Potvin C consequences [Two-Stage / GS Designs]

posted by Helmut Homepage – Vienna, Austria, 2022-06-27 16:49 (214 d 06:20 ago) – Posting: # 23094
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Hi Mittyri,

❝ OK, what about this:

power.tsd(method = "C", CV = 0.2, n1 = 12, theta0 = 1.25)

p(BE)    = 0.0511

power.tsd(method = "C", CV = 0.3, n1 = 12, theta0 = 1.25)

p(BE)    = 0.043743


❝ So T1E (OK, maximum type I error) depends on the CV, isn't it?


Yes, though not only on the CV but on n1 as well (though less so).

❝ Or may be I misunderstood your point and we should not verify T1E during estimation process since we are assuming that the framework was stated as acceptable in the Protocol?


In principle yes but I received a few deficiency letters asking for a “post hoc assessement of the Type I Error”. That’s not well-thought-out. Of course, we know n1 but the CV is just an estimate. The true one (used in the simulations of the framework) is unknown.

There are no problems with “Method B”. In the entire framework of CV/n1-combinations the T1E is controlled. When you explore a narrow grid (step size of CV 2% and of n1 2) you will get this (noncentral t-dis­tri­bu­tion instead of the shifted central t like in the paper):

[image]
Maximum Type I Error 0.048856 at CV 24% and n1 12.


As you already discovered, “Method C” can be problematic – though only in certain rare cases.

[image]
Maximum Type I Error 0.051250 at CV 22% and n1 12
(the yellow dot). Thick red contour at the bottom encloses T1E > 0.05.


IMHO, it was unfortunate by Potvin et al. to select the same adjusted α in both methods. Any ‘Type 2’ TSD will require more adjustment than its ‘Type 1’ counterpart.
BTW, 0.0294 in “Method B” is overly conservative; 0.0302 controls the Type I Error as well. On the other hand, for “Method C” you need 0.0282.

Consider to avoid this stuff in the future. See this post and followings for better alternatives.

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