Abstract
Aims
To characterize the pharmacokinetics of darbepoetin alfa and covariate relationships in haemodialysis (HD) and peritoneal dialysis (PD) patients.
Methods
Data were collected from 131 (63 HD and 68 PD) patients who received darbepoetin alfa intravenously. A total of 917 serum concentrations were available. The data were analysed by nonlinear mixed effect modelling using NONMEM with a model including endogenous erythropoietin production. In addition, the final model was evaluated using bootstrap resampling.
Results
The selected basic model was a two-compartment model with a combination of additive and the constant coefficient of variation error models. The significant covariates were weight (WT) for clearance (CL) and the volume of central compartment (V1), and the dialysis technique (DIA) for V1. The typical values of CL and V1 were 0.0807 l h−1 and 2.51 l, respectively. V1 in PD patients was 17% higher than in HD patients. With the introduction of WT in CL and WT and DIA in V1, interindividual variability decreased from 27.1% to 20.6% in CL and from 29.1% to 21.8% in V1. The mean parameter estimates from the bootstrap datasets were similar to those from the original dataset. Evaluation by bootstrapping showed that the final model was stable.
Conclusions
The results of the present analysis suggest no dosage regimen change is warranted for darbepoetin alfa in HD and PD patients over the range of distribution of covariates included in this study.
Keywords: darbepoetin alfa, intravenous, NONMEM, population pharmacokinetics
Introduction
Recombinant human erythropoietin (rHuEPO) has been used for the treatment of renal anaemia and other anaemias since it was first licensed nearly two decades ago [1, 2]. It is most commonly administered two to three times a week because of its relatively short circulating half-life. For the treatment of anaemia in dialysis patients in Japan, the recommended dosage was 1500–3000 IU intravenously two to three times a week.
Darbepoetin alfa (AranespTM), which stimulates erythropoiesis by the same mechanism as endogenous erythropoietin, has two more N-linked carbohydrate addition sites than the primary sequence of rHuEPO [3, 4], resulting in an approximately threefold longer elimination half-life in animal models [5] and in humans [6–8].
There have been several reports about the pharmacokinetics of darbepoetin alfa after intravenous or subcutaneous administration [6–8]. However, the demographic and physiopathological data on the effects of darbepoetin alfa have not yet been evaluated for the pharmacokinetic parameters using population pharmacokinetic analysis, compared with rHuEPO [9, 10]. We report here for the first time the results of population pharmacokinetic modelling of darbepoetin alfa after intravenous administration.
Materials and methods
Patient population and data collection
A total of 131 [63 haemodialysis (HD) and 68 peritoneal dialysis (PD)] Japanese adult patients were studied in four clinical studies. They received darbepoetin alfa at 10–90 µg intravenously with single or multiple dosing (every 1 or 2 weeks). HD patients were included in three clinical studies if they met the following criteria: chronic kidney disease undergoing haemodialysis for at least 3 months and receiving stable intravenous rHuEPO therapy three times weekly for at least 2 months before the studies and mean baseline haemoglobin (haematocrit) between 9 g dl−1 (25%) and 12 g dl−1 (35%). Exclusion criteria included major surgery within 3 months before enrolment (excluding vascular access surgery) and blood transfusions to treat anaemia within 1 month before enrolment. PD patients with end-stage renal failure undergoing stable PD and with mean baseline haemoglobin <10 g dl−1 for the patient not undergoing rHuEPO therapy or between 9 g dl−1 and 12 g dl−1 for the patient receiving rHuEPO therapy were included in the study. Patients who had received major surgery and blood transfusion within 1 month before enrolment were excluded. The demographic and physiopathological data are shown in Table 1 and are considered in the analysis.
Table 1.
Patient characteristics, median (range)
| HD patient | PD patient | Total | |
|---|---|---|---|
| Number of patients | 63 | 68 | 131 |
| Dialysis technique (HD/PD) | 63/0 | 0/68 | 63/68 |
| Gender (male/female) | 37/26 | 44/24 | 81/50 |
| Weight (kg) | 53.8 (35.5–67.0) | 57.4 (38.8–132.0) | 54.7 (35.5–132.0) |
| Body mass index (kg m−2) | 20.5 (14.7–29.4) | 22.2 (15.9–44.5) | 21.4 (14.7–44.5) |
| Age (years) | 64 (24–78) | 56 (23–84) | 60 (23–84) |
| Serum albumin (g dl−1) | 3.9 (3.2–4.6) | 3.5 (2.1–4.8) | 3.8 (2.1–4.8) |
| ALT (GPT) (IU l−1) | 10 (4–27) | 12 (4–41) | 11 (4–41) |
| Creatinine (mg dL−1) | 10.70 (4.98–16.50) | 10.29 (3.68–16.09) | 10.60 (3.68–16.50) |
| Red blood cell counts (×104 µl−1) | 308 (265–422) | 320 (211–421) | 317 (211–422) |
| White blood cell counts (µl−1) | 5400 (2400–12 500) | 5645 (3000–12 200) | 5500 (2400–12 500) |
| Platelet cell counts (×104 µl−1) | 15.2 (5.1–31.6) | 22.1 (7.5–50.1) | 17.7 (5.1–50.1) |
HD, Haemodialysis; PD, peritoneal dialysis; ALT, alanine aminotransferase.
