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PEDIATRICS |
From the Center for Drug Development Science, Georgetown University, Washington, DC (Dr Yim, Dr Peck, Dr Lee); Wyeth Research, Collegeville, Pennsylvania (Dr Zhou, Ms Buckwalter); and Amgen, Thousand Oaks, California (Dr Nestorov).
Address for reprints: Howard Lee, MD, PhD, Center for Drug Development Science, Department of Pharmacology, Box 571441, Georgetown University School of Medicine, Washington, DC 20057-1441.
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Key Words: Etanercept • population pharmacokinetics • modeling • juvenile rheumatoid arthritis • clinical trial simulation
, a naturally occurring cytokine, is believed to play a central role in the pathogenesis of rheumatoid arthritis (RA).3,4 Elevation of synovial TNF- levels has also been reported in patients with psoriatic arthritis5,6 and JRA.7-9
Etanercept, a TNF-inactivating biological response modifier, is a soluble, dimeric fusion protein consisting of 2 copies of the extracellular ligand-binding protein of the human p75 TNF receptor linked to the constant portion of the human immunoglobulin G1.10 The efficacy of etanercept has been demonstrated in adult patients with refractory RA11 as well as RA of early onset (
3 years).12 Etanercept was also shown to be superior to methotrexate in delaying bone erosion and joint space narrowing in a randomized, double-blind clinical trial of patients with early RA.12 Current indications of etanercept approved by the US Food and Drug Administration (FDA) since 1998 are RA, psoriatic arthritis, ankylosing spondylitis, and polyarticular course of JRA and psoriasis in adults.
Etanercept is slowly absorbed after subcutaneous (SC) injection, and the absolute bioavailability is approximately 58% in adults.13 In adults, etanercept has a relatively small volume of distribution of 12 ± 6Landis slowly absorbed to reach its peak serum concentration about 50 hours after injection14 and cleared from the body with a reported median half-life of 115 hours.15 The recommended etanercept dosing regimen for JRA patients (4-17 years) at the time of its initial approval was 0.4 mg/kg (up to 25 mg) twice weekly by SC injection. However, based on its slow absorption and elimination pharmacokinetic (PK) profile, a doubled dose with a half-frequency regimen (ie, 0.8 mg/kg [up to 50 mg]) of a once-weekly SC injection has been sought for patient convenience.
The objective of this study was to develop a population PK model of etanercept using time-concentration data in pediatric patients with JRA who received 0.4-mg/kg twice-weekly SC injections for up to 3 or 7 months to identify the PK parameters and their variability, coupled with the identification of significant covariates. In addition, to explore the implications of once-weekly dosing, we present the results of clinical trial simulations of concentrations for 0.4-mg/kg (up to 25 mg) SC twice-weekly and 0.8-mg/kg (up to 50 mg) SC once-weekly dosing regimens of etanercept, based on the final population PK model.
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MATERIALS AND METHODS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Population Pharmacokinetic Model Development
Population PK analysis was carried out using NONMEM (Version 5.1). First, a basic structural model based on first-order absorption and elimination was evaluated without incorporating any covariates. Various covariance structures between different kinds of variability were explored and modeled. After the structural model was determined, the covariate effect on the pharmacokinetic parameters was investigated graphically and then tested by estimation. All of the covariates were individually evaluated using a stepwise forward addition and backward elimination approach. Categorical covariates (eg, sex and race) were modeled using indicator variables. For continuous covariates, age, body weight, height, BSA, and baseline value of disease status indices such as BTSW, BPTG, BMDG, BVAS, and BCHA were explored. These continuous covariates were first standardized to data-derived median values, and their effects were modeled as proportionally affecting parameters. Model refinement was performed by deleting covariates that were already incorporated into the model.
