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Population Pharmacokinetics of Oxycodone in Children 6 Months to 7 Years Old

From the Metrum Research Group, Tariffville, Connecticut (Dr El-Tahtawy); the Department of Anesthesiology and Intensive Care, Kuopio University Hospital, Department of Pharmacology and Toxicology, University of Kuopio, Kuopio, Finland (Dr Kokki); and the Departments of Pharmacology and of Pediatrics, Weill Medical College of Cornell University, New York, New York (Dr Reidenberg).

Address for reprints: Bruce E. Reidenberg, MD, Departments of Pharmacology and Pediatrics, Weill Medical College of Cornell University, 1300 York Avenue, New York, NY 10021.

	ABSTRACT

TOP ABSTRACT METHODS RESULTS DISCUSSION REFERENCES

 
Young children are often undertreated for pain. One barrier to effective pain treatment is understanding the pharmacokinetic behavior of analgesics in this age group. Oxycodone is a commonly prescribed opioid for severe pain, yet little is known about its pharmacokinetics in young children. This article used population pharmacokinetic modeling to synthesize pharmacokinetic data from several studies into a model. A single population model that described the observed pharmacokinetics was developed. The combined data were best described with a 2-compartment linear model with different first-order absorption rates depending on route of administration. Weight was found to significantly influence both clearance (CL) and volume of distribution (Vd). The following model adequately describes the population pharmacokinetic profile of oxycodone where absolute bioavailability (F) is estimated for each administration route: CL/F = 55 x (body weight/70)^0.87; V/F= 86 x (body weight/70)^1.16. The interindividual coefficients of variation in CL and Vd were 20.2 and 19.7%, respectively. This finding confirms that the allometric scaling using the above model explained most of the variability in exposure observed among children. This model confirms using a weight-based dose for oxycodone without adjustment for age between 6 months and 7 years and is valuable for evaluating dosing schedules and dosing routes.

Key Words: Opioid • pediatric • pharmacokinetics

Although oxycodone has been widely used in a variety of clinical settings by pediatric pain specialists, data on oxycodone in children are limited.^7,12,16 These data show few differences between adults and children as young as 8 months old. At present, the initial dose of oxycodone is not standardized and is determined by local practice based on tradition. For practitioners in a locale that initiates therapy at a very low dose, the time required to properly titrate a patient to adequate relief may be frustratingly long. Sufficient information may exist within the data sets of articles to propose safe starting doses and dose intervals based on the predictable pharmacokinetic behavior of oxycodone. This article uses data from the investigations by Kokki et al¹⁶ to construct a mathematical model of the pharmacokinetic behavior of oxycodone in pediatric patients.

	METHODS

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Patient population description and plasma concentration sampling methods have been described.¹⁶ This open-label pharmacokinetic study was approved by the Ethics Committee of Kuopio University Hospital, the Finnish National Agency for Medicines was notified, and the study was conducted in accordance with the latest version of the Declaration of Helsinki. Briefly, pediatric patients receiving operative therapy at Kuopio University Hospital in Kuopio, Finland, were eligible unless they had conditions known to interfere with intramuscular or oral absorption of drugs or with hepatic metabolism or renal excretion of oxycodone. "The parents, and children old enough, were given oral and written information on the trial protocol and parents provided written consent."^16(p615) Forty children, aged 6 months to 7 years, were enrolled. Patients were premedicated with midazolam and ketamine; 17 received general anesthesia, whereas 21 received regional nerve block for their procedures. The pediatric anesthesiologists using best current practices provided intraoperative and postoperative analgesia. The oxycodone (Oxanest, Leiras Oy, Turku, Finland) dosage was 0.1 mL/kg via each of the routes of administration studied. Oxycodone concentration was assayed on blood samples drawn through indwelling catheters using a validated gas chromatography-mass spectrometry method with a linear range between 1 and 200 mg/L.¹⁶ A time-intensive pharmacokinetic sampling schedule was used. The previously reported pharmacokinetics used noncompartmental analysis.¹⁶ A total of 382 plasma concentrations that were obtained from 39 patients in 4 separate studies were included in the population pharmacokinetic analysis. The characteristics of the patients used in the population pharmacokinetic analysis were as follows: 39 children aged 6 to 88 months (mean, 39 months) whose weight ranged from 8 to 43 kg (mean, 16.3 kg) of whom 30 were boys and 9 were girls.

Pharmacokinetic Modeling
Two-compartment pharmacokinetic models with first-order elimination and absorption were used. All the data from all children in the 4 studies with different routes of administration were fitted simultaneously (Figure 1). For the buccal route of administration, single and dual absorption of first-order absorption rates were tried to reflect the reality that part of the dose will be swallowed.