The designs and conduct of all the studies complied with the ethical principles of good clinical practice, in accordance with the Declaration of Helsinki and local legal requirements. These studies were approved by institutional review boards at each centre. All patients provided written informed consent before enrolment.
Serial and sparse blood samples for serum preparation were collected in HD and PD patients. Serial blood samples in HD patients who received darbepoetin alfa at 10–60 µg were drawn from the veins of each patient before dosing and 0.5, 1, 2, 5, 8, 12, 24, 48, 96 and 168 h after dosing. For HD patients who received darbepoetin alfa at 90 µg, sampling of each patient was done at the above described points and 336 h after dosing. PD patients received darbepoetin alfa intravenously every 1 or 2 weeks. Sampling of each patient was performed prior to the initial dose and before dosing in weeks 2, 3 and 4. Additional samples were taken between 0.5 and 1 h after dosing in week 2 when possible.
Serum samples were analysed with the use of the Quantikine in vitro diagnostics rHuEPO enzyme-linked immunosorbent assay (ELISA) kit (R&D Systems, Minneapolis, MN, USA). The standard curve was constructed using darbepoetin alfa, and quality controls ensured individual assay quality. In validation tests, the intra-assay and inter-assay precision for spiked samples ranged from 5.1% to 11.0% and 4.4% to 6.1%, respectively. The interassay precision criterion for clinical serum samples was within 20%. The limit of quantification was 0.078 ng ml−1. A total of 917 concentration measurements were available.
Population pharmacokinetic analysis and model validation
The data were analysed by nonlinear mixed effect modelling using the NONMEM package software (version 5.0; Globomax LLC, Hanover, MD, USA). As the population pharmacokinetic model is used for prediction, it is important to develop a model with validation [11]. There are two types of method to evaluate the stability of the model. External validation is the application of the developed model to a dataset (validation dataset) from another study. Internal validation, the second type of validation, uses data splitting [12] and resampling techniques (cross-validation and bootstrapping) [11, 13]. Bootstrapping is a useful internal validation technique and has the advantage of using the entire dataset for model development. Therefore, the model build in this study was evaluated using bootstrapping.
The population pharmacokinetic modelling steps were as follows: (i) basic pharmacokinetic modelling using NONMEM and obtaining Bayesian individual parameter estimates; (ii) validation of the basic model using the bootstrap resampling technique; (iii) generalized additive modelling (GAM) for the selection of covariate candidates; (iv) final pharmacokinetic modelling to determine the covariate model; and (v) validation of the final model. The first-order conditional estimation with interaction method was used in all the analysis processes since three of four studies used the extensive sampling design. Initial pharmacokinetic parameter estimates of one- and two-compartment models with bolus administration for NONMEM modelling were calculated using the mean data obtained from all the HD patients that received darbepoetin alfa at a single 60-µg administration by WinNonlin (version 4.1; Pharsight Corp., Mountain View, CA, USA).
Step 1: basic pharmacokinetic modelling
One- or two-compartment model including the constant endogenous (or baseline) erythropoietin production were fitted with the darbepoetin alfa concentration–time data [14]. Interindividual variability in clearance (CL) was modelled using an exponential error model as follows:
 |
where CLi represents the hypothetical true clearance for the ith individual, θCL is the typical population value of clearance and η is an independent, identically distributed random variable with a mean of zero and variance ω2. Interindividual variability in the intercompartmental clearance (Q), volume of central compartment (V1), volume of peripheral compartment (V2) and baseline erythropoietin level (k0) were similarly modelled.
Residual variability was identically distributed and was modelled using the additive error, constant coefficient of variation (CCV) error or the combination of the additive and CCV error models. The combination of the additive and CCV error models is described by the following equation:
 |
where Cpij is the ith measured concentration in the jth individual and Cpmij is the ith concentration predicted by the model at the ith observation time for the jth individual. k0j is the baseline erythropoietin level for the jth individual. ɛ1 and ɛ2 are independent random variables with means of zero and variances of σ2. The magnitude of residual variability usually depends on measurement, dosing, sampling and model misspecification errors, and also on the presence of interoccasion variability [15]. To avoid having the complexity in the basic pharmacokinetic modelling, interoccasion variability was not considered since the pharmacokinetics of darbepoetin alfa did not depend on the duration of administration [7].