In the structural model development process, a decrease in the objective function value (OFV) by 
6.64 (P .01, df = 1) was used as a criterion. As for the covariate search process, its decrease by 10.83 (P .001, df =1) was used as an addition and deletion criterion for each covariate. However, physiological relevance and graphical exploration, including diagnostic plots and an individual prediction plot that were used to judge general goodness of fit, were considered more important in the final covariate selection. Diagnostic plots of observed versus model-based population or individual post hoc predicted values and various residual plots were used to detect any significant systemic deviation from the model fit. Checking of the individual plots was also invariably employed as part of graphical exploration.
Any jth observation of the ith individual (ie, etanercept serum concentration), Obsij, measured at time tj, was defined by the following equation:
 | (1) |
i is the set of the pharmacokinetic parameters for the ith individual, and 
ij represents the residual or unexplained intraindividual shift of the observation from the model prediction. It was assumed that all ij are symmetrically distributed around mean 0, with variance denoted by 
2.
For ik, the kth element of the ith individual's parameter set, the following model was employed:
 | (2) |
pop, k is the mean population parameter of the kth element, and 
ik represents the shift of the parameter of the ith individual from the population mean. Also, ik was further assumed to be an independent multivariate that was normally distributed, with mean 0 and a variance-covariance matrix 
with diagonal elements (
) such that the 
k is approximately the coefficient of variation of the kth parameter with respect to the typical value, pop, k. For residual error in the population PK analysis, additive, proportional, and combined additive and proportional random error models were tested. The first-order (FO) method was used throughout the analyses. In addition, first-order conditional estimation with interaction (FOCE-I) was applied to see if there was a dissimilarity of parameter estimates in the final population PK model, especially in the final estimates for interindividual variability. The 95% confidence intervals (CIs) for parameter estimates were determined by the resampling technique based on the bootstrap method. This was accomplished by creating resampled new data sets using the bootstrap procedure implemented in the Wings for NONMEM,18 with each of the same size as the original. To obtain more than 1000 successfully minimized resamples, we performed a total of 1500 bootstrap runs, 1102 of which met the criteria. The parameters were estimated from each new data set using the final model, which resulted in a bootstrap distribution of the parameter estimate. The 95% CIs were obtained for each parameter as the 2.5th and 97.5th percentiles.
Simulation of Concentrations
A Monte Carlo clinical trial simulation experiment was conducted to compare the predicted PK profiles of 200 virtual pediatric patients with JRA who randomly received either etanercept 0.4 mg/kg (up to 25 mg) SC twice weekly or 0.8 mg/kg (up to 50 mg) once weekly for 12 weeks. A covariate distribution model was separately developed using the covariate information from patients enrolled in the study used for the population PK model development to create a multijoint distribution of covariates. In the simulation, the final population PK model was used as the input-output model. Because the main purpose of this simulation experiment was to characterize the PK profiles of etanercept for 2 different dosing regimens, no trial protocol deviations were incorporated (ie, all enrolled subjects were assumed to be fully compliant to the assigned dosing regimen, and no dropouts or losses to follow up were considered). Pharsight Trial Simulator (Version 2.1.2, Pharsight Corporation, Mountain View, Calif) was used for simulation, and 100 replications were performed taking the parameter uncertainties into account. The steady-state mean, median, and 5th and 95th percentile concentration values at each time point were graphically displayed for 0.4-mg/kg SC twice-weekly and 0.8-mg/kg SC once-weekly regimens. More detailed descriptions about the simulation models are presented in the Results section.
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RESULTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Residual error model. Of 3 residual error models, the combined error model was selected based on the OFV (ie, the OFVs of the proportional error model and the additive error model were greater than the OFV of the combined error model by 229.3 and 102.7, respectively). Individual plots also showed that the combined error model better predicted the observed concentrations than other residual error models.
Correlation between CL and V. A correlation between clearance (CL) and volume of distribution (V) was found in graphical exploration. Therefore, by allowing the covariance structure between interindividual variability on CL and V, the OFV further decreased by 10.15. The addition of interindividual variability on first-order absorption rate (Ka) and its covariance with interindividual variability on CL and V also decreased the OFV by 12.60.
