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Antimicrobial Agents and Chemotherapy, November 2006, p. 3950-3952, Vol. 50, No. 11
0066-4804/06/$08.00+0     doi:10.1128/AAC.00337-06
Copyright © 2006, American Society for Microbiology. All Rights Reserved.

Impact of Sample Size on the Performance of Multiple-Model Pharmacokinetic Simulations

Vincent H. Tam,^1* Samer Kabbara,¹ Rosa F. Yeh,¹ and Robert H. Leary^2,

Department of Clinical Sciences and Administration, University of Houston College of Pharmacy, Houston, Texas,¹ Laboratory of Applied Pharmacokinetics, University of Southern California School of Medicine, Los Angeles, California²

Received 20 March 2006/ Returned for modification 31 July 2006/ Accepted 30 August 2006

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Monte Carlo simulations are increasingly used to predict pharmacokinetic variability of antimicrobials in a population. We investigated the sample size necessary to provide robust pharmacokinetic predictions. To obtain reasonably robust predictions, a nonparametric model derived from a sample population size of 50 appears to be necessary as the input information.

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Monte Carlo simulations are increasingly used to predict pharmacokinetic variability of antimicrobials in a population, based on well-characterized data from relatively few subjects. In contrast to simulation methods using only population means, the pharmacokinetic parameters (e.g., volume of distribution) used in Monte Carlo methods are generated based on the central tendency and dispersion of each parameter (2). Thus, the pharmacokinetic profiles simulated may more realistically represent a wide spectrum of patients with different capabilities of handling the drug. Coupled with additional data on pathogen susceptibility distribution and pharmacodynamic threshold exposures predicting favorable outcomes, the probability of an antimicrobial dosing regimen in achieving a predetermined pharmacodynamic target can be estimated prior to the initiation of therapy (8-10). The predictive performance of the simulations is likely dependent on the size of the sample population; therefore, we examined the sample size necessary to provide robust and realistic pharmacokinetic predictions.

(This study was presented in part at the 15th European Conference of Clinical Microbiology and Infectious Diseases, Nice, France, 1 to 4 April 2006.)

A universal population of 500 subjects was constructed. The underlying model structure was a two-compartment linear model with known parameter values (elimination rate constant, 0.3 h^–1; intercompartmental transfer rate constant from central to peripheral compartment, 1 h^–1; intercompartmental transfer rate constant from peripheral to central compartment, 0.3 h^–1; volume of distribution of the central compartment, 20 liters) and dispersions (coefficient of variation of 25% for all parameters). Normal distribution of parameter values and no correlation among the parameters were assumed. Serial concentrations over 24 h (at 0.25, 0.5, 1, 2, 4, 8, 12, and 24 h) in the central compartment were simulated after a 1,000-mg intravenous bolus dose for each subject. System noise was incorporated as a 4% coefficient of variation random error around the drug concentrations.

Using sample populations of various sizes (5, 10, 25, 50, and 125 random simulated pharmacokinetic profiles), the best-fit parameter estimates were determined using a nonparametric population analysis (nonparametric adaptive grid program; Laboratory of Applied Pharmacokinetics, Los Angeles, CA) (7). The estimation process was repeated in quadruplicate for each population of a stated size. Based on these best-fit model parameter estimates, the mean and standard deviation (SD) of the area under the concentration-time curve from time zero to infinity (AUC_0-) for each sample population were simulated using a multiple-model approach. Briefly, the nonparametric population analysis output consisted of a collection of discrete vector support points, each with an associated probability (an analog to a joint density function). Using the parameter estimates of each support point, the AUC_0- was computed by integrating the simulated serum concentrations with respect to time from time zero to infinity. The overall pharmacokinetic exposure and variability of the sample population were subsequently computed using the weighted average of the simulations from each of the discrete vector support points. To assess the impact of sample size on the reliability of predicting drug exposure and variability in the universal population, the true AUC_0- of the universal population was simulated using known parameter values and dispersions. Using various sample sizes as inputs, the performances of the simulations were compared based on the bias and precision of the AUC_0- predictions. The predictions were considered acceptable if bias/precision for the mean and variability (SD) of AUC_0- were <10% and <25%, respectively.

With different pharmacokinetic profiles used as input for the population analyses, the output files of the best-fit model also differed in the number of discrete vector support points. Using 5, 10, 25, 50, and 125 simulated pharmacokinetic profiles as input, the corresponding numbers/ranges of vector support points obtained were 5, 10, 24 to 25, 46 to 50, and 106 to 117, respectively. The true pharmacokinetic exposure in the universal population was 194.8 ± 109.9 mg · h/liter.