With the fixed and random effects chosen, empirical Bayes estimates of pharmacokinetic parameters were subsequently obtained using the POSTHOC option within NONMEM. The choice of a basic population model was based on monitoring Akaike’s information criterion (AIC). AIC values were calculated from the following equation: AIC = NONMEM objective function value + 2 × number of parameters in each structural model. The reliability of the model selection was checked by the visual inspection of plots of population or individual predicted vs. measured concentrations, weighted residuals vs. population predicted serum concentration and weighted residual vs. time.
Step 2: validation of a basic model using the bootstrap resampling technique
Resampling the original data with replacements generated 100 bootstrap samples. The resampling unit comprised the samples obtained from each patient. The appropriate structural model that best described the data from each sample was then determined. In some cases, the population pharmacokinetic parameter estimates from the basic model only selected by AIC were changed according to the dataset with or without a particular patient [16]. This was done to ensure that the model that best described the bootstrap data was not different from the basic model used for developing the population pharmacokinetic model in the subsequent step. In addition, the density plots of each pharmacokinetic parameter estimate were used to examine the adequacy of the basic model.
Step 3: selection of covariate candidates
Exploratory data analysis was performed on the empirical Bayesian parameter estimates obtained from the original dataset using the basic model selected in the previous step and treated as data to examine the distribution, shapes and relationships between covariates and individual pharmacokinetic parameter estimates.
The data were subjected to a stepwise (single term addition/deletion) procedure using the GAM procedure in Xpose (version 3.1) [17] running on the S-PLUS statistical software package (version 6.0; Insightful Corp., Seattle, WA, USA). Each covariate was allowed to enter the model in any of several functional representations. AIC was used for model selection [18]. At each step, the model was changed by the addition or deletion of the covariate that resulted in the largest decrease in AIC. The search was stopped when AIC reached a minimum value.
Step 4: population model building using NONMEM
For each NONMEM analysis, the improvement in fit obtained upon the addition of a covariate selected from step 3 to the regression model was assessed by changes in the NONMEM objective function. Minimization of the NONMEM objective function, equal to twice the negative log-likelihood of the data, is equivalent to maximizing the probability of the data. The change in the objective function of the NONMEM value is approximately χ2 distributed. A difference in the NONMEM objective function value of 3.84 and 7.88 denotes an improved fit at P < 0.05 and P < 0.005, respectively.
Continuous covariates were centred to their median values. For example, the relationship between CL and weight (WT) was described as follows:
 |
where CL represents the population parameter estimate, θCL is the value of the 54-kg patient and θCL_WT is the intercept of CL per kg weight difference. Dichotomous covariates were modelled as follows:
 |
where V1 represents the population parameter estimates, θV1 is the population value in the HD patient (DIA = 0) and θV1_DIA is the change of V1 when the dialysis technique is PD (DIA = 1).
The construction of the regression model for each structural model parameter was performed in three steps using the original dataset. The covariates were first screened one by one. A decrease in the objective function value of at least 3.84 was required to identify a significant covariate. Next, the full model was defined as incorporating all the significant covariates. Lastly, the final model was elaborated by backward elimination from the full model. An increase in objective function value of >7.88 was required for retention of the covariate screened at the first step.
Step 5: validation of the final population pharmacokinetic model
Bootstrap samples were generated by resampling with replacements and used for the evaluation of the stability of the final model built in step 4. The reported numbers of bootstrap replication are different among studies [11, 16, 19]. The final population pharmacokinetic model was fitted repeatedly to the 1000 additional bootstrap samples in this analysis. The mean values, standard errors and 95% confidence intervals (CIs) obtained from these bootstrap replicates were compared with those obtained from the original dataset. The 95% CIs of the original dataset were calculated by point estimates ± 1.96 × standard errors of estimates. The 95% CIs of the 1000 bootstrap replicates were calculated based on the 2.5 percentile and 97.5 percentile.
The initial serum concentration and the area under the serum concentration–time curve
The initial serum concentration (C0) and the area under the serum concentration–time curve (AUC) in each patient were obtained from the final population pharmacokinetic model using the POSTHOC option within NONMEM. The C0 was the individual predicted serum concentration at time zero. The AUC was estimated from the first dose amount/predicted clearance at the first dose in each individual.
