Reasons to go for Full Replicate [Design Issues]

posted by Helmut Homepage – Vienna, Austria, 2018-03-09 14:17 (1848 d 15:11 ago) – Posting: # 18508
Views: 3,923

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:

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

Correct. :-D 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 CVwT 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) <- 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,
      } 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, theta0=0.9, target=0.8, design=design, scaling=TRUE,
                regulator="EMA", dropout.rate=5)

    and change design to one of "2x2x4", "2x2x3", "2x3x3".
    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 Cmax 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 Cmax is larger than the one of AUC, you might end up with a situation to employ RSABE for Cmax (swR ≥ 0.294) and ABE for AUC (swR < 0.294).

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