Bioequivalence and Bioavailability Forum

Hi zizou,

good points! First of all I could reproduce your numbers; nice excursion into combinatorics.

library(PowerTOST)
CV  <- 0.262
dor <- 0.15
n.des  <- sampleN.TOST(CV=CV, details=F, print=F)[["Sample size"]]
n.adj  <- round(n.des/(1-dor)/2)*2
do     <- n.adj-n.des
n.TR   <- seq(n.adj/2-do, n.adj/2, 1)
n.RT   <- seq(n.adj/2, n.adj/2-do, -1)
res    <- matrix(nrow=length(n.TR), ncol=7, byrow=T, dimnames=list(rep(NULL, 5),
            c("n", "TR", "RT", "TR.do", "RT.do", "prob", "power")))
res[, 1] <- n.TR+n.RT
res[, 2] <- n.TR
res[, 3] <- n.RT
res[, 4] <- n.adj/2-n.TR
res[, 5] <- n.adj/2-n.RT
for (j in seq_along(n.TR)) {
  res[j, 6] <- sprintf("%.9f",
                (choose(n.adj/2, n.adj/2-n.TR[j])*
                choose(n.adj/2, n.adj/2-n.RT[j]))
                /choose(n.adj, do))
  res[j, 7] <- sprintf("%.5f", power.TOST(CV=CV, n=c(n.TR[j], n.RT[j])))
}
Sum.p  <- sum(as.numeric(res[, 6]))
res    <- data.frame(res)
print(res, row.names=F); cat("Sum p:", Sum.p, "\n")

  n TR RT TR.do RT.do        prob   power
 30 12 18     6     0 0.009530792 0.78425
 30 13 17     5     1 0.079178886 0.79345
 30 14 16     4     2 0.240364474 0.79877
 30 15 15     3     3 0.341851697 0.80051
 30 16 14     2     4 0.240364474 0.79877
 30 17 13     1     5 0.079178886 0.79345
 30 18 12     0     6 0.009530792 0.78425
Sum p: 1

❝ So in this example we have 65.8% (100*(1-p_4)) probability that we shoot ourselves in the foot .

Depends on how rigid the bullet is. Full metal jacket are not even the 6/0 (or 0/6)-cases (power 78.4%). The others (with a much higher probability) are soft-balls.

❝ Maybe not so big shot - planned number of subjects finished will be achieved , but sample size wasn't estimated with option of getting unbalanced in mind. Even though there is almost 2/3 probability that it will ends unbalanced (if assumptions are right, and no better GMR than expected, no lower CV estimated from residual mean square than expected, and no lower dropout-rate than expected).

Correct. I would be wary to assume very different dropout-rates in sequences. Theoretically they should occur at random (n_TR ~ n_RT). If we expect different dropout-rates a priori, IMHO this would also imply that we expect a true (!) sequence effect – which would confound the treatment effect. Opening a can of worms.

❝ "Remember, with great power comes great responsibility."

Power. That which statisticians are always calculating
but never have.    Stephen Senn (Statistical Issues in Drug Development, Wiley 2004, p197)