Results
Determination of a basic pharmacokinetic model
The serum concentrations vs. time are shown in Figure 1. The parameter estimates of various structural models are given in Table 2. As the previous review article has suggested that darbepoetin alfa is degraded mainly by erythropoietin receptor-mediated uptake in bone marrow [20], the basic model with nonlinear elimination was performed but convergence was not achieved. The combination of the additive and CCV error models (the combination error model) was found to describe intraindividual error better than the CCV error model or the additive error model. The stability of one and two compartments with the combination error model was examined in order to select the optimum basic pharmacokinetic model. The parameter estimates of one- and two-compartment models were obtained from 100 successful bootstrap replicate runs. Each parameter distribution of one- and two-compartments with the combination error model was in a narrow range and unimodal (data not shown). However, all of the AIC values obtained from the two-compartment with the combination error model were lower than those obtained from the one-compartment with the combination error model (median AIC difference −330, the range of the AIC differences −495 to −218). Therefore, the two-compartment with the combination error model was selected as the optimum basic pharmacokinetic model and was used in subsequent steps.
Figure 1.
Observed darbepoetin alfa serum concentrations vs. time. (a) Haemodialysis patient data. (b) Peritoneal dialysis patient data
Table 2.
Typical parameter estimates (standard errors) of various structural models
| One-compartment model | |||
|---|---|---|---|
| Parameter | CCV | Additive | Combination |
| θCL (l h−1) | 0.0738 (0.00219) | 0.0888 (0.00270) | 0.0784 (0.00237) |
| θQ (l h−1) | |||
| θV1 (l) | 2.91 (0.0627) | 2.87 (0.0716) | 2.92 (0.0715) |
| θV2 (l) | |||
| θk0 (ng ml−1) | 0.162 (0.00666) | 0.366 (0.0447) | 0.186 (0.00896) |
| ωCL (%) | 26.7 | 19.4 | 27.7 |
| ωQ (%) | |||
| ωV1 (%) | 18.6 | 27.8 | 25.3 |
| ωV2 (%) | |||
| ωk0 (%) | 44.4 | 52.2 | 42.4 |
| σ1 (%) | 15.8 | 10.8 | |
| σ2 (ng ml−1) | 0.918 | 0.0647 | |
| AIC | 149 | 1341 | 40 |
| Two-compartment model | |||
| Parameter | CCV | Additive | Combination |
| θCL (l h−1) | 0.0813 (NE) | 0.0749 (0.00241) | 0.0820 (0.00232) |
| θQ (l h−1) | 0.00714 (NE) | 0.0672 (0.0113) | 0.0604 (0.00843) |
| θV1 (l) | 2.84 (NE) | 2.74 (0.0735) | 2.77 (0.0731) |
| θV2 (l) | 0.710 (NE) | 0.582 (0.0505) | 0.503 (0.0440) |
| θk0 (ng ml−1) | 0.142 (NE) | 0.104 (0.0340) | 0.169 (0.00669) |
| ωCL (%) | 30.2 | 21.8 | 27.1 |
| ωQ (%) | 73.3 | 65.6 | 87.5 |
| ωV1 (%) | 25.7 | 30.2 | 29.1 |
| ωV2 (%) | 45.6 | 32.4 | 49.4 |
| ωk0 (%) | 48.1 | 93.1 | 44.8 |
| σ1 (%) | 9.78 | 6.50 | |
| σ2 (ng ml−1) | 0.505 | 0.0645 | |
| AIC | −235 | 592 | −273 |
θ andω represent population pharmacokinetic parameter estimate and interindividual variability, respectively (CL, clearance; Q, intercompartmental clearance between central and peripheral; V1, volume of central compartment; V2, volume of peripheral compartment; k0, baseline erythropoietin level). σ1 and σ2 represent residual variability. CCV, Constant coefficient of variation model; Additive, additive error model; Combination, combination of the additive and CCV; AIC, Akaike’s information criterion; NE, not estimated.
θ andω represent population pharmacokinetic parameter estimate and interindividual variability, respectively (CL, clearance; Q, intercompartmental clearance between central and peripheral; V1, volume of central compartment; V2, volume of peripheral compartment; k0, baseline erythropoietin level). σ1 and σ2 represent residual variability. CCV, Constant coefficient of variation model; Additive, additive error model; Combination, combination of the additive and CCV; AIC, Akaike’s information criterion; NE, not estimated.
Selection of covariate candidates
The GAM analysis indicated that CL is a function of weight (WT), creatinine (CR), red blood cell counts (RBC), that Q is a function of WT and dialysis technique (DIA), that V1 is a function WT, white blood cell counts (WBC) and DIA, that V2 is a function of DIA, and that k0 is a function of RBC and platelet cell counts (PLT) (data not shown).
