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Variability of the Model-Independent AUC: The One Sample Per Individual Case

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Abstract

A theory is developed for estimation of a population value of AUC along with its standard deviation, in the case, when only one concentration–time (C–t) sample is available for each individual. This theory is based on model-independent pharmacokinetics. Integration methods are classified due to their applicability to the presented approach. The main goal of this work is to establish a statistical hypothesis-testing procedure which would make single C–t samples usable for bioequivalence studies. An application of the theory to a number of integration methods currently in use is analyzed in detail. A real data illustration is included.

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REFERENCES

  1. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C. The Art of Scientific Computing, 2nd ed., Cambridge University Press, Cambridge, 1992.

    Google Scholar 

  2. 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 

  3. K. C. Yeh and R. D. Small. Pharmacokinetic evaluation of stable piecewise cubic polynomials as numerical integration functions. J. Pharmacokin. Biopharm. 17:721–740 (1989).

    Article  CAS  Google Scholar 

  4. 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 

  5. 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 

  6. L. B. Sheiner and S. L. Beal. Evaluation of methods for estimating population pharmacokinetic parameters: I. Michaelis-Menten model: Routine clinical pharmacokinetic data. J. Pharmacokin. Biopharm. 8:553–571 (1980).

    Article  CAS  Google Scholar 

  7. 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 

  8. S. L. Beal and L. B. Sheiner. NONMEM User's Guide, NONMEM Project Group, University of California, San Francisco, 1989.

    Google Scholar 

  9. H. Mager and G. Göller. Analysis of pseudo-profiles in organ pharmacokinetics and toxicokinetics. Stat. Med. 14:1009–1024 (1995).

    Article  CAS  PubMed  Google Scholar 

  10. W. Jawien. On continuity of Integration Methods for AUC. A Note. J. Pharmacokin. Biopharm. 26:125–130 (1998).

    Article  CAS  Google Scholar 

  11. R. E. Kirk. Experimental Design, 3rd ed., Brooks/Cole, 1995.

  12. H. Heinzl. A note on testing area under the curve when using destructive measurement techniques. J. Pharmacokin. Biopharm. 24:651–655 (1996).

    Article  CAS  Google Scholar 

  13. D. J. Schuirmann. A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. J. Pharmacokin. Biopharm. 15:657–680 (1987).

    Article  CAS  Google Scholar 

  14. J. Yuan. Estimation of variance for AUC in animal studies. J. Pharm. Sci. 82:761–763 (1993).

    Article  CAS  PubMed  Google Scholar 

  15. 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 

  16. M. L. Rocci Jr. and W. Jusko. LAGRAN program for area and moments in pharmacokinetic analysis. Comput. Prog. Biomed. 16:203–216 (1983).

    Article  Google Scholar 

  17. R. D. Purves. Bias and variance of extrapolated tails for area-under-the-curve (AUC) and area-under-the-moment-curve (AUMC). J. Pharmacokin. Biopharm. 20:501–510 (1992).

    Article  CAS  Google Scholar 

  18. R. C. Gagnon and J. J. Peterson. Estimation of confidence intervals for area under the curve from destructively obtained pharmacokinetic data. J. Pharmacokin. Biopharm. 26:87–102 (1998).

    Article  CAS  Google Scholar 

  19. A. J. Bailer and S. J. Ruberg. Randomization tests for assessing the equality of area under curves for studies using destructive sampling. J. Appl. Toxicol. 16:391–395 (1996).

    Article  CAS  PubMed  Google Scholar 

  20. F. Vandenhende, M. Comblain, M. H. Delsemme, W. Dewe, W. P. Hoffman, and B. Boulanger. Construction of an optimal destructive sampling design for noncompartmental AUC estimation. J. Pharmacokin. Biopharm. 27:191–212 (1999).

    Article  CAS  Google Scholar 

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  1. Collegium Medicum of Jagiellonian University, ul, Medyczna 9, 30-688, Kraków, Poland

    Wojciech Jawień

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  1. Wojciech Jawień
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Jawień, W. Variability of the Model-Independent AUC: The One Sample Per Individual Case. J Pharmacokinet Pharmacodyn 27, 437–464 (1999). https://doi.org/10.1023/A:1020921323001

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  • DOI: https://doi.org/10.1023/A:1020921323001

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