Tolstoy.newcastle.edu.au

Clinical Chemistry 48:91497–1504 (2002) Limited Sampling Strategy for the Estimation of Mycophenolic Acid Area under the Curve in Adult Tomasz Pawinski,1 Mike Hale,2 Magda Korecka,1 William E. Fitzsimmons,3 and Background: Significant relationships between the my-
prediction error for the AUC0–12h values not included in
cophenolic acid (MPA) area under the concentration–
the fit (i.e., the cross-validation error). The regression
time curve (AUC0–12h) and the risks for acute rejection
equation for AUC estimation that gave the best perfor-
and side effects have been reported. We developed a
mance for this model was: 7.75 ؉ 6.49c
0.76c0.5h
practical method for estimation of MPA AUCs. Regres-
2.43c2h. When we applied this model to the full data set,
sion equations were developed using repeated cross-
41 of the 50 (82%) estimated AUC values were within
validation for randomly chosen subsets, characterized
15% of the value of AUC0–12h calculated using all 12
statistically, and verified for acceptable performance.
concentrations.
Methods: Twenty-one renal transplant patients receiv-
Conclusions: This limited sampling strategy provides
ing 0.5 or 1.0 g of mycophenolate mofetil twice daily and
an effective approach for estimation of the full MPA
concomitant tacrolimus provided a total of 50 pharma-
AUC0–12h in renal transplant patients receiving concom-
cokinetic profiles. MPA concentrations were measured
itant tacrolimus therapy.
by a validated HPLC method in 12 plasma samples
2002 American Association for Clinical Chemistry
collected at predose and at 30 and 60 min; 2, 3, 4, 6, 8, 9,
10, 11, and 12 h; 1 and 2 weeks; and 3 months after
Mycophenolate mofetil (MMF),4 an ester prodrug of the transplantation. Twenty-six 1-, 2-, or 3-sample estima-
immunosuppressant mycophenolic acid (MPA), is widely tion models were fit (r2 ؍ 0.341– 0.862) to a randomly
used for the prevention of rejection in patients receiving selected subset of the profiles using linear regression
renal, heart, or liver transplants (1–3 ) and is under eval- and were used to estimate AUC0–12h for the profiles not
uation for its anti-graft-vs-host-disease effect in recipients included in the regression fit, comparing those esti-
of hematopoietic stem cell transplants. MMF is adminis- mates with the corresponding AUC0–12h values, calcu-
tered to patients who have undergone transplantation lated with the linear trapezoidal rule, including all 12
at a dosage of 0.5–1.5 g given twice daily. After oral timed MPA concentrations. The 3-sample models were
administration, MMF is rapidly and extensively absorbed constrained to include no samples past 2 h.
and hydrolyzed to MPA (4 ). The latter is metabolized by Results: The model using c0h, c0.5h, and c2h was superior
UDP-glucuronosyltransferase to the phenolic glucuronide to all other models tested (r2 ؍ 0.862), minimizing
of mycophenolic acid, which is pharmacologically inac-tive (5, 6 ).
MPA is avidly and extensively bound to plasma albu- min (7 ). Several investigators have reported a significant 1 Department of Pathology & Laboratory Medicine, University of Pennsyl- relationship between the MPA dose interval area under vania Medical Center, Philadelphia, PA 19104.
the plasma concentration–time curve (AUC) and the risks GlaxoSmithKline, Research Triangle Park, NC 27709.
3 Fujisawa Healthcare, Inc., Deerfield, IL 60015.
*Address correspondence to this author at: Department of Pathology & Laboratory Medicine, 7 Founders Pavilion, Hospital of the University ofPennsylvania, 3400 Spruce St., Philadelphia, PA 19104. Fax 215-662-7529; 4 Nonstandard abbreviations: MMF, mycophenolate mofetil; MPA, myco- phenolic acid; AUC, area under the plasma concentration–time curve; CsA, Received April 3, 2002; accepted May 16, 2002.
cyclosporine; LSS, limited sampling strategy; and CI, confidence interval.