Population model building and stability of the final population models
The population model with covariates was built using NONMEM on the basis of the result of GAM analysis. WT was found to be the predictor of both CL and V1, and then DIA was found to be a predictor of V1, with a log likelihood difference (LLD) of>3.84 (P< 0.05) between each model, in which WT or DIA was introduced singly, and the basic model including each pharmacokinetic parameter model without these covariates (Table 3). The full regression model was that following the equations CL = θCL × [1 + θCL_WT × (WT-54)] and V1 = θV1 × [1 + θV1_WT × (WT-54) + θV1_DIA × DIA]. The full model was tested against the reduced models (Table 3). All covariates included in each pharmacokinetic parameter were found to be significant (P< 0.005) and were kept in the final population model.
Table 3.
Effect of each covariate on structural model parameters and comparison of the full model and reduced model
| Regression models | LLD |
|---|---|
| Forward inclusion process | |
| Basic model | 0 |
| CL = θCL × [1 + θCL_WT × (WT-54)] | −53.5* |
| CL = θCL × [1 − θCL_CR × (CR-10)] | −0.124 |
| CL = θCL × [1 + θCL_RBC × (RBC-317)] | −2.25 |
| Q = θQ × [1 + θQ_WT × (WT-54)] | −0.783 |
| Q = θQ × (1 − θQ_DIA × DIA) | −0.001 |
| V1 = θV1 × [1 + θV1_WT × (WT-54)] | −52.3* |
| V1 = θV1 × [1 − θV1_WBC × (WBC-5500)] | −0.776 |
| V1 = θV1 × (1 + θV1_DIA × DIA) | −29.0* |
| V2 = θV2 × (1 − θV2_DIA × DIA) | −0.001 |
| k0 = θk0 × [1 + θk0_RBC × (RBC-317)] | −0.004 |
| k0 = θk0 × [1 − θk0_PLT × (PLT-17)] | −1.734 |
| Backward elimination process | |
| Full model | 0 |
| V1 = θV1 × [1 + θV1_WT × (WT-54) + θV1_DIA × DIA] | 61.0** |
| CL = θCL × [1 + θCL_WT × (WT-54)], V1 = θV1 × (1 + θV1_DIA × DIA) | 43.2** |
| CL = θCL × [1 + θCL_WT × (WT-54)], V1 = θV1 × [1 + θV1_WT × (WT-54)] | 14.0** |
LLD, log likelihood difference. Eachθ represents a population parameter estimate (CL, clearance; Q , intercompartmental clearance between central and peripheral; V1, volume of central compartment; V2 , volume of peripheral compartment; k0, baseline erythropoietin level; WT, weight; CR, creatinine; RBC, red blood cell counts; DIA, dialysis technique, DIA = 0 if the patients receiving HD, otherwise DIA = 1; WBC, white blood cell counts; PLT, platelet cell counts).
P < 0.05.
P< 0.005.
The final population pharmacokinetic model obtained from the previous step was fitted repeatedly to the 1000 bootstrapped samples. The typical parameter estimates of the final model using the original dataset and the mean parameter values obtained from the 1000 successful bootstrap replicate runs are provided in Table 4. The mean parameter estimates obtained with the 1000 bootstrap datasets were similar to those obtained with the original dataset. Diagnostic plots (Figure 2) of the final population pharmacokinetic model identified no systemic bias.
Table 4.
Typical population parameter estimates and stability of the final model
| Original dataset | |||
|---|---|---|---|
| Parameter | Typical values | Standard errors | 95% CIs |
| θCL (l h−1) | 0.0807 | 0.00195 | 0.0769, 0.0845 |
| θ Q (l h−1) | 0.0616 | 0.00755 | 0.0468, 0.0764 |
| θ V1 (l) | 2.51 | 0.0629 | 2.39, 2.63 |
| θ V2 (l) | 0.522 | 0.0407 | 0.442, 0.602 |
| θ k0 (ng ml−1) | 0.167 | 0.00629 | 0.155, 0.179 |
| θ CL_WT (kg−1) | 0.0195 | 0.00246 | 0.0147, 0.0243 |
| θ V1_WT (kg−1) | 0.0163 | 0.00214 | 0.0121, 0.0205 |
| θ V1_DIA | 0.170 | 0.0501 | 0.0718, 0.268 |
| ω CL (%) | 20.6 | ||
| ω Q (%) | 87.1 | ||
| ωV1 (%) | 21.8 | ||
| ωV2 (%) | 48.6 | ||
| ωk0 (%) | 45.4 | ||
| σ1 (%) | 6.53 | ||
| σ2 (ng ml−1) | 0.0634 | ||
| 1000 bootstrap replicates | |||
| Parameter | Mean values | Standard errors | 95% CIs |
| θCL (l h−1) | 0.0807 | 0.00188 | 0.0771, 0.0843 |
| θQ (l h−1) | 0.0647 | 0.0177 | 0.0143, 0.0949 |
| θV1 (l) | 2.52 | 0.0678 | 2.38, 2.66 |
| θV2 (l) | 0.527 | 0.0749 | 0.421, 0.762 |
| θk0 (ng ml−1) | 0.168 | 0.00850 | 0.146, 0.184 |
| θCL_WT (kg−1) | 0.0197 | 0.00274 | 0.0143, 0.0248 |
| θV1_WT (kg−1) | 0.0162 | 0.00225 | 0.0117, 0.0208 |
| θV1_DIA | 0.171 | 0.0527 | 0.0814, 0.281 |
| ωCL (%) | 20.5 | 1.87 | 16.9, 24.2 |
| ωQ (%) | 69.8 | 32.1 | 0.0115, 117 |
| ωV1 (%) | 21.4 | 2.85 | 15.9, 27.0 |
| ωV2 (%) | 51.0 | 12.4 | 28.6, 76.9 |
| ωk0 (%) | 43.1 | 8.37 | 28.3, 58.9 |
| σ1 (%) | 6.52 | 0.701 | 5.31, 8.16 |
| σ2 (ng ml−1) | 0.0633 | 0.0168 | 0.0205, 0.0984 |
