## Use of lower bound for power of two combined TOST [Power / Sample Size]

Dear All!

Let me ask another question regarding the quote from the Patterson/Jones book:

Seems to me that the authors recommend to use the lower bound as criterion for setting the targetpower, i.e. if an overall power of 0.8 is aimed for, the powers for the two metrics have to be chosen such that the lower bound >= 0.8.

Example with both metrics with equal variabilities (CV of both metrics 0.25):

Example with different variabilities (CVs 0.2 and 0.25):

Here we could set the targetpower for the first step lower than 0.9:

Do I understand that paragraph correct or read to much into it?

If I'm correct, do you think that such an approach is resonable?

Let me ask another question regarding the quote from the Patterson/Jones book:

Seems to me that the authors recommend to use the lower bound as criterion for setting the targetpower, i.e. if an overall power of 0.8 is aimed for, the powers for the two metrics have to be chosen such that the lower bound >= 0.8.

Example with both metrics with equal variabilities (CV of both metrics 0.25):

`sampleN.TOST(CV=0.25, targetpower=0.9)`

gives n=38 and power=0.908890.`power.TOST(CV=0.25, n=38)`

gives also power=0.908890.`lbound = 0.908890 + 0.908890 -1 = 0.81778`

Example with different variabilities (CVs 0.2 and 0.25):

`sampleN.TOST(CV=0.25, targetpower=0.9)`

gives n=38 and power=0.908890.`power.TOST(CV=0.2, n=38)`

gives power=0.9805344`lbound = 0.908890 + 0.9805344 -1 = 0.8894244`

Here we could set the targetpower for the first step lower than 0.9:

`sampleN.TOST(CV=0.25, targetpower=0.85)`

gives n=32 power=0.857257.`power.TOST(CV=0.2, n=32)`

gives power=0.9595363`lbound = 0.857257 + 0.9595363 -1 = 0.8167933`

Do I understand that paragraph correct or read to much into it?

If I'm correct, do you think that such an approach is resonable?

—

Regards,

Detlew

Regards,

Detlew

### Complete thread:

- Lower bound for power of two combined TOST? d_labes 2018-07-25 10:40
- Lower bound for power of two combined TOST? ElMaestro 2018-07-25 12:07
- Lower bound for power of two combined TOST? d_labes 2018-07-25 14:46
- Appendix D mittyri 2018-07-26 00:07
- Appendix D d_labes 2018-07-26 13:41

- Appendix D mittyri 2018-07-26 00:07

- Lower bound for power of two combined TOST? d_labes 2018-07-25 14:46
- Use of lower bound for power of two combined TOST d_labes 2018-07-26 14:29
- Use of lower bound for power of two combined TOST Ben 2018-08-06 18:11
- Use of lower bound for power of two combined TOST d_labes 2018-08-07 11:50

- Use of lower bound for power of two combined TOST Ben 2018-08-06 18:11

- Lower bound for power of two combined TOST? ElMaestro 2018-07-25 12:07