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

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

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

I would not use

» Is that also applicable for the 3x3x6 study?

Depends. If you want to evaluate it “all at once”,

But remember our previous conversation. I suggest to use the “two-at-a-time” approach (

» […] 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 C_{min}> C_{max}>_{partial}AUC > AUC_{0–∞}> AUC_{0–t}. If you would base it on the one of AUC you would compromise power for C_{max}. If this is a single dose study try to get the CV of C_{max}.» 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.

**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 2*n*–4).But remember our previous conversation. I suggest to use the “two-at-a-time” approach (

*i.e.*, perform two separate analyses T_{1}*vs.*R and T_{2}*vs.*R) instead. If you plan for that, you could estimate the sample size like a 2×2×2 crossover (see Detlew’s comment).—

Helmut Schütz

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

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*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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### Complete thread:

- Sample size determination for William Design Irene_I 2018-07-04 10:27 [Power / Sample Size]
- Williams’ design (all at once vs. two-at-a-time)Helmut 2018-07-04 11:32
- Williams’ design (all at once vs. two-at-a-time) Irene_I 2018-07-05 11:04

- Williams’ design (all at once vs. two-at-a-time)Helmut 2018-07-04 11:32