## Plausible to me too [Power / Sample Size]

Let P0= P(GMR<U)-P(GMR<L) regardless of what U and L are, as long as they are meaningful (U>L, and not negative). This quantitiy is easuily accessible via Power.TOST. If L and U are BE acceptance limits then P0 is power in a BE trial.

We can rewrite that as

P0=P(GMR in [L,U]), regardless of what U and L are, as long as they are meaningful (U>L, and not negative)

If we define L=0.8 and U=1.25 and GMR is within these limits, then we can say that P0 falls in (is composed of) three categories:

1. Those that have GMR in [L, 1.0]

2. Those that have GMR in [1.0, U]

3. Anything that isn’t 1 or 2.

Because “3” is anything else than 1 or 2, P1+P2+P3=P0.

and because 1 and 2 are mutually exclusive (can’t fall in both categories), except the zero-prob of GMR exactly 1.0. P1 and P2 are meaningfully additive, and P1+P2 will thus be the probability of having a passing study in which 1.0 isn’t in the acceptance range when L=0.8 and U=1.25. The probability we are looking for is P3, because this is a study fulfiling P(GMR in [L,U]) but not those that have GMR in [L, 1.0] and not those that have GMR in [1.0, U], therefore P3=P0-P1-P2, so we just plug in the relevant limits in Power.TOST and Bob’s your uncle.

We can rewrite that as

P0=P(GMR in [L,U]), regardless of what U and L are, as long as they are meaningful (U>L, and not negative)

If we define L=0.8 and U=1.25 and GMR is within these limits, then we can say that P0 falls in (is composed of) three categories:

1. Those that have GMR in [L, 1.0]

2. Those that have GMR in [1.0, U]

3. Anything that isn’t 1 or 2.

Because “3” is anything else than 1 or 2, P1+P2+P3=P0.

and because 1 and 2 are mutually exclusive (can’t fall in both categories), except the zero-prob of GMR exactly 1.0. P1 and P2 are meaningfully additive, and P1+P2 will thus be the probability of having a passing study in which 1.0 isn’t in the acceptance range when L=0.8 and U=1.25. The probability we are looking for is P3, because this is a study fulfiling P(GMR in [L,U]) but not those that have GMR in [L, 1.0] and not those that have GMR in [1.0, U], therefore P3=P0-P1-P2, so we just plug in the relevant limits in Power.TOST and Bob’s your uncle.

—

I could be wrong, but...

Best regards,

ElMaestro

"Pass or fail" (D. Potvin et al., 2008)

I could be wrong, but...

Best regards,

ElMaestro

"Pass or fail" (D. Potvin et al., 2008)

### Complete thread:

- Denmark Curiosa (1 in 90% CI in 0.8-1.25) zizou 2017-02-05 02:03 [Power / Sample Size]
- Kudos! Helmut 2017-02-05 19:16
- Kudos! ElMaestro 2017-02-05 21:15
- Joking! Helmut 2017-02-06 13:27
- Thanks, and DKMA ElMaestro 2017-02-06 13:46
- Power with a Danish twist Helmut 2017-02-07 15:23
- Danish ultra-conservatism d_labes 2017-02-08 10:57
- Danish ultra-conservatism Helmut 2017-02-08 11:47

- Danish ultra-conservatism d_labes 2017-02-08 10:57

- Power with a Danish twist Helmut 2017-02-07 15:23

- Thanks, and DKMA ElMaestro 2017-02-06 13:46
- Kudos to ElMaestro! d_labes 2017-02-06 15:06
- Plausible Helmut 2017-02-06 17:16
- Plausible to me too d_labes 2017-02-06 20:25
- Plausible to me tooElMaestro 2017-02-06 22:30
- Plausible to me too zizou 2017-02-06 22:42
- THX d_labes 2017-02-07 10:01

- Plausible to me too d_labes 2017-02-06 20:25

- Plausible Helmut 2017-02-06 17:16

- Joking! Helmut 2017-02-06 13:27

- Kudos! ElMaestro 2017-02-05 21:15
- 3D Helmut 2017-02-06 13:47
- Denmark Curiosa (1 in 90% CI in 0.8-1.25) d_labes 2017-02-06 14:54
- Denmark Curiosa (1 in 90% CI in 0.8-1.25) zizou 2017-02-08 21:03
- Alternative CI for BE decision d_labes 2017-02-09 11:18
- Alternative CI for BE decision ElMaestro 2017-02-09 11:36
- Alternative CI for BE decision d_labes 2017-02-09 11:48
- How decidedly odd ElMaestro 2017-02-09 13:28
- How decidedly odd zizou 2017-02-09 14:42

- How decidedly odd ElMaestro 2017-02-09 13:28
- Alternative CI for BE decision Helmut 2017-02-09 13:41
- No alternative d_labes 2017-02-09 20:37
- No alternative ElMaestro 2017-02-10 13:51
- No alternative? mittyri 2017-02-10 15:28
- Dinamarka? d_labes 2017-02-10 20:10

- OT: Czech beer d_labes 2017-02-10 19:57

- No alternative? mittyri 2017-02-10 15:28

- No alternative ElMaestro 2017-02-10 13:51

- No alternative d_labes 2017-02-09 20:37

- Alternative CI for BE decision d_labes 2017-02-09 11:48

- Alternative CI for BE decision ElMaestro 2017-02-09 11:36

- Alternative CI for BE decision d_labes 2017-02-09 11:18

- Denmark Curiosa (1 in 90% CI in 0.8-1.25) zizou 2017-02-08 21:03
- Denmark Curiosa (1 in 90% CI in 0.8-1.25): Gone Helmut 2019-11-08 12:47

- Kudos! Helmut 2017-02-05 19:16