Bioequivalence and Bioavailability Forum

Hi Nastia,

❝ Helmut, what was the final conclusions on the post?

I was wrong and we shouldn’t worry. See Detlew’s simulations.

❝ Are there any suggestions on how to deal with two metrics in adaptive trials?

❝ For example: a). Let us consider Type II design: first step - estimated power is less than target (80%) for C_max and more than target for AUC, besides 90%CI for AUC is OK.

❝ 1). We calculate 100(1-2α_adj) CI for C_max, should we also do it for AUC? It can fail.

❝ 2). Suppose further we go to the 2^nd stage. Should we use data from the 2^nd stage to estimate CI for AUC the second time? If yes, it possibly can fail, if not - how to explain the fact that we do not use the data?

Think about how we design a fixed sample design. Always based on the metric with the higher CV. I would go with your 2). How likely is it that AUC (which passed already in the first stage) will fail in the second? Let’s consider the example of the other post. I assumed the best, i.e., all studies in the ‘type II’ design passed with α 0.05. Now:

library(PowerTOST)
alpha <- c(0.05, 0.0294)
ns    <- c(28, 28 + 20)
CV    <- 0.20
res   <- data.frame(analysis = c("interim", "final"),
                    alpha = c(0.05, 0.0294), n = ns,
                    df = NA, power = NA, beta = NA)
for (j in 1:2) {
  if (j == 1) {
    n <- ns[j]
  } else { # workaround since we have 1 df less
    n <- ns[j] - 1
  }
  res[j, 4] <- n - 2
  res[j, 5] <- suppressMessages(
                 power.TOST(alpha = alpha[j],
                            CV = CV, n = n))
  res[j, 6] <- 1 - res[j, 5] }
res[, 5:6] <- signif(res[, 5:6], 4)
print(res, row.names = FALSE)

analysis  alpha  n df  power   beta
 interim 0.0500 28 26 0.9349 0.0651
   final 0.0294 48 45 0.9872 0.0128

❝ Another example: b). First step - estimated power is less than target (80%) for both metrics and adjusted level CI is outside the range. Should we use the largest observed CV to calculate the total sample size?

Yes.

❝ Would the study be overpowered for the second PK metric? Would it affect the TIE?

According to Detlew’s simulations, no.
Given, only ‘type I’ implemented which is more conservative anyhow.

Power2Stage:::power.tsd.2m(CV = c(0.3, 0.2), theta0 = rep(0.95, 2),
                           n1 = 28)
TSD with 2x2 crossover
Method B2m: alpha (s1/s2) = 0.0294 0.0294
Target power in power monitoring and sample size est. = 0.8
Power calculation via non-central t approx.
CV1 and GMR = 0.95 0.95 in sample size est. used
BE acceptance range = 0.8 ... 1.25

CVs = 0.3, 0.2; n(stage 1) = 28; GMR = 0.95, 0.95

1e+05 sims at theta0 = 0.95, 0.95 (p(BE) = 'power').
p(BE)    = 0.81339
p(BE) s1 = 0.46224
Studies in stage 2 = 52.48%

Distribution of n(total)
- mean (range) = 39.8 (28 ... 120)
- percentiles
 5% 50% 95%
 28  34  68

❝ To conclude: what is the best strategy to follow in this situation in order to avoid inflation of the TIE and the loss of power?

Estimate the sample size based on the metric with the higher CV. No inflation of the TIE and a gain in power for the other metric.

❝ (Some mad idea: is it possible to make some hybrid monster to combine both C_max and AUC in the same test for adaptive designs?

Take some Schützomycin?

❝ Something like C_max/AUC but with more powerful reflection of the situations (I dealt with a plenty of studies (BE and not proven BE) with C_max/AUC as an additional metric, only once it was outside the range)

As expected. C_max/AUC is generally less variable than C_max.

❝ ❝ Furthermore, a formulation-by-stage interaction term in the model is considered nonsense in the EMA’s Q&A.

❝

❝ What ANOVA model should be used for the second stage?

According to the Q&A:

stage, sequence, sequence × stage, subject(sequence × stage), period(stage), treatment.

As usual for the EMA, all effects fixed and the nested term subject(sequence × stage) superfluous.
The simple model

stage, sequence, sequence × stage, subject, period(stage), treatment.

gives exactly the same result.
I once received a deficiency letter for a ‘type 2’ study passing in the first stage (α 0.05!) where I dared to model subjects as a random effect… Interesting that there were no questions to use an adjusted α (would have passed as well but I followed my SAP which was approved by the BfArM and for “educational reasons” I didn’t show the adjusted CI).

❝ By the way, what about the code on R for the full decision tree?

Ask Detlew or inspect the sources of power.tsd() and power.tsd.2m().