Absorption model. Addition of lag time or a zero-order or combined absorption model did not improve the model fit. Based on these results, the 1-compartment model with first-order absorption and elimination, having interindividual variability on CL, V, and Ka in the covariance structure, was selected as the base structural model for the covariate search.
Covariate search. The covariate search for CL was performed first, followed by covariate searches for V and Ka. On the basis of the OFV change criteria (10.83 at P .001, df = 1), BSA (–142.4), sex (–20.8), and BCHA (–11.6) were added to CL. As for V, body weight and BTSW further decreased the OFV by 15.4 and 23.1, respectively. None of covariates turned out to be significant on Ka. From this full model (ie, BSA, sex, and BCHA on CL; body weight and BTSW on V), each covariate was removed one at a time in the same sequence of their addition. Deletion of all these covariates, except for BCHA on CL, increased the OFV significantly by more than 10.83. Therefore, BCHA on CL was removed from the model. Although removal of BTSW from V increased the OFV by 21.2, individual plots were better fitted without BTSW, and the scatter plot between the individual estimate of V and his or her BTSW did not show any notable relationship. Based on these findings, the model without BTSW on V was selected as the final covariate model.
Final model. Consequently, a 1-compartment first-order absorption and elimination PK model with interindividual variability on CL, V, and Ka, with covariates of sex and standardized BSA on CL and standardized body weight on V, adequately described the time-concentration profiles of etanercept after SC administration in pediatric patients with JRA. FOCE with the interaction estimation method was applied to the final PK model, and the parameter estimates, especially interindividual variability, were similar to the ones estimated by the FO method (data not shown). The model development process is summarized in Figure 1. In addition, Figure 2 shows the general goodness of fit for the final population PK model.
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Population Pharmacokinetic Model Parameters
The fixed- and random-parameter estimates with corresponding 95% confidence intervals from bootstrapping are summarized in Table II. The population mean of apparent clearance (CL/F, where F is bioavailability) in females was 0.0576 L/h (95% CI = 0.0525-0.0657 L/h), which was lower than the male value by 27%. Interindividual variability of CL/F was 29% (95% CI = 22%-35%) and was precisely estimated, judging by the narrow limit of the confidence interval. According to this analysis, the population value of apparent clearance for etanercept can be expressed as
 | (3) |
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The population mean of the apparent volume of distribution (V/F) was 7.88 L (95% CI = 3.03-8.69 L). The population value of the apparent volume of distribution for etanercept employing body weight standardized by its median value (ie, 30.8) can be obtained by
 | (4) |
The population mean of the Ka for etanercept was 0.05 h–1 (95% CI = 0.01-0.99 h–1), with an interindividual variability of 215%. This interindividual variability had a relatively wide 95% confidence interval (29%-1977%).
Half-life was calculated using the population means of CL/F and V/F, that is, half-life = 0.693 (V/CL) for medians for body weight of 30.8 kg and BSA of 1.071 m2. Females had a slightly longer half-life than males (94.8 and 70.7 hours for females and males, respectively). For residual error, additive error was 0.00103 mg/L (95% CI = 0.00052-0.025 mg/L), and proportional error was 30% (95% CI = 27%-36%).
Simulation of Concentration Profiles
Covariate distribution model. A correlation matrix between age (years), body weight (kg), and height (cm) was estimated separately for male and female subjects based on 69 JRA patients used for the population PK model development, and this was used as multijoint covariate distribution model. Based on graphical exploration of covariate distribution of the patients, body weight was assumed to be distributed lognormally, and normal distribution was used for other covariates. BSA was derived from simulated values of body weight and height using the following formula proposed by Haycock et al.20
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It was assumed that female subjects comprised 60% of all virtual patients per replicate, based on study A, in which female subjects consisted of 62% of the total. In addition, the lowest and highest possible values for each covariate were also entered using minimum and maximum values seen in study A.
