It is shown how the two treatments in a 2 × 2 crossover trial can be compared with respect to both mean response level and within-subject response variability. Various exact statistical inferences are described, including tests, confidence intervals, and certain decision rules to determine whether the target parameters are within given intervals of interest. These inferences are valid even with few subjects, and no distributional assumption is required about the between-subject variability. Certain general multi-step inferences based on stepwise tests and confidence intevals without multiplicity adjustment are also described that are of interest in this context. The inferences are easily implemented using available statistical software.
JonesBKenwardMGDesign and Analysis of Cross-over Trials. London: Chapman and Hall; 1989.
2.
SennS.Cross-over Trials in Clinical Research. New York: John Wiley and Sons; 1993.
3.
RatkowskyDAEvansMAAlldredgeJRCrossover Experiments: Design, Analysis and Application. New York: Marcel Dekker; 1993.
4.
ChowSCLiuJPDesign and Analysis of Bioavailability and Bioequivalence Studies. New York: Marcel Dekker; 1992.
5.
AndersonSHauckWWConsideration of individual bioequivalence. J Pharmaco Biopharm. 1990;18:259–273.
6.
HauckWWAndersonS.Types of bioequivalence and related statistical considerations. Int J Clin Pharmaco Ther Toxicol. 1992;30:181–187.
7.
AndersonS.Individual bioequivalence: a problem of switchability. Biopharmaceutical Report from the Biopharmaceutical Section of the American Statistical Association. 1993;2:1–11.
8.
ChowSCLiuJPRecent statistical developments in bioequivalence trials—a review of the FDA guidance. Drug Inf J.1994;28:851–864.
9.
GuilbaudO.Exact inference about the within-subject variability in 2 × 2 crossover trials. J Am Stat Assoc. 1993;88:939–946.
10.
SAS Institute Inc.SAS/STAT User's Guide. Version 6, 4th ed. Cary, NC; 1989.
11.
FleissJLThe Design and Analysis of Clinical Experiments. New York: John Wiley and Sons; 1986.
12.
LehmannELTesting Statistical Hypotheses. 2nd ed.New York: John Wiley and Sons; 1986.
BrownLDCasellaGHwangJTGOptimal confidence sets, bioequivalence, and the Limaçon of Pascal. J Am Stat Assoc. 1995;90:880–889.
15.
HochbergYTamhaneACMultiple Comparison Procedures. New York: John Wiley and Sons; 1987.
16.
BergerRLHsuJCBioequivalence trials, intersection-union tests and equivalence confidence sets. Stat Sci.1996;11:283–319.
17.
BrownLDHwangJTGMunkA.An unbiased test for the bioequivalence problem. Ann Stat. 1997;25: 2345–2367.
18.
WangW.Optimal unbiased tests for equivalence in intrasubject variability. J Am Stat Assoc. 1997;92: 1163–1170.
19.
SchuirmannDJOn hypothesis testing to determine if the mean of a normal distribution is contained in a known interval (Abstract). Biometrics. 1981;37: 617.
20.
SchuirmannDJA comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. J Pharmaco Biopharma. 1987;15:657–680.
21.
WestlakeWJBioequivalence testing—a need to rethink (Reader Reaction Response). Biometrics. 1981;37:591–593.
22.
BergerRLMultiparameter hypothesis testing and acceptance sampling. Technometrics. 1982;24:295–300.
23.
LiuJPChowSCOn the assessment of variability in bioavailability/bioequivalence studies. Comm Stat-Theory Meth. 1992;21:2591–2607.
24.
SnikerisFTingeyHBA two-step method for assessing bioequivalence. Drug Inf J.1994;28:709–722.
25.
HsuJCBergerRLStepwise confidence intervals without multiplicity adjustment for dose response, multiple endpoints, and toxicity studies. Technical Report 610, Department of Statistics, Ohio State University; 1997.
26.
AitchisonConfidence-region tests. J Roy Stat Soc, B.1964;26:462–476.
27.
KochGGThe use of non-parametric methods in the statistical analysis of the two-period change-over design. Biometrics. 1972;28:577–584.
