## Expected power answer [Power / Sample Size]

Dear BE-proff, dear All,

Taking into account that CV and GMR's of such a previous (pilot) trial are not the true values but estimates with uncertainty, as ElMaestro already pointed out. One answer to such a goal is using the so-called "expected power" implemented in

Let's play with your numbers step by step:

1. Taking into account uncertainty of CV, but assuming a known (true) GMR =0.95

Not so much more than using the conventional power assuming GMR and CV known.

2. Taking into account uncertainty of CV, but assuming a true GMR =1.19

Again slightly higher than using the conventional power.

3. Now taking into account uncertainty of CV

That result (!) should everyone convince that using the GMR from pilot studies with small number of subjects (or likewise from usually small stage 1 of a TSD) is not a good idea, as our captain already stated in his post above.

It results mainly from

BTW: Don't ask me for the theory behind expected power. It is something Bayesian.

If you are interested you may find a short tractatus at

https://github.com/Detlew/PowerTOST/tree/master/inst/doc

written by Ben (Benjamin Lang) who is also responsible for the implementation.

❝ Let's say I want to calculate sample size based on results of a previous study.

❝

❝ I have the following data:

❝ n=20

❝ CV=0.18 (for Cmax and AUC)

❝ GMR1 = 0.97

❝ GMR2=1.19

Taking into account that CV and GMR's of such a previous (pilot) trial are not the true values but estimates with uncertainty, as ElMaestro already pointed out. One answer to such a goal is using the so-called "expected power" implemented in

`PowerTOST::exppower.TOST()`

and `expsampleN.TOST()`

.Let's play with your numbers step by step:

1. Taking into account uncertainty of CV, but assuming a known (true) GMR =0.95

`expsampleN.TOST(CV=0.18, theta0=0.95, prior.parm = list(m=20, design="2x2"), prior.type="CV")`

++++++++++++ Equivalence test - TOST ++++++++++++

Sample size est. with uncertain CV

-------------------------------------------------

Study design: 2x2 crossover

log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8

BE margins = 0.8 ... 1.25

Ratio = 0.95

CV = 0.18 with 18 df

Sample size (ntotal)

n exp. power

18 0.823287

Not so much more than using the conventional power assuming GMR and CV known.

2. Taking into account uncertainty of CV, but assuming a true GMR =1.19

`expsampleN.TOST(CV=0.18, theta0=1.19, prior.parm = list(m=20, design="2x2"), prior.type="CV")`

++++++++++++ Equivalence test - TOST ++++++++++++

Sample size est. with uncertain CV

-------------------------------------------------

Study design: 2x2 crossover

log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8

BE margins = 0.8 ... 1.25

Ratio = 1.19

CV = 0.18 with 18 df

Sample size (ntotal)

n exp. power

180 0.801466

Again slightly higher than using the conventional power.

3. Now taking into account uncertainty of CV

**and**GMR =1.19`expsampleN.TOST(CV=0.18, theta0=1.19, prior.parm = list(m=20, design="2x2"), prior.type="both")`

++++++++++++ Equivalence test - TOST ++++++++++++

Sample size est. with uncertain CV and theta0

-------------------------------------------------

Study design: 2x2 crossover

log-transformed data (multiplicative model)

Design characteristics:

df = n-2, design const. = 2, step = 2

alpha = 0.05, target power = 0.8

BE margins = 0.8 ... 1.25

Ratio = 1.19 with 18 df

CV = 0.18 with 18 df

Upper bound of expected power = 0.802418

Sample size search (ntotal)

n exp. power

Search for improved starting value based on nct approximation for conditional power:

4130 0.769089

4146 0.769157

4162 0.769219

4194 0.769354

4258 0.769619

4386 0.770131

...

619480 0.800000

Final search:

619480 0.800000

619478 0.800000

619476 0.800000

3 iterations

619478 0.800000

That result (!) should everyone convince that using the GMR from pilot studies with small number of subjects (or likewise from usually small stage 1 of a TSD) is not a good idea, as our captain already stated in his post above.

It results mainly from

*"... there is 50% chance the true GMR is worse."*And power is heavily influenced by deviations in the GMR as we already know from the power analysis functions f.i.` pa.ABE()`

BTW: Don't ask me for the theory behind expected power. It is something Bayesian.

If you are interested you may find a short tractatus at

https://github.com/Detlew/PowerTOST/tree/master/inst/doc

written by Ben (Benjamin Lang) who is also responsible for the implementation.

—

Regards,

Detlew

Regards,

Detlew

### Complete thread:

- Sample Size II BE-proff 2016-12-28 08:14 [Power / Sample Size]
- Please see the answer to your previous post mittyri 2016-12-28 09:17
- Please see the answer to your previous post BE-proff 2016-12-28 10:35
- Another Master's answer mittyri 2016-12-28 11:38

- Please see the answer to your previous post BE-proff 2016-12-28 10:35
- Sample Size II ElMaestro 2016-12-28 10:52
- Expected power answerd_labes 2016-12-28 13:42
- Sample Size and regulators DavidManteigas 2016-12-28 18:11
- Sample Size and sponsors d_labes 2016-12-28 19:24
- Sample Size and spongulators ElMaestro 2016-12-28 22:22

- Sample Size and regulators mittyri 2016-12-29 11:44
- Sample Size and regulators Helmut 2016-12-29 12:39

- Sample Size and sponsors d_labes 2016-12-28 19:24

- Please see the answer to your previous post mittyri 2016-12-28 09:17