Input-output model. The final population PK model developed in previous sections was used as the pharmacostatistical input-output model in the simulation experiment. To incorporate parameter uncertainty into the simulation, graphical exploration and descriptive analysis of bootstrapped parameter estimates were performed to identify the distribution of each parameter estimate. Based on the results of this exploratory analysis, lognormal distribution was assumed for the uncertainty of Ka, the interindividual variability on the volume of distribution and Ka, and the additive component of the residual error. All other parameter estimates were assumed to be normally distributed. In addition, a correlation matrix between parameter estimates, fixed and random, was developed to account for the relationships among them. This matrix, coupled with the distribution information described above, was incorporated into the simulation platform, allowing each replicate in the simulation to use a different set of parameter estimates but to keep the relationship between parameter estimates, leading to a more physiologically plausible combination of parameters in individual patients.
The distribution of individual PK parameters in the simulation was set to lognormal, which was observed by graphical exploration of the Bayesian post hoc individual parameters of patients in study A. The correlation between interindividual variability on CL and V was incorporated, and each PK parameter was allowed to vary from individual to individual. Residual variability was also incorporated using the additive and proportional components estimated in the final population PK model. The residual variability was assumed to vary continuously at each measurement, and this was reasonable to take into account noise caused by assay error or other unexplained variability for each measurement.
Trial execution model. The simulation experiment was a single center, double-blind, randomized, parallel, 12-week study to compare the PK profiles of etanercept 0.4-mg/kg (up to 25 mg) SC twice-weekly and 0.8-mg/kg (up to 50 mg) SC once-weekly dosing regimens in pediatric patients with JRA. The total number of subjects was 200, and a block-stratified randomization method (block size = 4, stratified on sex, randomization ratio = 1:1) was used to adjust for different population standard values for clearance/F in female and male patients. The block randomization was adopted to balance the number of subjects assigned to each regimen.
Etanercept was given to each patient at hour 0 on days 1 and 4 of every week for 0.4-mg/kg SC twice-weekly dosing or at hour 0 on day 1 of every week for 0.8-mg/kg SC once-weekly dosing, respectively. The treatment phase was 12 weeks, and at week 12, intensive hourly samples after the dose were obtained. In addition, individual simulated PK parameters and covariates were measured at the beginning of the study. No lead-in, placebo run-in, or follow-up phase was considered, and no deviation from the study protocol was incorporated.
Final simulation results. The distribution of covariates of simulated subjects was comparable to that of patients of study A. In addition, the distributions of covariates in simulated subjects between dosing regimens were similar. To see if the simulation adequately simulated individual concentration values at various time points at steady state, an overlay plot was produced for 0.4-mg/kg SC twice-weekly dosing (Figure 3). From Figure 3, it is clear that most observed concentrations in study A fall in the range between the 5th and 95th percentile values of the simulated concentrations.
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Figure 4 illustrates the steady-state mean concentrations as well as the 5th and 95th percentiles at each sampling time for both the 0.4-mg/kg SC twice-weekly and 0.8-mg/kg SC once-weekly dosing regimens from the simulation experiment. Because residual variability was simulated such that it varied at every point the measurement was made and very intense hourly samplings were taken in the simulation, the lines show slightly noticeable zigzag patterns, especially for the 5th and 95th percentiles. Compared with the 0.4-mg/kg twice-weekly regimen, the mean steady-state peak and trough etanercept concentrations for 0.8-mg/kg once-weekly dosing were 11% higher and 18% lower, respectively (Table III). These results demonstrated that the 2 dosing regimens give widely overlapping concentration profiles at steady state.
