## Tricky question, lengthy answer [Power / Sample Size]

Thanks again for your answers Helmut, that's really helpful !

Unfortunately I am not sure to completely understand the following :

» Although you plan for a 3×6×3 Williams’ design, the two parts will be

If my understanding is correct,

However, what should I do if I want the sample size for a power of 90% to detect BE for both comparisons ? If I assume that there is not correlation between both comparisons, and be n =

Is it correct to calculate the sample size only based on one comparison?

Furthermore, while the two parts of the trial will be evaluated as incomplete block designs, it seems to me that the original sequences and periods are preserved (e.g. an observation from period 3 is still coded as period 3), so that the degree of freedom would not be the same as for the conventional 2x2x2 crossover, no?

Lastly, when you said no multiplicity adjustment procedure was needed, was it implied that I should specify that BE between the clinical and marketed formulation will be tested first, before the food effect (i.e. hierarchical testing)? It is just to be in accordance with EMA and FDA.

Unfortunately I am not sure to completely understand the following :

» Although you plan for a 3×6×3 Williams’ design, the two parts will be

*evaluated*as incomplete block designs (IBD), having the same degrees of freedom as the conventional 2×2×2 crossover. Hence, in`sampleN.TOST()`

use the argument `design="2x2x2"`

*and not*`design="3x6x3"`

. You will get a small reward:`library(PowerTOST)`

» sampleN.TOST(CV=0.3, design="2x2x2", targetpower=0.9,

» print=FALSE)[["Sample size"]]

» [1] 52

» sampleN.TOST(CV=0.3, design="3x6x3", targetpower=0.9,

» print=FALSE)[["Sample size"]]

» [1] 54

If my understanding is correct,

`sampleN.TOST(CV=0.3, design="3x6x3", targetpower=0.9, print=FALSE)[["Sample size"]]`

would give me the sample size necessary for a power of 90% to detect BE for at least one given comparison (either A vs B or C vs B) if I evaluated all data at the same time, while `sampleN.TOST(CV=0.3, design="2x2x2", targetpower=0.9, print=FALSE)[["Sample size"]]`

would give me the sample size for a given comparison if I evaluated the data two at a time (keeping in mind that I should potentially increase the result so that the sample size is a multiple of 6).However, what should I do if I want the sample size for a power of 90% to detect BE for both comparisons ? If I assume that there is not correlation between both comparisons, and be n =

`sampleN.TOST(CV=0.3, design="2x2x2", targetpower=0.9, print=FALSE)[["Sample size"]]`

, then:`power.TOST(CV=0.3, design="2x2x2", n=n) * power.TOST(CV=0.3, design="2x2x2", n=n)`

would evaluate to less than 0.9.Is it correct to calculate the sample size only based on one comparison?

Furthermore, while the two parts of the trial will be evaluated as incomplete block designs, it seems to me that the original sequences and periods are preserved (e.g. an observation from period 3 is still coded as period 3), so that the degree of freedom would not be the same as for the conventional 2x2x2 crossover, no?

Lastly, when you said no multiplicity adjustment procedure was needed, was it implied that I should specify that BE between the clinical and marketed formulation will be tested first, before the food effect (i.e. hierarchical testing)? It is just to be in accordance with EMA and FDA.

### Complete thread:

- Sample Size Calculation for Drug Effect and Food Effect study Olivbood 2019-05-08 16:16
- Tricky question, lengthy answer Helmut 2019-05-08 18:02
- Tricky question, lengthy answer Olivbood 2019-05-08 19:20
- Tricky question, lengthy answer Helmut 2019-05-09 00:47

- Tricky question, lengthy answerOlivbood 2019-05-10 21:11
- Tricky question, lengthy answer Helmut 2019-05-14 14:11
- Degrees of freedom of TaaTP d_labes 2019-05-14 16:01
- Use of incomplete block design? Olivbood 2019-05-23 22:30
- Radio Yerevan answers Helmut 2019-05-24 11:28

- Use of incomplete block design? Olivbood 2019-05-23 22:30

- Degrees of freedom of TaaTP d_labes 2019-05-14 16:01

- Tricky question, lengthy answer Helmut 2019-05-14 14:11

- Tricky question, lengthy answer Olivbood 2019-05-08 19:20

- Tricky question, lengthy answer Helmut 2019-05-08 18:02