## Method for replicate design [Nonparametrics]

Dear DLabes!

❝ can anybody give me a hint about non-parametric evaluation of BE (average) within replicate cross-over design (2-sequence-4-period and/or 4-sequence-4-period)?

First of all congratulations for being the first colleague posting in my personal favorite category “Nonparametrics”
… but such a difficult question!
To my knowledge there’s simply no specific method published at all.
Since replicate designs were at least to some degree submitted to the FDA, tmax did not play an important role, because evaluation of early exposure (partial AUC up to median tmax of the reference – rather than a direct comparison of tmax itself) performed by a parametric method is considered the standard over there.

❝ This will be needed for Tmax evaluation, for which most guidances recommend a non-parametric evaluation.

You are right. But if you go beyond the conventiona 2×2 design, nonparametrics will leave you out in the rain. I know of just two publications (for a 2-treatment, 2-period, 4-sequence design1 and a 6×3 Williams’ design2), although
• both of them don’t deal with confidence intervals,
• rely on normal approximations (i.e., are not exact), and
• don’t help you in the case of a 2×4 or 4×4 replicate design…
One possibility comes into my mind: Performing a parametric evaluation of the replicate design, but not on the untransformed raw data of tmax, but on the ranks within each period.
But I must confess, I have neither done such an analysis myself nor seen it anywhere…

1. Elswick RK, Uthoff VA. A nonparametric approach to the analysis of the two-treatment, two-period, four-sequence crossover model. Biometrics. 1989;45(2):663–7.
2. Bellavance F, Tardif S. A nonparametric approach to the analysis of three-treatment three-period crossover designs. Biometrika. 1995;82(4):865–75. doi:10.1093/biomet/82.4.865.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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