View larger version (14K): [in this window] [in a new window]   Figure 1. Pharmacokinetic structural model for different routes of administration of oxycodone formulations. Parameters are central (V2) and peripheral (V3) compartmental volumes, total body clearance (CL), intercompartmental rate transfers (K23, K32), rate of absorptions (K12, K42, K52) for oral, buccal (BU), and intramuscular (IM) routes of administrations, with their absolute bioavailability (F1, F4, F5), respectively. IV, intravenous; Soln, solution.

A population pharmacokinetic analysis was conducted using pooled pharmacokinetic data from 4 conditions: intravenous, intramuscular, oral, and sublingual. The data set contained pooled pharmacokinetic, demographic/covariate, and dosing information from all 4 conditions. Data were analyzed using nonlinear mixed-effects modeling with the NONMEM software system, version V, level 1.1 with the PREDPP model library and NMTRAN subroutines (GloboMax LLC, Hanover, Md). Models were developed on personal computer workstations with Intel Pentium 4 processors (Intel, Santa Clara, Calif), Windows XP Professional operating system (Microsoft Corp, Redmond, Wash), and the Compaq Visual Fortran Compiler version 6.6B (Hewlett-Packard, Palo Alto, Calif). The first-order conditional estimation method with — interaction (FOCE-INT) was employed for all model runs. Individual estimates of pharmacokinetic parameters were obtained using POSTHOC (an empirical Bayes estimation method). The random-effect models sufficiently described the error distributions. For this analysis, all interindividual errors were described by exponential error models on selected parameters (Equation 1).

(1)

where

• P_i is the true parameter value for individual i,
  
• is the typical population value (geometric mean) of the parameter, and
  
• ^Pi are individual-specific interindividual random effects for individual i and parameter P and are assumed to be independently and identically distributed: N(0, ²).
  

The data could not support a full covariance block for the omega matrix. Modeling began with the assumption of no covariance between interindividual random effects (diagonal omega matrix). Later, the covariance between CL and Vd was estimated. For pharmacokinetic observations in this analysis, the residual error model was initially described by a combined additive and proportional error model (Equation 2).

(2)

where

• C_ij is the jth measured observation (plasma concentration) in individual i,
  
• _ij is the jth model predicted value (plasma concentration) in individual i, and
  
• _pij and _aij are proportional and additive residual random errors, respectively, for individual i and measurement j and are assumed to be independently and identically distributed:N(0, ²). For each administration route, separate residual errors were explored.
  

A covariate modeling approach emphasizing parameter estimation rather than stepwise hypothesis testing was implemented for this population pharmacokinetic analysis. First, predefined covariate-parameter relationships were identified based on exploratory graphics and scientific reality, and a full model was constructed, avoiding colinearity in predictors. Graphical exploration, including diagnostic plots and omega-covariate plots, was used to judge general goodness of fit and appropriate 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 fits was also employed as part of judging the model performance for each patient. Model parameters were estimated, and assessment of any remaining trends was conducted by graphical inspection of all covariate effects. Inferences about clinical relevance of parameters were based on the resulting parameter estimates of the full model and measures of estimation precision. The criteria for successful runs were restricted to successful convergence using FOCE with interaction, good diagnostics for the model fit for all data of the different routes of administrations, and reasonable estimates for fixed-effect and random-effect parameters.

In addition to the model fit diagnostics, models were compared using the objective function value. A decrease on the objective function value that corresponds to a chi-square distribution with a = 0.01 and degrees of freedom equal to the difference in the number of estimated parameters between the 2 models was used as the criteria for model comparisons.

Interindividual variability could not be incorporated on all fixed-effects parameters to get successful FOCE runs. For residual variance, a separate residual error was assigned for each of the routes of administration. Initially, a combined additive and proportional error model was used with 8 parameters to be estimated for the residual error. Because of the limitations of the data, convergence was not possible with all the desired parameters. The final model used only 1 additive error for both intravenous and intramuscular administration, whereas oral and buccal administration used separate proportional error.

Various absorption models were evaluated for the buccal route, but only the model that best described the data (as determined by the log likelihood criterion and visual inspection) is presented. Absorption of oxycodone from the buccal route was best described by the biexponential absorption model. This model was adopted to accommodate the fact that some of the buccal dose would be absorbed through oral route. This model was initially preferred over a mono-exponential, as it gives a slightly better fit to the buccal data over the mono-exponential model; but was not chosen, as the model did not meet our criteria for a successful run in terms of a complete successful convergence with reasonable estimate for precision.

After we established the structural pharmacokinetic model, we incorporated known physiologic relationships into the covariate-parameter models. For example, the change in physiologic parameters as a function of body size is both theoretically and empirically described by an allometric model (Equation 3).^17-21

(3)

where: the typical value of a model parameter (TVP) was described as a function of individual body weight (WT_i), normalized by a reference weight (WT_ref), which was 70 kg. _TVPis an estimated parameter describing the typical pharmacokinetic parameter value for an individual with weight equal to the reference weight and _allo is an allometric power parameter (which can be estimated or fixed to a value of 0.75 for CLs, and a value of 1 for anatomical volumes).

