Bioequivalence and Bioavailability Forum

Hi ElMaestro,

❝ It sounds like a derivative of Potvin's method B with both alphas 0.0294 (1-2*0.0294=0.9412=94.12%), but the performance isn't one that is published. It is not at all demanding to do this type of study assuming you can generally handle two-stage approaches, but I am a little uncertain when you mention that the influence of stage should be verified, I don't quite know what this means. Do they talk about anova and assessment of the stage effect through a p-level, comparison of results with and with a stage term or what?

❝ Mauricio, do you think there could be alternative translations of the sentence in question?

In the meantime I know what happened. Naturally the original is in Portuguese. In my experience people at the ANVISA sometimes misunderstand English papers/regulations. Company X provided the original to a professional translator who produced what Mauricio posted. It channeled to company Y (I have it in all its doubtful beauty). Hardly better than what Google-translate produces.

❝ Hötzi, do you want to publish the performance of this approach in AAPSJ or JPPS with me if I do the simulations and draft the ms?

I don’t see the purpose. We discussed already more than three years ago that a minimum stage 2 might inflate the Type I Error. Not rocket-science. Here an example at the location of the maximum inflation of Potvin’s Method B (n₁ 12, CV 24%):

library(Power2Stage)
n1     <- 12
CV     <- 0.24
method <- c("Potvin", "EMA Q&A", "ANVISA", "Potvin-opt", "Potvin-opt-mod",
            "Kieser-Rauch")
min.n2 <- c(0, 2, 0.5*n1, 0, 0.5*n1, 0)
alpha  <- c(0.0294, 0.0294, 0.0294, 0.0302, 0.0302, 0.0304)
res    <- data.frame(method = method, alpha = alpha,
                     min.n2 = min.n2, TIE = NA)
for (j in 1:nrow(res)) {
  res$TIE[j] <- power.tsd(alpha = rep(res$alpha[j], 2), n1 = n1, CV = CV,
                          min.n2 = res$min.n2[j], theta0 = 1.25)$pBE
}
print(res, row.names = FALSE)

        method  alpha min.n2      TIE
        Potvin 0.0294      0 0.048762 ← TIE controlled by chance
       EMA Q&A 0.0294      2 0.048762 ← stupid and meaningless
        ANVISA 0.0294      6 0.048791 ← higher TIE but OK
    Potvin-opt 0.0302      0 0.049987 ← TIE controlled
Potvin-opt-mod 0.0302      6 0.050196 ← inflated TIE due to n₂ ≥ 50% n₁
  Kieser-Rauch 0.0304      0 0.050270 ← inflated TIE

We all know that Potvin’s adjusted α for Method B was a lucky punch. It has nothing to do with Po­cock’s 0.0294 (which is for a group-sequential design with fixed total sample size N, superiority, parallel groups, known variance, and one interim at exactly N/2). Kieser & Rauch lamented about that and stated that the correct Po­cock’s α for equivalence is 0.0304. Sorry guys, only for GSDs.
If we force a minimum n₂, the TIE will always increase. Contrary to the EMA (stating ‘For example, using 94.12% confidence intervals…’) seemingly ANVISA mandates 0.0294, which is crap. By chance, the TIE is still maintained but this is not necessarily the case for other methods.

If I’m in the right mood I’ll write letter to ANVISA.