On the contrary, my dear Dr. Watson! [Two-Stage / GS Designs]

posted by Helmut Homepage – Vienna, Austria, 2019-10-11 11:52 (736 d 12:07 ago) – Posting: # 20684
Views: 3,466

Hi ElMaestro,

» I remember having heard EU regulators mention preference for method C out of consideration for the type I error.

What? Where?

» But I can't seem to find a presentation from anyone saying so.

Would surprise me if there is any.

» Do you […] have a link or a presentation by a regulator where this was stated?

Nope. The collaborative work about the type I error was removed from the work plan last year (Paola Coppola’s presentation at BioBridges 2018):

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No work plans published this year for both parties due to Brexit. However, there is an unequivocal preference towards methods demonstrating analytically strict control of the TIE.1,2,3 In my experience European regulatory statisticians hate simulation-based methods.

On Wednesday’s workshop I endured a frustrating chat with a statistician of the Austrian agency AGES. Collection of errors and misconceptions:Was like talking to a brick wall or a conversation with your TV set.

Yesterday I sent a clarification  e-mail  rant to Thomas Lang (AGES, member of the BSWP). I don’t expect to get a reply. [Edit: One month later. Expectation realized.]


  1. König F, Wolfsegger M, Jaki T, Schütz H, Wassmer G. Adaptive two-stage bioequivalence trials with early stopping and sample size re-estimation. 2014. doi:10.13140/RG.2.1.5190.0967.
  2. König F, Wolfsegger M, Jaki T, Schütz H, Wassmer G. Adaptive two-stage bioequivalence trials with early stopping and sample size re-estimation. Trials. 2015; 16(Suppl 2);P218. doi:10.1186/1745-6215-16-S2-P218.
  3. Maurer W, Jones B, Chen Y. Controlling the type 1 error rate in two-stage sequential designs when testing for average bioequivalence. Stat Med. 2018; 37(10): 1587–1607. doi:10.1002/sim.7614.
  4. Kieser M, Rauch G. Two-stage designs for cross-over bioequivalence trials. Stat Med. 2015; 34(16): 2403–16. doi:10.1002/sim.6487.

  1. An all too often overlooked detail: If the interim is at <½N (due to dropouts) one has to use an error-spending function (e.g., Lan and DeMets, Jennison and Turnbull) to control the TIE.
  2. One mio simulations of a narrow grid (step size 2); TIEmax at n1 12 and CV 24%. Approximations by the shifted central t and the non­central t, exact by Owen’s Q. Go for a cup of coffee. The exact method is very slow.
    library(Power2Stage)
    method <- "B"
    alpha  <- rep(0.0294, 2)
    GMR    <- 0.95
    target <- 0.80
    n1     <- 12   # location of the
    CV     <- 0.24 # maximum empiric TIE
    power  <- c("shifted", "nct", "exact")
    res    <- data.frame(method = method, alpha = alpha[1],
                         GMR = GMR,
                         target = sprintf("%.0f%%", 100 * target),
                         power = power)
    for (j in 1:nrow(res)) {
      start        <- proc.time()[[3]]
      res$TIE[j]   <- power.tsd(method = method, alpha = alpha,
                                n1 = n1, CV = CV, GMR = GMR,
                                targetpower = target,
                                theta0 = 1.25,
                                pmethod = power[j],
                                nsims = 1e6)$pBE
      res$speed[j] <- proc.time()[[3]] - start
      cat(sprintf("%7s: %6.2f", power[j], res$speed[j]),
          "seconds\n")
    } # patience, please!
    res$speed <- signif(res$speed / res$speed[1], 3)
    print(res, row.names = FALSE)
     method  alpha  GMR target   power      TIE speed
          B 0.0294 0.95    80% shifted 0.048959  1.00
          B 0.0294 0.95    80%     nct 0.048762  1.57
          B 0.0294 0.95    80%   exact 0.048925 41.80


    With alpha = rep(0.0301, 2):
     method  alpha  GMR target   power      TIE speed
          B 0.0301 0.95    80% shifted 0.050004  1.00
          B 0.0301 0.95    80%     nct 0.049790  1.57
          B 0.0301 0.95    80%   exact 0.049786 41.30

Dif-tor heh smusma 🖖
Helmut Schütz
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