Pawinski et al.: LSS in Monitoring MPA AUC for rejection (4, 8 –15 ) and hematologic side effects (12-h samples were not obtained for two profiles at 3 (14, 16 ). A Ͼ10-fold range of MPA AUC values has been months) or because MPA concentrations were below the observed in renal and heart transplant patients who lower limit of quantification (Ͻ0.2 mg/L in six samples received a fixed dose of 1 g of MMF twice daily for 1 profile at 2 weeks and in one or more samples for 10 (12, 14, 17 ). Thus the interindividual variability of MPA profiles obtained during week 1), which precluded the use of these profiles in this investigation. There were no Recent clinical investigations suggest that improved restrictions on the type of food consumed starting no effectiveness and tolerability will result from the incorpo- sooner than 1 h after the MMF dose. Plasma samples were ration of MPA therapeutic drug monitoring into routine stored at Ϫ20 °C until analysis. The study protocol re- clinical practice, providing effective MMF dose individu- ceived Institutional Review Board approval. Written in- alization in renal and heart transplant patients (2, 11– formed consent was obtained from each study patient.
13, 15, 18 ). A target range of 30 – 60 mg ⅐ h/L for the MPAAUC has been proposed for guidance of MMF dosage to optimal values in renal and heart transplant patients Plasma MPA concentrations were measured by a vali- receiving concomitant cyclosporine (CsA) and steroid dated HPLC method (22 ). Full 12-h AUC values were immunosuppression (12, 13, 15 ). However, the routine calculated using the linear trapezoidal rule.
measurement of the full 12-h dose interval MPA AUC isvery impractical and would be cost-prohibitive. Recent studies have therefore focused on the development and Limited sampling strategy (LSS) evaluation. Repeated cross- use of abbreviated sampling schemes for the reliable validation was used to evaluate each LSS, similar to a estimation of MPA AUC0–12h. Results from three such bootstrap procedure. These are important general tech- studies have concluded that inclusion of a 6-h sample is niques for the evaluation of bias and for estimating the critical for the reliable estimation of the MPA AUC0–12h precision of a study parameter (23, 24 ). Below, we present (19 –21 ). Inclusion of a 6-h timed sample is impractical, however, for routine practice in many centers because ofpatient inconvenience. In our experience this is a very important practical factor that limits the use of abbrevi- of the 50 MPA concentration profiles, using each set ated sampling approaches in clinical practice. With these of 12 MPA concentrations. A data set containing 50 considerations in mind, we investigated the development records (one per profile) was then constructed that of a limited sampling procedure using one, two, or three included the variables DOSE, PATIENT, SAMPLING samples. For 1-sample regressions, each time point over the entire 12-h interval was tested. For the 2-sample regressions, the predose sample was tested with each time 0h, c0.5h, c1h, c2h, c3h, c4h, c6h, c8h, c9h, point over the 12-h interval. For the 3-sample regressions, Step 2. In this step the data set was repeatedly ran- the predose sample was tested with each combination of domly divided into two groups of 25 each: a training two samples from the first 2 h. To minimize the effect ofunfavorable sampling on the linear regression modeling, group and an evaluation (or testing) group. The we used repeated cross-validation, similar to the “boot- training group records were used to determine the strap” approach, to identify the most robust models.
relationship (i.e., regression coefficients) betweenMPA AUC 0–12h and each of the 26 previously de- scribed linear regression models. This process of randomly dividing the data sets into two equal groups, a training and an evaluation group, was recipients of a kidney transplant. Patients received 0.5 g repeated a total of 50 times. Each time this was done (n ϭ 11) or 1 g (n ϭ 10) of MMF twice daily by the oral the 26 linear regression models were fit to the MPA route for the duration of the study. Each patient received AUC 0–12h by use of the MPA concentrations at the concomitant tacrolimus, initially at an oral dose of 0.2 selected sampling times for the 25 records in the mg ⅐ kgϪ1 ⅐ dayϪ1 and then dose-adjusted to achieve a training group, using multiple linear regression anal- steady-state blood concentration of 15 ␮g/L. MPA phar- ysis (SPSS-GP, Ver. 10 for Windows). This produced macokinetic profiles were determined 1 and 2 weeks and 3 months after transplantation. Plasma samples (EDTA) where ␤1–␤n are regression coefficients, ⌱ is the y- were collected at the following 12 times after an overnight intercept, n is the nominal sample collection time, fast: predose and 0.5, 1, 2, 3, 4, 6, 8, 9, 10, 11, and 12 h after and c1–cn are MPA concentration values measured at the morning dose of MMF. Only full 12-sample profiles times 1 through n. The distributions of the y-intercept were included in this investigation. Thus, profiles were and regression coefficients for each of the 26 models excluded from this study because samples were missing Clinical Chemistry 48, No. 9, 2002 pressed as a percentage. Mean estimation error [with95% confidence intervals (CIs)] was calculated as thearithmetic mean of the prediction errors for the 50patient profiles for each individual model.
role of the sponsorsGlaxoSmithKline and Fujisawa Healthcare, Inc. partici-pated in the data analysis and manuscript preparation.