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DISCUSSION |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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In the structural model-building process, neither the zero-order nor the combined first- and zero-order absorption model was as good as the simple first-order absorption model. This is understandable because the frequency of pharmacokinetic sampling during the absorption and early distribution phases in study A was insufficient to enable the application of elaborate absorption models such as zero order or combined. The wide 95% CIs of interindividual variability for V and Ka can also be accounted for by this sparse sampling, making these parameter estimates less useful. However, the 95% CIs for other parameters indicated that they were precisely estimated.
To make sure that the number of bootstrap runs and simulation replicates was large enough, we compared the CIs of PK parameters and time-simulated concentration profiles from varying numbers of successfully minimized bootstrap runs (ie, 50, 100, 200, 400, 1000, and 1102) and replicates (ie, 10, 25, 50, and 100), respectively. We found that the means and CIs obtained from more than 200 bootstrap runs were similar regardless of the number of bootstrap runs. Likewise, the number of simulation replicates we adopted here (ie, 100) was found to be large enough to yield reliable results (data not shown).
Interestingly, this analysis confirmed that the estimated population parameters were similar to those reported previously in other disease populations.19 For example, apparent clearance (CL/F) was 0.0576 L/h for females and 0.0772 L/h for males in pediatric patients whose BSA is 1.071 m2 (Table II), and these were similar to adult values of 0.132 ± 0.85 L/h (mean ± SD),14 assuming they weigh 70 kg and are 170 cm tall (ie, BSA = 1.8 m2). In addition, the mean population apparent clearance values observed in adult RA patients were 0.117 L/h for females and 0.138 L/h for males,19 which are comparable to the present results in pediatric patients when gender, body weight, and height are taken into account.
To check if the covariates included in the final PK model are significant, randomization tests were conducted. One thousand data sets in which the covariate of interest was "randomly" reshuffled to individual subjects were refit using the final model, and the difference of the OFV between the base (ie, no covariate) model and the final model was calculated. The P values based on the quantiles of randomized data sets in which the OFV was smaller than the OFV of the base model were .006 (sex on CL), <.0001 (BSA on CL), and .051 (body weight on V), respectively. These results support that those covariates are significant or marginally significant in the case of body weight on V.
To clarify the gender difference in CL/F, we also performed an additional 1162 sets of bootstrapping for the ratio of CL/F in female/male pediatric patients, and a median ratio of 0.77 (95% CI = 0.67-0.93) was obtained. A similar but statistically insignificant difference was obtained from the population PK analysis of adult RA patients, in which standardized body weight was also incorporated as a significant covariate for explaining the difference in CL/F among patients.19 Not much is known about the elimination mechanism of etanercept, and we do not have an appropriate explanation for this gender difference observed both in children and adults. A gender difference in liver blood flow due to differences in cardiac output seems to be an inadequate answer because the CL of etanercept did not differ significantly in patients with heart failure.21 Furthermore, the clinical implication of this observed gender difference in the population analysis is not clear, and so far, no gender differences have been reported with respect to either the efficacy or safety of etanercept. In fact, the 23% difference in CL/F between different genders was similar to the interindividual variability in this parameter (ie, 29% CV, Table II), making the gender difference in the efficacy or safety of etanercept due to the difference in the clearance less likely. Other covariates related to disease severity (eg, BTSW) were also screened for their contribution to PK parameters, but none of them was significant, implying that both severe and mild patients do not differ in their PK behaviors.