θ and ω represent population pharmacokinetic parameter estimate and interindividual variability, respectively (CL, clearance; Q, intercompartmental clearance between central and peripheral; V1, volume of central compartment; V2, volume of peripheral compartment; k0, baseline erythropoietin level; WT, weight; DIA, dialysis technique, DIA = 0 if the patients receiving HD, otherwise DIA = 1). σ1 and σ2 represent residual variability.
Figure 2.
Diagnosis plots of the final population pharmacokinetic model. (a) Population predicted vs. observed serum concentration. (b) Individual predicted vs. observed serum concentration. (c) Weighted residual vs. population predicted serum concentration. (d) Weighted residual vs. time
The C0 and the AUC obtained from the final population pharmacokinetic model
There were no marked differences in the distributions and the geometric mean values in the C0 and the AUC between weight categories (Figure 3a,b). The distributions and geometric mean values in the C0 and the AUC of HD patients were similar to those of PD patients (Figure 3c,d).
Figure 3.
C0 and AUC obtained from the final population pharmacokinetic model. Open circles represent individual parameter estimates. Bars are the geometric mean in each category. (a,b) C0 and AUC in each weight category. 1, Weight lower then 33th percentile (n = 43); 2, weight between 33th and 66th percentile (n = 43); 3, weight higher than 66th percentile (n = 45). (c,d) C0 and AUC in haemodialysis (HD) patients (n = 63) and peritoneal dialysis (PD) patients (n = 68)
Discussion
There is no obvious difference in the pharmacokinetic profiles of rHuEPO after intravenous administration among subjects with normal renal function, patients with chronic renal failure including patients undergoing HD, and PD patients [21]. Since the previous review suggests that rHuEPO and darbepoetin alfa are mainly degraded by erythropoietin receptor-mediated uptake in bone marrow [20], in the same way as rHuEPO, it seems likely that there is no difference in the pharmacokinetics of darbepoetin alfa among normal subjects, HD and PD patients. However, the pharmacokinetics of darbepoetin alfa in patients undergoing dialysis needs to be evaluated. The purpose of this study was to characterize the pharmacokinetics of darbepoetin alfa and covariate relationships in HD and PD patients. The reliability of the results obtained from population pharmacokinetic analyses depends on the modelling procedure. Therefore, evaluation of basic (covariate free) and final (covariate model) population pharmacokinetic models was performed using bootstrapping because of the advantage of being able to use all the datasets in model building.
In consideration of the capacity limited degradation process for darbepoetin alfa [20], the basic pharmacokinetic model with nonlinear elimination was used but convergence was not achieved. This result indicates that the pharmacokinetics of darbepoetin alfa is linear in HD and PD patients within the dose range in this study. The previous report also supported this result [7].
The final population pharmacokinetic model includes only the two physical factors, i.e. body weight (WT) on CL and V1, and dialysis technique (DIA) on V1. Although as with rHuEPO, the main sites of the degradation of darbepoetin alfa have not yet been identified, the previous review suggests that rHuEPO and darbepoetin alfa are mainly degraded following erythropoietin receptor-mediated uptake by the target cells [20]. This may indicate that the pharmacokinetics of darbepoetin alfa is not markedly influenced by the ordinary xenobiotic metabolism index, such as hepatic and renal function. Previous reports support the results of our study. There is no population pharmacokinetic study of rHuEPO and darbepoetin alfa in HD and PD patients. As for subcutaneous rHuEPO, previous studies have indicated that WT is a determinant of CL/F and V/F in critically ill patients admitted to an intensive care unit [10], and serum creatinine and age are determinants of the elimination rate constant (kel) in healthy volunteers [9]. Apart from WT, no other patient characteristics, including serum creatinine or age, were found to influence significantly the pharmacokinetics of darbepoetin alfa in our study. The discrepancy of the determinants for pharmacokinetic parameters between our study and a previous study [9] may derive from differences in the subjects’ backgrounds. Our results will provide more pragmatic and useful information for anaemia treatment.
