Williams’ design (all at once vs. two-at-a-time) [Power / Sample Size]

posted by Helmut Homepage – Vienna, Austria, 2018-07-04 13:32 (2154 d 07:25 ago) – Posting: # 19017
Views: 3,574

Hi Irene,

❝ […] sample size determination for conducting William Design (3 treatment - 3 period - 6 sequence) bioequivalence. […] the drug product we would like to compare has about 19.03% intra-subject CV for AUC.

Since you have to show BE for all PK metrics you should estimate the sample size based on the one which has the highest CV. Generally the order is Cmin > Cmax > partialAUC > AUC0–∞ > AUC0–t. If you would base it on the one of AUC you would compromise power for Cmax. If this is a single dose study try to get the CV of Cmax.

❝ Usually, we calculate the sample size by intra-subject CV from the previous study and referred to Diletti table […].

I would not use any of the published sample size tables anymore sinceI suggest to use suitable software instead (see this post). R and package PowerTOST are open source and free of cost.

❝ Is that also applicable for the 3x3x6 study?

Depends. If you want to evaluate it “all at once”, i.e., use one pooled variance, no (different degrees of freedom in a 2×2×2 n–2 and in a 3×6×3 2n–4).
But remember our previous conversation. I suggest to use the “two-at-a-time” approach (i.e., perform two separate analyses T1 vs. R and T2 vs. R) instead. If you plan for that, you could estimate the sample size like a 2×2×2 crossover (see Detlew’s comment).

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