Irene_I
☆

Indonesia,
2018-07-04 10:27
(818 d 14:35 ago)

Posting: # 19016
Views: 2,727

## Sample size determination for William Design [Power / Sample Size]

Dear All,

I would like to ask about sample size determination for conducting William Design (3 treatment - 3 period - 6 sequence) bioequivalence. We would like to compare two test product with one reference product. Based on available literature, the drug product we would like to compare has about 19.03% intra-subject CV for AUC. Usually, we calculate the sample size by intra-subject CV from the previous study and referred to Diletti table (E Diletti, D Hauschke, and VW Steinijans, Sample size determination for bioequivalence assessment by means of confidence intervals). Is that also applicable for the 3x3x6 study? Or, is there any other method to determine sample size for william design?

I would be very thankful for your help.

Thank you very much.

Regards,
Irene I

Helmut
★★★

Vienna, Austria,
2018-07-04 11:32
(818 d 13:30 ago)

@ Irene_I
Posting: # 19017
Views: 2,300

## Williams’ design (all at once vs. two-at-a-time)

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 since
• only certain combinations of the assumed GMR, CV, and desired power are provided and
• power is a highly nonlinear function, making interpolation not a trivial task.
I 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).

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
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Irene_I
☆

Indonesia,
2018-07-05 11:04
(817 d 13:58 ago)

@ Helmut
Posting: # 19022
Views: 2,210

## Williams’ design (all at once vs. two-at-a-time)

Dear Helmut,

Thank you very much for your explanation. It helps us a lot. I think I would just go with the two at a time statistical analysis.

Regards,
Irene I