Twenty-six models were developed and analyzed fortheir ability to estimate MPA AUC0–12h based on a limitednumber of samples. A total of 50 full MPA pharmacoki-netic profiles were used to test the performance of thesemodels. The MPA AUC0–12h values ranged from 9.5 to90.8 mg ⅐ h/L (median value, 33.3 mg ⅐ h/L; mean Ϯ SD,35.6 Ϯ 17.8 mg ⅐ h/L). The medians, means Ϯ SD, and(ranges) for cmax, tmax, and c0h were, respectively: 7.6mg/L, 9.5 Ϯ 6.2 mg/L (1.6 –31.2 mg/L); 1 h, 2.1 Ϯ 2.7 h Fig. 1. MPA concentrations as a function of time plotted for the 50 fullpharmacokinetic profiles.
(0.5–11 h); and 1.73 mg/L, 1.94 Ϯ 1.43 mg/L (0.2–5.2 Concentrations are the mean Ϯ SD (error bars). f, mean MPA concentrations for mg/L). The mean (Ϯ SD) MPA concentrations at the patients receiving 0.5 g of MMF twice daily; Œ, mean MPA concentration values studied time points are displayed in Fig. 1.
for patients receiving 1 g of MMF twice daily.
When we used the repeated cross-validation procedure described above, the best model for predicting the full Step 3. Each of the linear regression equations (26 MPA AUC0–12h was 3-time point model 10 (c0h, c0.5h, c2h; models) obtained in step 2 was used to estimate theMPA AUC for the 25 profiles in the correspondingevaluation set. This step was repeated for each of the Table 1. Multiple regression analysis to correlate 50 times the data set was randomly divided.
abbreviated MPA AUC values with AUC values calculated Step 4. “Residuals” were calculated for each of the 25 using the full set of 12 timed MPA concentrations.
0 –12h values in the evaluation group by taking the difference between the natural log (ln) of MPA AUC estimated by the regression equation. This procedure produced a total of 1250 (i.e., 25 ϫ 50) prediction residuals. Note that these are not the usual regression residuals, as the regression comes from the training set, whereas the residuals come from the application of the derived regression equation to the evaluation set. The distribution of the entire set of residuals was examined (mean, median, SD, and symmetry) to assure that the selected limited sample equation for prediction of MPA AUC produced a distribution of estimated MPA AUC values in the evaluation sets that met certain statistical criteria (mean value for the entire set of residuals close to 0 and with a very small SD). The model (of the 26) that yielded the most favorable distribution (mean near zero, smallest range encompassing most of the resid- uals) of residuals was selected as providing the best performance. Once the general model (of the 26) was selected, the proposed regression coefficients were taken as the median of the distribution of regression coefficient values described in step 2. These final LSS models were used to calculate prediction error for each patient, using the equation (estimated AUC Ϫ measured AUC)/measured AUC) ϫ 100 and ex- Pawinski et al.: LSS in Monitoring MPA AUC Table 2. Distribution of intercepts, coefficients, and residuals and summary statistics for repeated cross-validation for MPA AUC estimation models 1, 7, and 10.
r2 ϭ 0.862). Not only did this model have the highest r2 concentration was obtained for MPA concentrations at 8 h value, but the SD of the prediction residuals (0.0391) was (Table 1). Equations for estimation of MPA AUC values much better than that obtained for all of the other models and details of the limited sampling strategies evaluated in tested (Tables 1 and 2; Fig. 2). The 2-sample model that this study are summarized in Table 1. Linear regression had the best r2 value (0.793) was model 7 (c0h, c2h). The SD analysis plots of the estimated AUC vs the corresponding of the prediction residuals (0.4174) for model 7 was more measured full MPA AUC0–12h values for models 1, 7, and than 10-fold larger than that for model 10, and the mean 10 are displayed in Fig. 2. The bias of LSS-derived prediction error of 11.9% Ϯ 50.6% was almost double that estimates was analyzed by calculating the mean predic- for model 10 (6.1% Ϯ 19%). There was poor correlation tion error for the estimates i.e., the mean for the residuals between the full MPA AUC0–12h and each of the single [difference between ln(estimated AUC) and ln(measured MPA concentrations obtained at times up to the first 2 h AUC)]. The distribution for coefficients and a statistical (r2 ϭ 0.341– 0.434; Table 1).
