/min) r r 2 S0I MAD* % 30 % 50 GFR (521) 55.3 26.1 1.000 1.000 1.0000 0.00 100 100 CG (491) 46.4 20.4 0.672 0.452 1.1342 10.94 63.75 87.37 Nank (177) 58.7 19.4 0.692 0.479 0.9697 12.45 58.19 81.36 MDRD 4 (521) 45.9 18.9 0.747 0.558 1.1796 9.92 65.64 91.55 MDRD 5 (521) 44.6 18.5 0.757 0.574 1.2138 10.75 63.34 91.94 MDRD 6 (521) 44.1 18.3 0.763 0.581 1.2286 10.47 63.53 92.13 Abbreviations: GFR, glomerular filtration rate; r, correlation coefficient; r 2, 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.

306 Gonwa et al. 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 Method (n) GFR SD r r 2 (n) GFR SD r r 2 GFR (270) 30.1 7.5 1.000 1.000 (913) 71.4 23.9 1.000 1.000 CG (242) 35.0 10.7 0.255 0.065 (867) 58.8 21.2 0.577 0.333 Nank (119) 46.0 13.1 0.346 0.119 (416) 68.8 18.6 0.522 0.305 MDRD 6 (270) 31.4 9.0 0.450 0.202 (913) 54.7 18.4 0.657 0.432 5 Years Posttransplant Method (n) GFR SD r r 2 (n) GFR SD r r 2 GFR (146) 28.8 9.2 1.000 1.000 (324) 66.6 20.6 1.000 1.000 CG (140) 29.8 9.8 0.340 0.116 (303) 50.8 19.2 0.538 0.29 Nank (55) 42.7 15.5 0.596 0.355 (117) 65.9 16.1 0.559 0.312 MDRD 6 (146) 28.1 9.2 0.564 0.318 (324) 49.6 16.1 0.647 0.419 Abbreviations: GFR, glomerular filtration rate; R, correlation coefficient; R 2, coefficient of determination; CG, Cockcroft-Gault; Nank, Nankivell; MDRD, Modification of Diet in Renal Disease; n, number of determinations. 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 Figure 1. Creatinine clearance predicted by the Cockcroft-Gault equation compared with the glomerular filtration rate (GFR) per 1.73 m 2 measured by I 125 -iothalamate at the pretransplant evaluation and at 3 months, 1 year, and 5 years posttransplant.

Estimation of GFR Before and After OLT 307 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 reports 11 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 Figure 2. GFR predicted by the 6-variable Modification of Diet in Renal Disease (MDRD) equation compared with GFR per 1.73 m 2 measured by I 125 -iothalamate at the pretransplant evaluation and at 3 months, 1 year, and 5 years posttransplant. and accepted as reasonably accurate. In the MDRD Study, r and r 2 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 m 2 ), 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 r 2 ) 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 Figure 3. GFR predicted by the Nankivell equation compared with GFR per 1.73 m 2 measured by I 125 - iothalamate at the pretransplant evaluation and at 3 months, 1 year, and 5 years posttransplant.

308 Gonwa et al. Table 8. Regression Equations for Comparing Calculated GFR to Measured GFR Cockcroft-Gault Pretransplant GFR 27.66071 0.776781 CG 3 months post GFR 25.64229 0.569141 CG 1 year post GFR 17.07224 0.842556 CG 5 years post GFR 16.82167 0.85794 CG MDRD 6 Variable Pretransplant GFR 23.68275 0.864908 MDRD 3 months post GFR 17.41549 0.771961 MDRD 1 year post GFR 9.417705 1.065179 MDRD 5 years post GFR 7.080935 1.112458 MDRD Nankivell Pretransplant GFR 7.160441 0.885988 Nank 3 months post GFR 10.16776 0.726897 Nank 1 year post GFR 4.372697 0.905875 Nank 5 years post GFR 1.959625 0.990234 Nank Abbreviations: GFR, glomerular filtration rate; CG, Cockcroft-Gault; MDRD, Modification of Diet in Renal Disease; Nank, Nankivell. 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. Further-

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