CL was dependent on WT, but the difference in interindividual variability for CL between the final (CL with WT) and basic model (CL without WT) was 6.5%. The result indicates that WT could not explain a large part of the interindividual variability in CL. V1 was influenced by WT and DIA. The V1 values corresponded to the blood plasma volume. V1 can be attributed to the increase in plasma volume with increasing WT. The estimate of V1 in PD patients was 17% higher than that in HD patients. The ratio of extracellular body fluid to total body water after HD in HD patients was less than that of PD patients [22]. The dependence on DIA for V1 may be ascribed to the difference in extracellular body fluid described above. With the introduction of WT and DIA in V1, interindividual variability decreased from 29.1% to 21.8%. As is the case with CL, WT and DIA could not explain a large part of the interindividual variability in V1.
There were no obvious differences in the distributions and the geometric mean values in the C0 and the AUC between weight categories and between dialysis techniques. These results indicate that C0 and AUC are not markedly changed according to WT and DIA.
The results of the present analysis suggest no dosage regimen change is warranted for darbepoetin alfa in HD and PD patients over the range of distribution of covariates included in this study. The pharmacokinetic and pharmacodynamic (or clinical end-point) modelling of darbepoetin alfa in dialysis patients remains to be investigated to confirm the conclusion that a WT- and DIA-adjusted dosage regimen does not improve the interindividual variability of clinical response.
The final population pharmacokinetic model built in the study was fitted to the bootstrap samples. The mean parameter estimates obtained with the 1000 bootstrap datasets were similar to those obtained with the original dataset. This indicates that the final model was not changed according to the dataset with or without a particular patient, i.e. the final model is stable.
Acknowledgments
We thank Mr Kaname Hasegawa and Mr Kazuki Kawakami for their excellent technical assistance.
References
- 1.Wineals CG, Oliver DO, Pippard MJ, Reid C, Downing MR, Cotes PM. Effect of human erythropoietin derived from recombinant DNA on the anaemia of patients maintained by chronic haemodialysis. Lancet. 1986;2:1175–8. doi: 10.1016/s0140-6736(86)92192-6. [DOI] [PubMed] [Google Scholar]
- 2.Eschbach JW, Egrie JC, Downing MR, Browne JK, Adamson JW. Correction of the anemia of end-stage renal disease with recombinant human erythropoietin. Results of a combined phase I and II clinical trial. N Engl J Med. 1987;316:73–8. doi: 10.1056/NEJM198701083160203. [DOI] [PubMed] [Google Scholar]
- 3.Elliott S, Lorenzini T, Asher S, Aoki K, Brankow D, Buck L, Busse L, Chang D, Fuller J, Grant J, Hernday N, Hokum M, Hu S, Kundten A, Levin N, Komorowski R, Martin F, Navarro R, Osslund T, Rogers G, Rogers N, Trail G, Egrie J. Enhancement of therapeutic protein in vivo activities through glycoengineering. Nat Biotechnol. 2003;21:414–21. doi: 10.1038/nbt799. [DOI] [PubMed] [Google Scholar]
- 4.Elliott S, Egrie J, Browne J, Lorenzini T, Busse L, Rogers N, Ponting I. Control of rHuEPO biological activity. The role of carbohydrate. Exp Hematol. 2004;32:1146–55. doi: 10.1016/j.exphem.2004.08.004. [DOI] [PubMed] [Google Scholar]
- 5.Egrie JC, Dwyer E, Browne JK, Hitz A, Lykos MA. Darbepoetin alfa has a longer circulating half-life and greater in vivo potency than recombinant human erythropoietin. Exp Hematol. 2003;31:290–9. doi: 10.1016/s0301-472x(03)00006-7. [DOI] [PubMed] [Google Scholar]
- 6.Macdougall IC, Gray SJ, Elston O, Breen C, Jenkins B, Egrie J. Pharmacokinetics of novel erythropoiesis stimulating protein compared with epoetin alfa in dialysis patients. J Am Soc Nephrol. 1999;10:2392–5. doi: 10.1681/ASN.V10112392. [DOI] [PubMed] [Google Scholar]
