Bioequivalence and Bioavailability Forum

Dear Helmut,

❝ ❝ […] In a 2*2 cross-over BE study. If we want to test the Tmax betweent different treatments. Which test statistic should be used? Wilcoxon signed rank test or Wilcoxon rank sum test?

❝

❝ The former (aka Wilcoxon T test).

❝ The latter (aka Mann–Whitney U test, Mann–Whitney–Wilcoxon test, Wilcoxon–Mann–Whitney test) is for independent samples (parallel design).

Here you err!

The Wilcoxon signed rank test¹ can only applied if you neglect period effects. It tests the within-subject treatment differences against zero and is therefore a non-parametric analogon of the paired Student t-test.

To account for period effects you have to apply the Wilcoxon–Mann–Whitney test² with sequence as grouping factor if you evaluate a 2x2 cross-over design. This test is sometimes also called Hauschke test. Guess why .
In case of a parallel design the grouping factor is of course the treatment, as you correctly stated.

The cited example you quote uses the correct test.
And I suppose Phoenix 8.0 / Crossover object does the same

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¹ V. W. Steinijans and E. Diletti
"Statistical Analysis of Bioavailability Studies: Parametric and Nonparametric Confidence Intervals"
Eur J Clin Pharmacol (1983) 24:127-136

² D. HAUSCHKE, V. W. STEINIJANS and E. DILETTI
"A distribution-free procedure for the statistical analysis of bioequivalence studies"
International Journal of Clinical Pharmacology, Therapy and Toxicology,
Vol. 28 No. 2 -1990 (72-78) / Vol.30, Suppl. No. 1 -1992 (pp,S37-43)