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

❝ 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 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.

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

- 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.

- Jones B, Kenward MG.
*Design and Analysis of Cross-Over Trials.*Boca Raton: Chapman & Hall, CRC Press; 3^{rd}edition 2015.

*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:

- Sample size tools for various designs Achievwin 2020-09-28 03:58 [Power / Sample Size]
- Sample size tools for various designsHelmut 2020-09-28 11:31