summary for the distribution of the residuals for models The correlation between single MPA concentration 1, 7, and 10 are summarized in Table 2. Prediction errors values at time points later than 2 h and full MPA for the abbreviated AUC profiles are summarized in Table AUC0–12h values are summarized in Table 1. The best 3. The median and mean Ϯ SD for the prediction error for value for r2 (0.686) for a model containing only a single model 10 were 3.0% and 6.1% Ϯ 19%, respectively. For Clinical Chemistry 48, No. 9, 2002 There is a significant relationship between the dose-interval MPA AUC and risk for acute rejection based onretrospective investigations of MPA concentration vs bi-opsy-confirmed rejection rates in renal and heart trans-plant patients and on prospective investigations of MPAconcentrations vs biopsy-confirmed rejection rates in re-nal transplant patients (8 –12 ). Subsequent studies haveconfirmed the increased risk for acute rejection associatedwith decreased values for MPA AUC and, in addition,have reported an increased risk for hematologic sideeffects associated with increasing MPA AUC values (13–16 ). There is an emerging consensus that individualizingMMF dosage to achieve a target MPA AUC within therange 30 – 60 mg ⅐ h/L will provide a lower risk for acuterejection and hematologic side effects (13–16, 25 ). Becausethere is a Ͼ10-fold range in the MPA AUC valuesachieved using fixed daily doses of MMF (12–14, 17 ), atherapeutic drug monitoring approach would be neededto keep all patients in the 30 – 60 mg ⅐ h/L range, support-ing the importance of MPA therapeutic drug monitoringas a standard of practice.
Measurement of MPA AUC0–12h using a full set of samples (e.g., 8 –14 timed samples) is very demanding ofskilled personnel time and laboratory resources and re-quires considerable quantities of the patient’s blood andat least 12 h of time in a medical center. In our experience,the three samples in the 2-h postdose time period definedby this new sampling scheme provide a testing strategythat our clinical colleagues find is a practical approach,whereas sampling schemes that include a greater numberof samples or a larger time interval are unacceptable (T.
Pawinski, unpublished observation).
A conclusion drawn by other investigators about ab- breviated sampling schemes is that inclusion of a 6-htimed sample is critical to obtaining an abbreviated sam-pling model with the best predictive performance. Forexample, coefficients of determination (r2) of 0.87, 0.74,and 0.76 were obtained for models with sampling timesof 1, 2, and 6 h; 0, 0.5, and 2 h; and 0, 1.5, and 6 h,respectively, in an investigation involving 61 patients(19 ). Bland–Altman analysis of these data showed that themean error for the model with the best r2 value was Ϯ 9.5mg ⅐ h/L (19 ). It is unclear whether this conclusion would Fig. 2. Linear regression plots of MPA AUC values predicted using have been reached by use of a cross-validation approach, regression models 1 (top; single sample is predose MPA concentra- which is the recommended standard of practice for the tion), 7 (middle; two samples: predose MPA concentration and 2-h evaluation of a CsA LSS (26 ). In another investigation, the MPA concentration), and 10 (bottom; three samples: predose MPA r2 value was 0.84 for the best model tested, a 4-sample concentration and 0.5- and 2-h MPA concentrations) vs the corre-sponding 50 MPA AUC values calculated from the full sets of 12 timed model with sample times of 0, 1, 3, and 6 h, but was only samples by the linear trapezoidal rule.
0.63 for a model that used five samples obtained within2 h of the MMF dose (0, 0.25, 0.75, 1.25, and 2 h) (21 ). Thepredictive performance analyses reported for these two this model, in 41 of 50 (82%) of the profiles, the estimation models were 95% CIs of Ϫ26.3% to 32.5% and Ϫ45.3% to of the values was within Ϯ 15% of the value using all 12 52.7%, respectively (21 ). The improved performance samples over 12 h. For the other models, the estimate was achieved by the addition of the 6-h timed sample in these within Ϯ 15% of the actual value in only Յ62% of the 50 two studies was attributed to the fact that in both studies the patients did not fast overnight (27 ). Meal consump- Pawinski et al.: LSS in Monitoring MPA AUC Table 3. Prediction errors for the abbreviated MPA AUC profiles.