- 7.Allon M, Kleinman K, Walczyk M, Kaupke C, Messer-Mann L, Olson K, Heatherington AC, Maroni BJ. Pharmacokinetics and pharmacodynamics of darbepoetin alfa and epoetin in patients undergoing dialysis. Clin Pharmacol Ther. 2002;72:546–55. doi: 10.1067/mcp.2002.128374. [DOI] [PubMed] [Google Scholar]
- 8.Lerner G, Kale AS, Warady BA, Jabs K, Bunchman TE, Heatherington A, Olsson K, Messer-Mann L, Maroni BJ. Pharmacokinetics of darbepoetin alfa in pediatric patients with chronic kidney disease. Pediatr Nephrol. 2002;17:933–7. doi: 10.1007/s00467-002-0932-0. [DOI] [PubMed] [Google Scholar]
- 9.Hayashi N, Kinoshita H, Yukawa E, Higuchi S. Pharmacokinetic analysis of subcutaneous erythropoietin administration with nonlinear mixed effect model including endogenous production. Br J Clin Pharmacol. 1998;46:11–19. doi: 10.1046/j.1365-2125.1998.00043.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 10.Chakraborty A, Natarajan J, Guilfoyle M, Morgan N, Vercammen E, Cheung W. Population pharmacokinetics of erythropoietin in critically ill subjects. J Clin Pharmacol. 2005;45:193–202. doi: 10.1177/0091270004269520. [DOI] [PubMed] [Google Scholar]
- 11.Ette EI. Stability and performance of a population pharmacokinetic model. J Clin Pharmacol. 1997;37:486–95. doi: 10.1002/j.1552-4604.1997.tb04326.x. [DOI] [PubMed] [Google Scholar]
- 12.Roecker EB. Prediction error and its estimation for subset-selected models. Technometrics. 1991;33:459–68. [Google Scholar]
- 13.Efron B. Estimating the error rate of a prediction rule: improvement on cross-validation. J Am Stat Assoc. 1983;78:316–31. [Google Scholar]
- 14.Schoemaker RC, Cohen AF. Estimating impossible curves using NONMEM. Br J Clin Pharmacol. 1996;42:283–90. doi: 10.1046/j.1365-2125.1996.04231.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 15.Karlsson MO, Sheiner LB. The importance of modeling interoccasion variability in population pharmacokinetic analyses. J Pharmacokinet Biopharm. 1993;21:735–50. doi: 10.1007/BF01113502. [DOI] [PubMed] [Google Scholar]
- 16.Takama H, Tanaka H, Sudo T, Tamura T, Tanigawara Y. Population pharmacokinetic modeling and model validation of a spicamycin derivative, KRN5500, in phase 1 study. Cancer Chemother Pharmacol. 2001;47:404–10. doi: 10.1007/s002800000257. [DOI] [PubMed] [Google Scholar]
- 17.Jonsson EN, Karlsson MO. Xpose—an S-PLUS based population pharmacokinetic/pharmacodynamic model building aid for NONMEM. Comput Meth Programs Biomed. 1999;58:51–64. doi: 10.1016/s0169-2607(98)00067-4. [DOI] [PubMed] [Google Scholar]
- 18.Hastie TJ. Generalized additive models. In: Chambers JM, Hastie TJ, editors. Statistical Models in S. Pacific Grove, CA: Wadsworth and Books/Cole Advanced Books & Software; 1992. pp. 249–307. [Google Scholar]
- 19.Ishibashi T, Yano Y, Oguma T. Population pharmacokinetics of platinum after nedaplatin administration and model validation in adult patients. Br J Clin Pharmacol. 2003;56:205–13. doi: 10.1046/j.1365-2125.2003.01871.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 20.Jelkmann W. The enigma of the metabolic fate of circulating erythropoietin (Epo) in view of the pharmacokinetics of the recombinant drugs rhEpo and NESP. Eur J Haematol. 2002;69:265–74. doi: 10.1034/j.1600-0609.2002.02813.x. [DOI] [PubMed] [Google Scholar]
- 21.Macdougall IC, Roberts DE, Coles GA, Williams JD. Clinical pharmacokinetics of epoetin (recombinant human erythropoietin) Clin Pharmacokinet. 1991;20:99–113. doi: 10.2165/00003088-199120020-00002. [DOI] [PubMed] [Google Scholar]
- 22.Plum J, Schoenicke G, Kleophas W, Kulas W, Steffens F, Azem A, Grabensee B. Comparison of body fluid distribution between chronic heamodialysis and peritoneal dialysis patients as assessed by biophysical and biochemical methods. Nephrol Dial Transplant. 2001;16:2378–85. doi: 10.1093/ndt/16.12.2378. [DOI] [PubMed] [Google Scholar]