Our finding that BSA was better in explaining the variability for CL/F than body weight is worth noting. BSA decreased the objective function value by 142.4, which is greater than the decrease of 136.4 after adding body weight to the model. To see if the PK profiles at steady state of the BSA-based regimen differ from those of the body weight–based regimen (ie, 0.4 mg/kg), an additional simulation experiment with 100 replicates (n = 100 per each regimen) was performed. To obtain the dose per unit BSA for the BSA-based regimen, we assumed that a patient who weighed the data-derived median (ie, 30.8 kg) and a patient whose BSA was the data-derived median (ie, 1.071 m2) received the same dose of etanercept. Therefore, 11.5 mg/m2 (= 0.4 mg/kg x 30.8 kg/1.071 m2) was selected as the dose-per-unit BSA for the BSA-based regimen in the simulation. The mean doses for both regimens were 13.3 mg (body weight–based regimen) and 12.9 mg (BSA-based regimen), and the ranges were [4, 25] and [6.0, 24.1], respectively. The median and 5th and 95th percentiles of serum etanercept concentrations in each quartile group of body weight (ie, 23 kg, >23 and 31, >31 and 43, and >43) are summarized in Figure 5. In the middle 2 quartiles, the 2 regimens did not yield different PK profiles. Interestingly, the simulated PK profiles of the body weight–based regimen were slightly lower than those of the BSA-based regimen in the first quartile, and this was reversed in the highest quartile group. Therefore, the current body weight–based regimen in patients weighing equal to or less than 23 kg may yield slightly lower concentrations compared to patients weighing >23 kg. However, it is not sure if this will lead to clinically significant differences in efficacy for the treatment of patients with JRA by etanercept. Clearly, this should be further investigated in future research.
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In additional NONMEM analyses, we compared the OFVs of different BSA formulas—Mosteller,22 Gehan and George,23 Boyd,24 and DuBois and DuBois.25 They yielded OFVs of 4783.0, 4781.2, 4779.1, and 4785.6, respectively, which was quite similar to 4780.3 found with the Haycock formula. Likewise, there was no noticeable change in diagnostic plots (not shown) between different formulas. In this study, we have chosen to keep the Haycock formula-driven BSA for the population PK analysis and the clinical trial simulation.
Although some clinical trial data for etanercept have been published, knowledge about the relationship between its pharmacokinetics and pharmacodynamics is still scarce. In part, this scarcity arises from the fact that the target diseases of etanercept involve long-term processes, and, therefore, the pharmacodynamics of etanercept is challenging to quantify. For example, the response to etanercept gradually rises to a plateau within 1 year in both RA12 and JRA.16 In contrast, the pharmacokinetic steady state is achieved within 2 weeks or so. The full pharmacodynamic response is therefore much more slowly achieved than the pharmacokinetic steady state. A better pharma-cokinetic parameter correlate for a clinical measure such as ACR20 (the American College of Rheumatology definition) might be cumulative exposure (eg, AUC) rather than instantaneous serum concentrations.19 Using this approach, it may be postulated that the 0.8-mg/kg once-weekly regimen simulated in this report would exhibit clinically similar effects to the 0.4-mg/kg twice-weekly regimen because average concentrations at steady state are similar.
As for the safety of etanercept in pediatric patients, the frequency of adverse events in the 0.4-mg/kg twice-weekly group was not significantly different from that of the placebo group.16 The maximum tolerated dose of etanercept has not been established in humans, and toxicology studies performed in monkeys at doses up to 30 times the human dose gave no evidence of dose-limiting toxicities.15 At the moment, we do not have an answer to whether the degree of immunosuppression by etanercept would increase with the rise in peak concentrations by about 11% after switching to the 0.8-mg/kg once-weekly regimen from the 0.4-mg/kg twice-weekly regimen, as might be expected.
In summary, concentration-time profiles for different doses of etanercept were adequately modeled using a 1-compartment first-order absorption model in this report. Sex and body surface area were influential covariates on clearance, and the volume of distribution was affected by body weight. The concentration simulations for the 0.4-mg/kg twice-weekly and 0.8-mg/kg once-weekly dosing regimens showed overlapping profiles that support interchangeability between these dosing regimens. On the basis of this simulation analysis, the US Food and Drug Administration approved in October 2003 the dosing regimen of etanercept 0.8 mg/kg SC once weekly for pediatric patients with JRA along with 50 mg SC once weekly in adults.26
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FOOTNOTES |
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Submitted for publication April 21, 2004; Revised version accepted October 7, 2004.
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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