<؊15%
a Number of LSS-estimated MPA AUC values that were within 15% (Ϯ15%), more than 15% higher (Ͼ15%), or more than 15% lower (ϽϪ15%) than the values obtained tion causes an increase in tmax and a decrease in cmax, but model. A commonly used approach for establishing esti- no significant change in value for the 12-h MPA AUC mation models is to perform a multiple stepwise linear (28 ). According to the authors’ suggestion, the predictive regression on the total set of full AUCs (19 ). When we performance of 2-h limited sampling schemes is dimin- used that approach, we obtained a r2 value of 0.74 and a ished by not including maximum concentrations for at prediction error of 7.6% Ϯ 26.7%, (median, 6.5%; 95% CI, least some of the profiles (27 ). Inclusion of the 6-h sample Ϫ51.9% to 67.5%), and the model estimated MPA AUC to would eliminate most, if not all such cases and thereby within 15% of the full value in 56% of the profiles. Our improve the accuracy of the prediction model. In practice, estimation model using the repeated cross-validation ap- we favor adopting a rule of not using the abbreviated proach was significantly better, with a r2 value of 0.862, profile to estimate MPA AUC if the predose concentration prediction error of 6.1% Ϯ 19%, (median, 3.0%; 95% CI, is unusually high, indicating noncompliance with the Ϫ33.1% to 32%), and estimation of MPA AUC to within procedure (dosing inadvertently started before obtaining 15% of the value (when all 12 samples are used to the predose sample or lack of overnight fasting). In our calculate MPA AUC) in 82% of the profiles. To test for the investigation, food intake of each study participant’s effect of adding a 6-h sample to our 3-sample model, we choosing was permitted 1 h after the oral MMF dose, used the repeated cross-validation approach to derive the following an overnight fast. This produced an average model for this case. Indeed, some improvement was tmax of 2.1 Ϯ 2.7 h (median, 1 h; range, 0.5–11 h) that is achieved by adding the 6-h sample: the r2 was 0.891, the greater than that cited by Willis et al. (1.71 Ϯ 1.22 h) ( 21 ), prediction error was 3.5% Ϯ 19.2% (median, 2.9%; 95% CI, 42.6% to 59.2%), and the estimated MPA AUC values factor for establishing an accurate abbreviated sampling were within 15% of the full MPA AUC result in 86% of the profiles. Thus a small improvement in the predictive We believe that the statistical method used to establish performance was achieved, although the degree of im- the model deserves serious consideration for its impor- provement over the three samples in a 2-h model is small tance in deriving a robust limited sampling estimation and would not justify adding a fourth sample and a total Clinical Chemistry 48, No. 9, 2002 time of 6 h to the procedure. In addition, the exercise the present study, we used repeated cross-validation, presented here applied a much more stringent challenge similar to the bootstrap procedure, by randomly assigning in applying regression results to data points not included data sets to either the training set or the evaluation set, as in the regression, repeated 50 times using random divi- if a group of independent investigators had each ran- sion of the data sets to reduce the impact of sampling domly chosen their own training and testing sets and then variation on the assessment. Fitting regressions to the pooled their results. This produced a distribution of entire data set causes issues involving model selection prediction residuals that will be less sensitive to the choice of observations allocated to the training and evaluation Another recommended abbreviated sampling strategy sets because each observation will be in either set many includes samples collected at 0 and 75 min and 4 h (13 ).
times. This procedure enables a more meaningful com- To test for the possibility that a 3-sample model based on parison of the different potential models (i.e., the differing these time points would provide an even better estimation number of sample time points and different time points), of the MPA AUC based on all 12 timed samples, we based on a criterion of shortest range or tightest clustering evaluated an additional set of 3 timed MPA concentra- (smallest SD) of the prediction residuals. The conclusions tions: 0, 1, and 4 h. The 1-h sample was chosen because the regarding the use of three sampling times within the first timed samples in our investigation did not include 75 min 2 h after a dose of MMF described here are similar to those and the former was the closest in time to the latter. The found from a set of MPA AUC data for a cohort of renal 3-time point model produced by the repeated cross- transplant patients who were receiving MMF and con- validation approach is: MPA AUCϭ5.03 ϩ 3.36c comitant CsA immunosuppression (M. Hale, unpublished 5.44c4h. The r2 value for the regression analysis observation). In the latter case, although the equation of MPA AUC estimated by this 3-sample model vs the 50 coefficients derived were different, the development of a full MPA AUCs is 0.748 and the prediction error is as reliable model based on three samples obtained within the follows: mean Ϯ SE, 7.3% Ϯ 28.7%; median, 3.5%; 95% CI, first 2 h after a dose of MMF was accomplished.
Ϫ35.1% to 76.9%. In this case, 50% of the estimated MPAAUC values were within 15% of the full MPA AUC values. Thus the use of this abbreviated sample model did 1. The European Mycophenolate Mofetil Cooperative Study Group.
not improve on the predictive performance of the 0, 30 Placebo-controlled study of mycophenolate mofetil combined with min, and 2 h model. Other investigators (13 ) have re- cyclosporin and corticosteroids for prevention of acute rejection.
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