Bioequivalence and Bioavailability Forum

Hi kms,

first of all please search the forum before posting. There are dozens of threads discussing these issues in the categories RSABE / ABEL and Power / Sample Size. I will extend ElMaestro’s answers a little bit.

❝ 3. Which is better design? Full or Partial replicate? Why?

❝ ❝ Which is better food: chicken or veg?

When it comes to food, both are fine if properly cooked. When it comes to replicate designs, full. Full stop.

❝ ❝ Full replicate is tougher on volunteers, because there will be more periods.

Only in 4-period replicate designs. If you are worried about dropouts or are concerned about blood loss, consider one of the 3-period full replicate designs, i.e., TRT|RTR or TRR|RTT. BTW, the loss in power due to drop­outs¹ is small.

❝ ❝ Partial replicate is fine. RTR/RRT/TRR is a very good design.

It is not even a bad design. Partial replicates, i.e., TRR|RTR|RRT and TRR|RTR are lousy designs. Reasons:

• If we evaluate a study with the FDA’s mixed-effects model for ABE², it might happen that the optimizer fails to converge. This is independent from software. Search the forum for data sets where both SAS and Phoenix/WinNonlin failed. Then we have a study without a result. Great.
  Remedy in SAS lingo: Specify the covariance structure with TYPE=FA0(1) – instead of TYPE=FA0(2) as recommended by the FDA. State it in the protocol and initiate a controlled correspondence with the FDA or you might end up with an R-t-R.
  
• RSABE/ABEL was developed entirely based on simulations. The fundamental publications explored full replicates only. Simulations of partial replicate designs with heteroscedasticity (CV_wT ≠ CV_wR) are very tricky.
  
• Sample size estimation. If we have data of a pilot study performed in a full replicate design, we can take different CV_wT and CV_wR into account. In many cases CV_wT < CV_wR. Then we get an incentive (i.e., a smaller sample size of the pivotal study). In partial replicates we have to assume CV_wT = CV_wR and go full throttle.
  
• Study cost ~ fixed cost + number of treatments × (cost / treatment). Furthermore, the sample size of 4-period replicates is roughly ⅔ the one of 3-period replicates. Hence, we will save also in the fixed cost (less pre-/post study exams).
  From the economic perspective the 4-period full replicate is always the winner. From the ethical perspective I leave it to you to decide whether it is better to torture less subjects more often or the other way ’round.
  
  
  
  
  
  
  
  
• The so-called “extra-reference design” TRR|RTR is biased in the presence of period effects and should never ever be used.

❝ ❝ Note here are proponents of RTR/TRT design types on this forum, …

Correct. But not only here.

❝ ❝ … albeit I believe there isn't an explicit solid regulatory support for that type.

Mentioned in the EMA’s Q&A document. Requires that at least twelve eligible subjects are in sequence RTR – a condition which is always fulfilled in practice (see this post).
Backstory: In my presentations I argued against partial replicates and recommended (if only three periods are preferred: dropouts, limited blood samples) the TRT|RTR instead. Then the Ukrainian agency asked the EMA’s PKWP for a clarification. The omniscient oracle has spoken.

❝ ❝ Fitting RTR/RRT/TRR for FDA may be tricky, since the stats model -if I get it right- in SAS's world doesn't work well.

Not only in SAS.

❝ ❝ It has to do with the lack of an intra-subject variance component for Test.

Correct. The model is over-specified (since T is not repeatedly administered). Even if the optimizer converges, the estimate of CV_wT is plain nonsense.

❝ 4. What is the SAS code for Randomization of Full and Partial Replicates?

Please do your homework first. Hints: SAS-codes for the FDA’s RSABE and ABE are given in the progesterone guidance and for the EMA’s ABEL in the Q&A document. For the Health Canada’s ABEL you have to use a mixed-effects model.

