Plausible to me too [Power / Sample Size]

posted by ElMaestro  – Belgium?, 2017-02-06 22:30  – Posting: # 17026
Views: 19,629

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.

I could be wrong, but...

Best regards,
ElMaestro

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

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