With respect to mean AUC_0-, the predicted values were unbiased (<10%) regardless of the sample population size used. As the sample population size increased, a trend toward a more precise estimation of AUC_0- was observed (Table 1). A sample population size of 10 was found to be necessary to achieve the predetermined performance standard for estimating the AUC_0- in the universal population. In contrast, the SD of the AUC_0- in the universal population was more difficult to capture (Table 2). In all sample sizes, the true SD of the AUC_0- in the universal population was underpredicted. However, a trend toward more-accurate and -consistent estimation of drug exposure variability in the universal population was noted as the sample population size increased. A sample population size of 50 was found to be necessary for estimating the SD in the universal population satisfactorily.

View this table: [in this window] [in a new window]

TABLE 1. Performance of the various sample sizes on the estimation of mean drug exposure (AUC0-)a

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TABLE 2. Performance of the various sample sizes on the estimation of variability of drug exposure (SD of AUC0-)a

Monte Carlo simulation is an improved research technique over the traditional method in predicting the likely outcome based on prior information. When used appropriately, it holds great potential for improving the drug development process and patient care in the clinical setting. However, one should realize the limitation that it is only a research tool. The clinical relevance of the results is highly dependent on the quality of the input information. One question often debated among investigators in this field is how much prior known information is necessary to derive robust and realistic simulated information; more specifically, how many subjects constitute a reasonably informative sample population? Since the objective of most population pharmacokinetic studies is not to compare the outcomes of two groups, the use of power analysis alone may not be applicable to facilitate sample size predetermination.

With Monte Carlo simulation, the distributions of the model parameter values must be known and used as inputs. In practice, the distributions of pharmacokinetic parameter values are often unknown and empirically assumed (1, 4-6). In this study, we used a multiple-model simulation approach which does not require any assumption concerning the shape of the model parameter distributions (e.g., normal, log normal, multimodal, etc.). The joint probability function of the discrete support points from the best-fit model was used in place of the model parameter distributions. The concept of multiple-model dosage design was originally proposed by Jelliffe et al., who intended to formulate a dosage regimen that would most precisely achieve a predetermined pharmacokinetic target (3). Since nonparametric population pharmacokinetic models are explicitly designed to provide parameter estimates with the highest likelihood of accounting for the observations in a population, they will also give the most precise prediction of variability in the same population. Distribution functions of the parameter estimates are not assumed; instead, the best-fit model is represented by a collection of discrete models, each with their respective probabilities.

In order to assess the impact of sample size on the performance of Monte Carlo simulations, we formulated a theoretical population of 500 subjects with known pharmacokinetic parameter values and dispersions (the reference universal population). This approach was necessary to achieve the objective of the study, as clinical data sets are not appropriate for this purpose. In any clinical pharmacokinetic data set, the true value of the pharmacokinetic exposure and variability is unknown. Therefore, it would be impossible to assess the performances of different sets of simulated pharmacokinetic profiles. Although we used only 500 subjects with one model structure in our study, other universal population sizes, model structures, and parameter variabilities could certainly be used. The purpose of this study was not to exhaustively evaluate every aspect of Monte Carlo simulation. Rather, it highlighted an objective approach in which such a specific question in research methodology could be addressed. Our results are consistent with our expectations. As sample population size increases, more-realistic predictions of drug exposure can be made in the universal population. Mean drug exposure in a population is easier to capture, but it is imperative that the variability of drug exposure also be realistically predicted, if the goal is to accurately estimate the probability of a dosing regimen in achieving a predetermined pharmacodynamic target (11). Models with subpopulations such as multimodal parameter distributions may require many more patients (perhaps >100), but these considerations are outside the scope of the present study. Simulation studies using too few subjects as input may not be very robust, and the results should be interpreted with caution unless they are validated by subsequent observations.

In summary, our results reaffirm that the inferring capability of Monte Carlo simulation is dependent on sample population size. In order to obtain reasonably robust pharmacokinetic predictions, a nonparametric model derived from a sample population size of 50 appears to be necessary as the input information. These results may facilitate the design of future population pharmacokinetic and simulation studies.

 
This investigation benefited from communications and a critical review by Roger W. Jelliffe.

 
* Corresponding author. Mailing address: University of Houston College of Pharmacy, 1441 Moursund Street, Houston, TX 77030. Phone: (713) 795-8316. Fax: (713) 795-8383. E-mail: vtam{at}uh.edu.

Published ahead of print on 5 September 2006.

Present address: Pharsight Corporation, Cary, N.C.

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Antimicrobial Agents and Chemotherapy, November 2006, p. 3950-3952, Vol. 50, No. 11
0066-4804/06/$08.00+0     doi:10.1128/AAC.00337-06
Copyright © 2006, American Society for Microbiology. All Rights Reserved.

This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Reprints and Permissions Copyright Information Books from ASM Press MicrobeWorld Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Tam, V. H. Articles by Leary, R. H. Search for Related Content PubMed PubMed Citation Articles by Tam, V. H. Articles by Leary, R. H.