Bioequivalence and Bioavailability Forum

Hi Amira,

❝ Yes, he actually missed the terminal phase, his AUC0-t is about 17% of his AUC0-inf, also check his figure

❝

❝

THX, very helpful. Comparing the profiles of both treatments around ten hours (does the drug undergo enterohepatic recycling?) clearly shows that the terminal phase is not reached. Given what we see for T – whatever the software suggests – I would say it starts at 24 hours. Since you cannot estimate λ_z for R, your 17% are too low. True number? Impossible to tell.

❝ What we could do?

❝

❝ 1- Extrapolate to 72 h

No (unknown λ_z).

❝ 2- Use AUC common (0-12)

Makes sense to me. Regulatory acceptance unclear (not stated in any guideline so far).

❝ 3- or based on the results of the current study could we make another stage on 12 subjects (knowing that the first one was performed on 24)?

No. Three reasons (regulatory, ethical, statistical):

1. The intention to perform a two-stage design would have to be stated in the protocol together with the planned method and adjusted α <0.05. You can’t change the design because you don’t like the original outcome.
   
2. Your sample size estimation was based on a fixed sample design with α 0.05. A TSD likely require more subjects, which was not approved by the ethics committee.
   
3. If you already assessed the study (say, after excluding the subject) the entire α was already ‘consumed’. Nothing is ‘left’ for a pooled analysis.
   Even if you didn’t assess the study for BE yet, #1 and #2 are still problematic. Requires an amendment to the SAP and approval by both parties. Especially the agency will think that’s fishy. 

❝ 4- Exclude the subject from stat evaluation of AUC(0-t) and include in all other parameters (as long as it does not jeopardize the acceptance of the study)

IMHO, the most realistic approach. This is what I do in my studies for decades. But again, all conditions for exclusion – detailed! – stated in the protocol. Mine have one entire page of definitions (vomiting, diarrhea, missing samples, dealing with time deviations, unreliable λ_z, etc.), which will lead to the ITT- (PK insofar possible, even for dropouts) and PP-datasets.
Whether a post hoc exclusion will be accepted, no idea. But yes, I agree with ElMaestro that the subject did not follow the protocol and therefore, might be excluded from the comparison of AUC (only).
C_max is still reliable because you had all concentrations before t_max and five decreasing ones after it. Since C_max generally is more variable than AUC, likely the study was powered for it and you might easily pass AUC:

library(PowerTOST)
CV.AUC  <- seq(0.10, 0.25, 0.025)
CV.Cmax <- CV.AUC * 1.5 # arbitrary but higher than ones of AUC
res     <- data.frame(CV.AUC = CV.AUC, CV.Cmax = CV.Cmax, n = NA,
                      pwr.Cmax = NA, pwr.AUC = NA,
                      elig.AUC = NA, pwr.AUC.elig = NA, pwr.loss.pct = NA)
theta0  <- 0.95 # assumed T/R-ratio of both PK metrics
target  <- 0.80 # ≥80% power
for (j in 1:nrow(res)) {
  tmp         <- sampleN.TOST(CV = CV.Cmax[j], theta0 = theta0,
                              targetpower = target, print = FALSE)
  res[j, 3:4] <- tmp[7:8]          # Sample size, achieved power
  res[j, 5]   <- power.TOST(CV = CV.AUC[j], theta0 = theta0, n = res$n[j])
  res[j, 6]   <- res$n[j] - 1      # AUC: one less eligible subject
  res[j, 7]   <- suppressMessages( # we know that it’s unbalanced
                   power.TOST(CV = CV.AUC[j], theta0 = theta0, n = res[j, 6]))
  res[j, 8]   <- 100 * (res[j, 7] - res[j, 5]) / res[j, 5]
}
print(signif(res, 4), row.names = FALSE)

 CV.AUC CV.Cmax  n pwr.Cmax pwr.AUC elig.AUC pwr.AUC.elig pwr.loss.pct
  0.100  0.1500 12   0.8305  0.9883       11       0.9800      -0.8473
  0.125  0.1875 18   0.8386  0.9896       17       0.9854      -0.4216
  0.150  0.2250 24   0.8227  0.9868       23       0.9833      -0.3468
  0.175  0.2625 32   0.8247  0.9868       31       0.9844      -0.2436
  0.200  0.3000 40   0.8158  0.9848       39       0.9828      -0.2098
  0.225  0.3375 48   0.8022  0.9815       47       0.9796      -0.1981
  0.250  0.3750 58   0.8007  0.9807       57       0.9790      -0.1668

As usual the impact of dropouts – or in your case of an excluded subject – on power is pretty low. Have a look at the function pa.ABE() of PowerTOST and the example in its vignette.