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Construction of an Optimal Destructive Sampling Design for Noncompartmental AUC Estimation

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Abstract

Based on toxicokinetic studies of a destructive sampling design, this work was aimed at selecting the number of time points, their locations, and the number of replicates per time point in order to obtain the most accurate and precise noncompartmental estimate of the area under the concentration-time curve (AUC). From a prior population pharmacokinetic model, the design is selected to minimize the scaled mean squared error of AUC. Designs are found for various sample sizes, number of time points, and a distribution of animals across time points from being very unbalanced to balanced. Their efficiencies are compared both theoretically and based on simulations. An algorithm has been implemented for this purpose using the symbolic resolution and numerical minimization capabilities of Mathematica TM and an example of its use is provided. This method provides efficient tools for constructing, validating, and comparing optimal sampling designs for destructive sampled toxicokinetic studies.

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REFERENCES

  1. ICH. Guideline on the assessment of systemic exposure in toxicity studies. Fed. Register 60:11263-11268 (1995).

    Google Scholar 

  2. A. J. Bailer and W. W. Piegorsch. Estimating integrals using quadrature methods with an application in pharmacokinetics. Biometrics 46:1201-1211 (1990).

    Article  CAS  PubMed  Google Scholar 

  3. A. J. Bailer. Testing for the equality of area under the curves when using destructive measurement techniques. J. Pharmacokin. Biopharm. 16:303-309 (1988).

    Article  CAS  Google Scholar 

  4. K. C. Yeh and K. C. Kwan. A comparison of numerical integrating algorithms by trapezoidal, Lagrange and spline approximation. J. Pharmacokin. Biopharm. 6:79-98 (1978).

    Article  CAS  Google Scholar 

  5. R. D. Purves. Optimum numerical integration methods for estimation of area-under-the curve (AUC) and area-under-the moment-curve (AUMC). J. Pharmacokin. Biopharm. 20:211-226 (1992).

    Article  CAS  Google Scholar 

  6. D. Z. D'Argenio. Optimal sampling times for pharmacokinetic experiments. J. Pharmacokin. Biopharm. 9:739-756 (1981).

    Article  Google Scholar 

  7. F. Mentré, P. Burtin, Y. Merlé, J. Van Bree, A. Mallet, and J. L. Steimer. Sparse-sampling optimal designs in pharmacokinetics and toxicokinetics. Drug Inform. J. 29:997-1019 (1995).

    Google Scholar 

  8. F. Mentré, A. Mallet, and D. Baccar. Optimal design in random-effects regression models. Biometrika 84:429-442 (1997).

    Article  Google Scholar 

  9. A. C. Atkinson and A. N. Donev. Optimum Experimental Design, Clarendon Press, Oxford, UK, 1992.

    Google Scholar 

  10. D. A. Beatty and W. W. Piegorsch. Optimal statistical design for toxicokinetic studies. Statist. Meth. Med. Res. 6:359-376 (1997).

    Article  CAS  Google Scholar 

  11. A. J. Bailer and W. W. Piegorsch. MSE considerations when using quadrature rules. ASA Proceedings of the Biopharmaceutical Section, pp. 177-182 (1990).

  12. D. Katz and D. Z. D'Argenio. Experimental design for estimating intervals by numerical quadrature, with applications to pharmacokinetic studies. Biometrics 39:621-628 (1983).

    Article  CAS  PubMed  Google Scholar 

  13. W. W. Piegorsch and A. J. Bailer. Optimal design allocations for estimating area under curves for studies employing destructive sampling. J. Pharmacokin. Biopharm. 17:493-507 (1989).

    Article  CAS  Google Scholar 

  14. G. C. G. Wei. Experimental design for estimating area under the curve by trapezoidal approximation in destructive sampling. Drug Inform. J. 31:1237-1242 (1997).

    Google Scholar 

  15. R. P. Brent. Algorithms for Minimization Without Derivatives, Prentice-Hall, Englewood Cliffs. NJ, 1973.

    Google Scholar 

  16. J. R. Nedelman and E. Gibiansky. The variance of a better AUC estimator for sparse, destructive sampling in toxicokinetics. J. Pharm. Sci. 85:884-886 (1996).

    Article  CAS  PubMed  Google Scholar 

  17. V. Brun. A generalization of the formula of Simpson for non-equidistant ordinates. Nord. Mat. Tidskr. 1:10-15 (1953).

    Google Scholar 

  18. M. M. Bishop, S. E. Fienberg, and P. W. Holland. Discrete Multivariate Analysis, MIT Press, Cambridge, MA, 1975.

    Google Scholar 

  19. K. C. Yeh. Estimation and significance tests for area under the curve derived from incomplete blood sampling. ASA Proceedings of the Biopharmaceutical Section, pp. 74-81 (1990).

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Authors and Affiliations

  1. Statistical and Mathematical Sciences, Eli Lilly & Company, 11 rue Granbonpré, B-1348, Mont-Saint-Guibert, Belgium

    Francois Vandenhende

  2. Department of Biostatistics, Limburgs Universitair Centrum, Universitaire Campus, B-3590, Diepenbeek, Belgium

    Muriel Comblain

  3. Statistical and Mathematical Sciences, Eli Lilly & Company, 11 rue Granbonpré, B-1348, Mont-Saint-Guibert, Belgium

    Marie-Helene Delsemme, Walthere Dewe & Bruno Boulanger

  4. Statistical and Mathematical Sciences, Eli Lilly & Company, 2001 West Main, P.O. Box 708, Greenfield, Indiana, 46140

    Wherly P. Hoffman

Authors
  1. Francois Vandenhende
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  2. Muriel Comblain
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  3. Marie-Helene Delsemme
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  4. Walthere Dewe
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  5. Wherly P. Hoffman
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  6. Bruno Boulanger
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Vandenhende, F., Comblain, M., Delsemme, MH. et al. Construction of an Optimal Destructive Sampling Design for Noncompartmental AUC Estimation. J Pharmacokinet Pharmacodyn 27, 191–212 (1999). https://doi.org/10.1023/A:1020606006936

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  • DOI: https://doi.org/10.1023/A:1020606006936

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