Sample size tools for various designs [Power / Sample Size]

posted by Helmut Homepage – Vienna, Austria, 2020-09-28 11:31 (31 d 10:04 ago) – Posting: # 21946
Views: 228

Hi Achievwin,

» share tools (R-, SAS code and excel spreadsheet) for computing Sample size from ISCV for Parallel, 2x2, 3x3 and 4x4 BE study designs) …

The CV and T/R-ratios are assumptions (or estimates if obtained from previous studies). Hence, sample size estimation (not computation or calculation), if you don’t mind. ;-)

I recommend the [image] package PowerTOST. For the implemented designs see here and there. You can also run scripts in the browser (see this post).
If you are dealing with a higher-order design, I recommend the “Two at a Time” approach instead of “All at Once” (pooled ANOVA). See the vignette. That means to estimate the sample size of the study like for a 2×2×2 design.
<nitpick>

In a parallel design you get only the total (pooled) CV.
For the intra- (and inter-) subject CV you need a crossover.

</nitpick>
If you want sumfink in M$ Excel, consider FARTSSIE which estimates the sample size based on the noncentral t-distribution. Note that the sample size for replicate designs is only approximate and for reference-scaling wrong (since no algebraic solution exist and therefore, simulations are required). For 2×2×2 studies you can also implement approximations based on the central t-distribution.1 However, I don’t recommend that because in borderline cases the sample size will be higher than necessary:

library(PowerTOST)
res <- data.frame(method = c("exact", "noncentral", "central"))
for (j in 1:nrow(res)) {
  res$n[j] <- sampleN.TOST(CV = 0.22, theta0 = 0.95, targetpower = 0.8,
                           method = res$method[j], details = FALSE,
                           print = FALSE)[["Sample size"]]
}
print(res, row.names = FALSE)
    method  n
     exact 22
noncentral 22
   central
24


Some SAS code based on the noncentral t-distribution is given by Jones and Kenward.2 AFAIK, no code for reference-scaling is in the public domain. You are on your own – good luck and be prepared for extreme run­times.

» … also if we can compute ISCV or ANOVA CV from the confidence intervals.

Sure – if you know also the sample size and design. For the underlying algebra see this presentation (slides 26–30). Implemented in PowerTOST’s functions CVfromCI() / CI2CV(). See also the vignette. Example:

library(PowerTOST)
signif(CVfromCI(lower = 0.9800, upper = 1.1257, design = "2x2x4", n = c(62, 63)), 4)
# [1] 0.497



  1. Hauschke D, Steinijans VW, Diletti E, Burke M. Sample Size Determination for Bioequivalence Assessment Using a Multiplicative Model. J Pharmacokinet Biopharm. 1992; 20(5): 557–61. doi:10.1007/BF01061471.
  2. Jones B, Kenward MG. Design and Analysis of Cross-Over Trials. Boca Raton: Chapman & Hall, CRC Press; 3rd edition 2015.

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