Summary
For a two-way cross-over design, which appears to be the most common experimental design in bioavailability studies, 95%-confidence limits for expected bioavailability can be obtained by classical analysis of variance (ANOVA). If symmetry of the confidence interval is desired about zero (differences) or unity (ratios) rather than about the corresponding point estimator, Westlake's modification can be used. Two nonparametric methods and their adaptations to bioavailability ratios are reviewed, one based on Wilcoxon's signed rank test (Tukey), and the other on Pitman's permutation test. The necessary assumptions and the merits of these procedures are discussed. The methods are illustrated by an example of a comparative bioavailability study. A FORTRAN program facilitating the procedures is available from the authors upon request.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abt K (1977) Cross-over Versuchspläne: Grenzen der Anwendung und der parametrischen Auswertung. Paper presented at the Annual Meeting of the Austro-Swiss Region of the International Biometric Society, Krems/Austria, September 1977
Anttila M, Kahela P, Panelius M, Yrjänä T, Tikkanen R, Aaltonen R (1979) Comparative bioavailability of two commercial preparations of carbamazepine tablets. Eur J Clin Pharmacol 15: 421–425
Armitage P (1981) Bioequivalence testing — a need to rethink: note by editor. Biometrics 37: 593–594
Cochran WG, Cox GM (1957) Experimental design; 2nd ed. Wiley, New York, pp 117–147
Fluehler H, Hirtz J, Moser HA (1981) An aid to decision-making in bioequivalence assessment. J Pharmacokinet Biopharm 9: 235–243
Geigy Wissenschaftliche Tabellen (1980), Vol. 3; 8th ed. Thieme, Stuttgart, p 163
Grieve AP (1982) The two-period changeover design in clinical trials. Biometrics 38: 517
Grizzle JE (1965) The two-period change-over design and its use in clinical trials. Biometrics 21: 467–480. Correction note (1974) Biometrics 30: 727
Hollander M, Wolfe DA (1973) Nonparametric statistical methods. Wiley, New York
Kirkwood TBL (1981) Bioequivalence testing — a need to rethink. Biometrics 37: 589–591
Koch GG (1972) The use of non-parametric methods in the statistical analysis of the two-period change-over design. Biometrics 28: 577–584
Kramer WG, Kolibash AJ, Bathala MS, Visconti JA, Lewis RP, Reuning RH (1977) Digoxin bioavailability: evaluation of a generic tablet and proposed FDA guidelines. J Pharm Sci 66: 1720–1722
Loo JCK, Riegelman S (1968) New method for calculating the intrinsic absorption rate of drugs. J Pharm Sci 57:918–928
Mandallaz D, Mau J (1981) Comparison of different methods for decision-making in bioequivalence assessment. Biometrics 37: 213–222
Mantel N (1977) Do we want confidence intervals symmetrical about the null value? Biometrics 33: 759–760
Mau J (1981) Die Verwendung von Fiduzialwahrscheinlichkeiten zur Beurteilung der Bioäquivalenz. To be published in the Proceedings of the 27th meeting of the German region of the International Biometric Society, Bad Nauheim, March 1981
Metzler CM (1974) Bioavailability — a problem in equivalence. Biometrics 30: 309–317
Ostle B (1966) Statistics in research. Iowa State University Press, Iowa
Rietbrock N, Alken RG, Ebert W (1979) Vergleichende Untersuchung der absoluten Bioverfügbarkeit von vier oralen Digoxin-Präparaten. Arzneim Forsch (Drug Res) 29: 1742–1745
Rodda BE, Davis RL (1980) Determining the probability of an important difference in bioavailability. Clin Pharmacol Ther 28: 247–252
Royen T (1978) Randomisierungstests zum Vergleich verbundener Stichproben. EDV in Medizin und Biologie 9: 104–106
Selwyn MR, Dempster AP, Hall NR (1981) A Bayesian approach to bioequivalence for the 2 × 2 changeover design. Biometrics 37: 11–21
Shirley E (1976) The use of confidence intervals in biopharmaceutics. J Pharm Pharmacol 28: 312–313
Shirley EAC, Unwin PF (1978) The analysis of data from comparative bioavailability studies. Eur J Drug Metab Pharmacokinet 3: 165–170
Spriet A, Beiler D (1978) Table to facilitate determination of symmetrical confidence intervals in bioavailability trials with Westlake's method. Eur J Drug Metab Pharmacokinet 3: 129–132
Steinijans VW (1981) Verteilungsfreier Punktschätzer und Vertrauensgrenzen für Bioverfügbarkeitsquotienten. To be published in the Proceedings of the 27th meeting of the German Region of the International Biometric Society, Bad Nauheim, March 1981
Steinijans VW, Eicke R, Ahrens J (1982) Pharmacokinetics of theophylline in patients following short-term intravenous infusion. Eur J Clin Pharmacol 22: 417–422
Upton RA, Sansom L, Guentert TW, Powell JR, Thiercelin JF, Shah VP, Coates PE, Riegelman S (1980) Evaluation of the absorption from 15 commercial theophylline products indicating deficiencies in currently applied bioavailability criteria. J Pharmacokinet Biopharm 8: 229–242
Vila JL, Martinez R, Giménez J, Llabrés M (1980) MANOVA of statistical moments in biopharmaceutical studies: a numerical example with three equally spaced doses of amoxicillin. J Pharmakokinet Biopharm 8: 411–420
Wagner JG, Nelson E (1963) Per cent absorbed time plots derived from blood level and/or urinary excretion data. J Pharm Sci 52: 610–611
Wallenstein S, Fisher AC (1977) The analysis of the two-period repeated measurements crossover design with applications to clinical trials. Biometrics 33: 261–269
Westlake WJ (1972) Use of confidence intervals in analysis of comparative bioavailability trials. J Pharm Sci 61: 1340–1341
Westlake WJ (1973) Use of statistical methods in evaluation of in vivo performance of dosage forms. J Pharm Sci 62: 1579–1589
Westlake WJ (1974) The use of balanced incomplete block designs in comparative bioavailability trials. Biometrics 30: 319–327
Westlake WJ (1976) Symmetrical confidence intervals for bioequivalence trials. Biometrics 32: 741–744
Westlake WJ (1979) Statistical aspects of comparative bioavailability trials. Biometrics 35: 273–280
Westlake WJ (1981) Bioequivalence testing — a need to rethink: response. Biometrics 37: 591–593
Wilcoxon F, Katti SK, Wilcox RA (1973) Probability levels for the Wilcoxon signed rank test. In: Harter HL, Owen DB (eds) Selected Tables in Mathematical Statistics, Vol.I. American Mathematical Society, Providence, Rhode Island
Yeh KC, Kwan KC (1978) A comparison of numerical integrating algorithms by trapezoidal, Lagrange, and spline approximation. J Pharmacokinet Biopharm 6: 79–81
Zech K, Borner K, v. Stetten O (1980) Monitoring of serum or saliva theophylline concentrations by a new radioimmunoassay. Anal Chem 301: 114
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Steinijans, V.W., Diletti, E. Statistical analysis of bioavailability studies: Parametric and nonparametric confidence intervals. Eur J Clin Pharmacol 24, 127–136 (1983). https://doi.org/10.1007/BF00613939
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00613939