α and 1–β [Power / Sample Size]

posted by Helmut Homepage – Vienna, Austria, 2017-12-27 13:31  – Posting: # 18102
Views: 26,141

Hi Yura,

» » If the protocol was approved by the IEC and the competent regulatory agency
»
» yes, explanations are needed for estimating the sample size and design (that to reduce it)
Sure. But once explanations (better: assumptions) were accepted (i.e., the protocol approved) that’s the end of the story. That’s why I’m extremely wary of using the term “forced bioequivalence” in a regulatory context (see also this post and followings).
IMHO, post hoc power is crap. The chance to get one which is higher than planned is ~50%. Run my simulation code and at the end:

cat(nsims, "simulated studies with \u201Cpost hoc\u201D power of",
    "\n  \u2265 target    :", sprintf("%5.2f%%",
    100*length(res[, 3][res[, 3] >= target])/nsims),
    "\n  \u2265 achieved  :", sprintf("%5.2f%%",
    100*length(res[, 3][res[, 3] >= plan[["Achieved power"]]])/nsims),
    "\n  \u2265 0.90      :", sprintf("%5.2f%%",
    100*length(res[, 3][res[, 3] >= 0.9])/nsims),
    "\n  [0.95, 0.99]:", sprintf("%5.2f%%",
    100*length(res[, 3][res[, 3] >= 0.95 & res[, 3] <=0.99])/nsims),
    "\n  \u2265 0.95      :", sprintf("%5.2f%%",
    100*length(res[, 3][res[, 3] >= 0.95])/nsims), "\n")


With your example (CV 0.25, GMR 0.95, target power 80%, n 28, 105 simulations):

1e+05 simulated studies with “post hoc” power of
  ≥ target    : 49.92%
  ≥ achieved  : 48.02%
  ≥ 0.90      : 22.93%
  [0.95, 0.99]:  8.40%
  ≥ 0.95      :  9.70%

Although the study was performed with 28 subjects for ~81% power, the chance to get a post hoc power of ≥ 90% is ~23% and ≥ 95% is ~10%. That’s clearly not “forced BE” and none of these studies should be questioned by regulators.*
I suggest to reserve this term to the context of study planning.

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