---

1. R-code to assess the impact of dropouts for various designs. Give the dropout-rate in percent.
   library(PowerTOST)
power.final <- function(CV, theta0, target, design, scaling=TRUE,
                        regulator, dropout.rate) {
  if (design %in% c("parallel", "2x2x2r")) stop("design not supported.")
  if (scaling) { # RSABE or ABEL
    if (regulator == "FDA") {
      res <- sampleN.RSABE(CV=CV, design=design, theta0=theta0,
                           targetpower=target, print=FALSE, details=FALSE)
    } else { # EMA or HC
      res <- sampleN.scABEL(CV=CV, design=design, theta0=theta0,
                            targetpower=target, regulator=regulator,
                            print=FALSE, details=FALSE)
    }
  } else {       # ABE
    res <- sampleN.TOST(CV=CV, design=design, theta0=theta0,
                        targetpower=target, print=FALSE, details=FALSE)
  }
  washouts <- as.integer(substr(design, nchar(design), nchar(design)))-1
  eligible <- res[["Sample size"]]
  for (j in 1:washouts) {
    eligible <- eligible*(1-dropout.rate/100)
  }
  eligible <- round(eligible)
  if (scaling) {
    if (regulator == "FDA") {
      pwr <- suppressMessages(power.RSABE(CV=CV, design=design,
                                          theta0=theta0, n=eligible))
    } else {
      pwr <- suppressMessages(power.scABEL(CV=CV, design=design,
                                          theta0=theta0, n=eligible,
                                          regulator=regulator))
    }
  } else {
    pwr <- suppressMessages(power.TOST(CV=CV, design=design,
                                       theta0=theta0, n=eligible))
  }
  cat("\nDesign", design,
      "\nStudy started with", res[["Sample size"]], "subjects (achieved power",
      sprintf("%.1f%%).", 100*res[["Achieved power"]]),
      "\nStudy finished with", eligible, "eligible subjects (power",
      sprintf("%.1f%%).", 100*pwr), "\n\n")
}
   Of course we will see more dropouts in 4-period designs but is this larger loss in power compared to the 3-period designs relevant?
   Examples for CV 0.4, GMR 0.9, EMA’s ABEL, dropout-rate 5%. Call the function with
   power.final(CV=0.4, theta0=0.9, target=0.8, design=design, scaling=TRUE,
            regulator="EMA", dropout.rate=5)
   and change design to one of "2x2x4", "2x2x3", "2x3x3".
   Gives:
   Design 2x2x4
Study started with 30 subjects (achieved power 80.7%).
Study finished with 26 eligible subjects (power 75.9%).
Design 2x2x3
Study started with 46 subjects (achieved power 80.7%).
Study finished with 42 eligible subjects (power 77.7%).
Design 2x3x3
Study started with 42 subjects (achieved power 80.1%).
Study finished with 38 eligible subjects (power 76.3%).
   
   Coming back to one of your questions:
   

   ❝ 2. Can we go for 2 way crossover, when ISCV > 30% also?
   

   
   Sometimes we are not allowed to expand the acceptance range (i.e., if we are not able to provide a clinical justification). Remember that for the EMA scaling would be acceptable for C_max and for Health Canada for AUC… Let’s see (as above, but additionally design="2x2x2", scaling=FALSE):
   Design 2x2x4
Study started with 68 subjects (achieved power 80.7%).
Study finished with 58 eligible subjects (power 75.0%).
Design 2x2x3
Study started with 100 subjects (achieved power 80.0%).
Study finished with 90 eligible subjects (power 76.2%).
Design 2x3x3
Study started with 102 subjects (achieved power 80.7%).
Study finished with 92 eligible subjects (power 77.0%).
Design 2x2x2
Study started with 134 subjects (achieved power 80.1%).
Study finished with 127 eligible subjects (power 78.2%).
   
   
2. For the FDA you can use RSABE for any PK metric. Since generally the variability of C_max is larger than the one of AUC, you might end up with a situation to employ RSABE for C_max (s_wR ≥ 0.294) and ABE for AUC (s_wR < 0.294).