Model Validation Using Prediction Intervals
A predictive check model evaluation step²² was performed to assess the performance of the final model and parameters. Data were simulated with the final model and its parameter estimates under the same experimental design of the original data. One hundred Monte Carlo simulation replicates of the original data set were generated using the final population pharmacokinetic model. Distributions of a characteristic of the simulated data were compared with the distribution of the same characteristic in the observed data set. The characteristic of interest was the mean concentration across all data points within each individual (C_avg). The simulated data from the 100 virtual trials (3900 subjects) were assembled, and the similarity between the actual observed data and simulated data was examined by comparing the 95% predictions intervals of the simulated data with the original observed data.

	RESULTS

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The data were well described by a 2-compartment model with first-order absorption and elimination. A dual absorption model for the buccal route was tried to mimic two separate mechanisms for buccal absorption, as part of the dose would be absorbed through the oral route. The fit of the data was equally good, but there was no improvement of variance estimation or decrease of the objective function. In addition, the estimation of the dual absorption parameters and their variance terms were not very well estimated because of the low number of children. The more parsimonious model was chosen as the final model.

The chosen final model has 12 fixed-effect parameters and 8 random-effect parameters as shown in Table I. Clearance and Vd are standardized to a 70-kg person using the allometric size model. The final population pharmacokinetic parameters are standardized to a 70-kg person using the allometric size model. The remaining interindividual coefficients of variation in CL and Vd were 20.2 and 19.7%, respectively. Effects of gender and age on oxycodone were poorly defined, and no conclusive trends were identified. Although gender and age were not significant in any further improvement of the model, we cannot exclude their effects because of the limitation of the data.

The output of the model is displayed in Figures 2, 3, 4, 5.

View larger version (31K): [in this window] [in a new window]   Figure 2. Goodness of fit plots for the final population model. Top panel, observed versus predicted and individual predicted plasma oxycodone levels. The solid line represents the line of identity. Bottom panel, weighted residual versus predicted plasma oxycodone levels and time, respectively.

View larger version (34K): [in this window] [in a new window]   Figure 3. Fit of concentrations predicted by the pharmacokinetic models (solid heavy line) to the actual plasma concentrations during the first 12 hours after a single-dose administration of oxycodone (0.1 mg/kg). The observed data are represented by the open circles; the population predicted fit is represented by the solid thick line.

View larger version (22K): [in this window] [in a new window]   Figure 4. Observed and predicted oxycodone concentrations of 4 typical children during the first 12 hours after a single dose of oxycodone by intramuscular (IM), intravenous (IV), oral (PO), and buccal (0.1 mg/kg) administration. The dotted line represents the fit predicted by the typical pharmacokinetic model parameters. The solid line shows the fit of the post hoc estimates of the population model; circles represent the observed concentrations.

View larger version (28K): [in this window] [in a new window]   Figure 5. The observed data are plotted as individual points. The solid lines represent the median values of the 100 simulated data sets (using 0.1 mg/kg dose), whereas the upper and lower dashed lines represent the 97.5th and 2.5th quantiles of the simulated data, respectively.

A good fit was shown between the observed and the population or the individual predicted plasma oxycodone concentrations (Figure 2, top panel). Also, no systematic relationship is seen in the weighted residual plots (Figure 2, bottom panel), which confirms that the model provides an adequate description of the data. For the structural model, the disposition model was parameterized in CL and Vd and different Fs for the bioavailability of the different oral and parenteral routes of administrations. The absolute bioavailability of the immediate-release oral solution (oral, buccal) and intramuscular administration were determined in this study because an intravenous reference dose was included in the data set.

The model fit was examined for each child's data. Figure 4 shows 4 typical children's observed and predicted oxycodone concentrations during the first 12 hours after a single dose of oxycodone by intramuscular, intravenous, oral, and buccal (0.1 mg/kg) administration. The fit predicted by the typical pharmacokinetic model parameters or the fit of the post hoc estimates of the population model describe the individual observed concentrations quite well.

Last, Figure 5 displays median, 97.5th, and 2.5th quantiles of the simulated data as lines with the observed data plotted as individual points. Less than 5% of the observed data lies above or below the 95% prediction intervals. No biased pattern or any tendency of overestimation or underestimation for the different route of administration data is observed. This finding gives confidence in the model performance in predicting not only the expected mean exposures but also the extreme expectation of exposures after various oxycodone administrations.

