Bioequivalence and Bioavailability Forum

Power with a Danish twist [Power / Sample Size]

posted by Helmut  – Vienna, Austria, 2009-05-08 15:23 (5833 d 15:46 ago) – Posting: # 3660
Views: 9,286

Dear ElMaestro!

❝ I am still wondering about the Danish policy for BE [...]

You are not alone.

❝ *: What's the real power at CV=65%, R/T=95%, 38 sbj (19 in each seq)??

Good question. I think we are pushing software to the limits, i.e., running into troubles of getting a rasonable value of the noncentral t-distribution (numeric precision,...).
Fartssie comes up with -0.0278 (!), StudySize 2.01 simply gives up (-, with 20 subjects/sequence gives 0.421%), and my R-code
a       <- 0.05     # alpha
CV      <- 0.65     # intra-subject coefficient of variation
Theta1  <- 0.8      # lower acceptance limit
Theta2  <- 1/Theta1 # upper acceptance limit
Limit   <- 20000    # Upper Limit for Search
Ratio   <- 0.95
SigmaW  <- sqrt(log(1+CV^2))
s       <- sqrt(2)*SigmaW
for (Aimed in c(0.00001,0.0001,0.0005,0.001,0.005,0.01,0.5,0.7,0.8,0.9))
  {
  n     <- 4        # start value of sample size search
  repeat{
    df    <- n-2
    t1    <- qt(1-a,df)
    t2    <- -t1
    nc1   <- sqrt(n)*((log(Ratio)-log(Theta1))/s)
    nc2   <- sqrt(n)*((log(Ratio)-log(Theta2))/s)
    prob1 <- pt(t1,df,nc1)
    prob2 <- pt(t2,df,nc2)
    power <- prob2-prob1
    n     <- n+2
    if(power >= Aimed | (n-2) >= Limit) break
  }
Total   <- n-2
if(Total == Limit){
  cat("Aimed",Aimed*100,"%, CV",CV*100,"%, Stopped at Limit",Limit," Power",power*100,"%\n")
  } else
  cat("Aimed",Aimed*100,"%, CV",CV*100,"%, Sample Size",Total," Power",power*100,"%\n")
}
gets stuck at 40 subjects (power 0.454%)...

The nasty point in the Danish requirement are formulations with low CVs.
The current guideline states

"The clinical and analytical standards imposed may also influence the statistically determined number of subjects. However, generally the minimum number of subjects should be not smaller than 12 unless justified."

whereas the BE-draft comes up with

"The minimum number of subjects in a cross-over study should be 12."

1. Have you ever seen a BE study which was performed in less than 12 subjects including a justification of the sample size like: "low variability, small sample size in order to meet Danish requirements, "?
   
2. What about the draft? If we read "should be" = "has to be" it will be quite nasty.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна! 
Helmut Schütz


The quality of responses received is directly proportional to the quality of the question asked. 🚮
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Complete thread:

• Power with a Danish twist ElMaestro 2009-05-05 19:49 [Power / Sample Size] 
  • population parameter martin 2009-05-05 21:32
    • population parameter ElMaestro 2009-05-05 21:48
      • population parameter martin 2009-05-05 22:59
  • Wrong Question Answer in Danish d_labes 2009-05-08 09:49
    • Danish numbers d_labes 2009-05-08 15:53
      • Danish numbers ElMaestro 2009-05-08 20:19
  • Power with a Danish twistHelmut 2009-05-08 13:23
    • Power with a Danish twist d_labes 2009-05-08 16:06
      • Power with a Danish twist Helmut 2009-05-08 16:15
    • Power with a Danish twist ElMaestro 2009-05-08 19:40
  • Power with a Danish twist Helmut 2009-05-08 16:56
    • Power with a Danish twist ElMaestro 2009-05-08 19:17