	DISCUSSION

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The final population pharmacokinetic model provided a good description of the pediatric data from the different studies. Goodness of fit criteria revealed that the final model was consistent with the observed data and that no systematic bias remained. The data displayed in Figure 2 are scattered closely and randomly around the line of identity, which indicates the model fits the data well. The homogenous and random distributions of weighted residuals indicate the error model was suitable for describing the variance of the data. The model validation results provided evidence that both the fixed-effects and random-effects components of the final model were reflective of the observed data as well. The fact that less than 5% of the data are located outside the 2.5 to 97.5 quantiles range suggests that the model well describes the central tendency and the variability of the data for all routes of administration. This performance is accomplished despite the large number of parameters and the low number of patients who participated in the studies. The predictive check shows there is no bias at any phase of the blood profile, which makes the model useful in predicting the extremes of oxycodone blood concentration.

The data collected from the 4 studies were not designed for population analysis. The variability associated with the buccal administration route was attributed in part to the loss of some of the doses through spitting or drooling. One of the goals of the current work was to explore how nonlinear mixed-effects modeling could be used to analyze heterogeneous experimental data in a small number of children using intensive sampling, whose data is also characterized by large variability. To our knowledge, this is the first time a population approach is used to model oxycodone in children.

The size model explained most of the variability in CL and Vd of oxycodone in children. This finding reinforces the use of weight-based dosing for oxycodone in children in this age group. This information shows that it is not necessary to give smaller weight-based doses to younger children compared to older children within this age group. The CL and Vd parameters were strongly related to weight with power values of 0.875 and 1.16, respectively. These values agree very well with the published data^17-21 that suggest assigning 0.75 and 1.0 as exponents for CL and Vd, respectively. The use of the per-kilogram size model instead of the allometric size model has led to the misconception that children need a higher dose, as they may have enhanced capacity to metabolize drugs (because of relatively large liver size or increased hepatic blood flow). This model helps support the selection of a starting dose of 0.1 mg/kg of oxycodone for moderate to severe pain in children 6 months to 7 years.

Like recent studies of hepatically metabolized intravenous milrinone by Bailey et al²³ and voriconazole by Walsh et al²⁴ in children under 6 years old, our model shows that weight is more important than age as a covariate. In this article, we have the additional information regarding oral dosing, which is not available for milrinone or voriconazole in children. Intravenous midazolam use in the pediatric intensive care unit was modeled by de Wildt et al²⁵ in patients sicker than those we studied. Like oxycodone, milrinone, and voriconazole, midazolam is hepatically metabolized, and the model of midazolam pharmacokinetics in children showed that age was not an important covariate compared to weight. Ramakrishnan et al²⁶ studied intravenous montelukast in children with asthma and identified total body water as more predictive than weight and both more predictive than age. Taken together, these are interesting findings because the known developmental regulation of the cytochrome C P450 (CYP) system elucidated by de Wildt et al²⁷ would predict an increasing CL with increasing age in the ages under study. The modeling results showing this to be a nonsignifcant covariate is surprising and likely attributable to changes in CYP activity that are subtle relative to the interindividual variability of these lipid soluble medications.

The principle of patient weight being a more important predictor of CL in children than age has also been recently shown with 2 nucleoside analogs: an antiretroviral abacavir studied by Jullien et al²⁸ and an oncolytic clofaribine studied by Bonate et al.²⁹ These drugs' CL is dependent on intracellular phosphorylation more than on hepatic metabolism, and the separately derived models from different patient populations have both determined weight or body surface area to be a more important covariate than age.

The situation is quite different for renally excreted drugs such as aminoglycosides. A recent study by de Hoog et al³⁰ with a derived model has shown that adjusting dose interval for gestational age in newborns is critical to pharmacokinetically managed amikacin dosing. In more mature children, the developmental changes in renal CL are subtle, and dose adjustment for age is unnecessary, as has been demonstrated for carbapenem antibacterial drugs.³¹

The mathematical treatment of the data described in this article allows for more clear interpretation of unique as well as common pharmacokinetic characteristics of oxycodone in children in terms of the large intersubject variability. With this model, assessments of the effect of dose adjustment can be made without putting additional children at risk in a study. Furthermore, quantitative assessments of the contributions of absorption at different sites (sublingual space vs intestine) can be made noninvasively. Finally, this model can be used to create mathematical simulations of proposed clinical trials so that the optimal design of a future clinical trial can be effected.

DOI: 10.1177/0091270006286433

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TOP ABSTRACT METHODS RESULTS DISCUSSION REFERENCES

 

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in ISI Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Request Permissions Request Reprints Citing Articles Citing Articles via ISI Web of Science (3) Citing Articles via Google Scholar Google Scholar Articles by El-Tahtawy, A. Articles by Reidenberg, B. E. Search for Related Content PubMed PubMed Citation Articles by El-Tahtawy, A. Articles by Reidenberg, B. E. Social Bookmarking                   What's this?