## Estimation of CVw and/or CVwR [Power / Sample Size]

Hi Alyssa,

» Usually ISCV result of the 3 way crossover or 4 way crossover, replicate study published in the PAR is CVwR or CVw?

There are no rules (it depends on what the assessor decides to include of the study report). However, since the study was a replicate design with reference-scaling, possibly it is CVwR (more important).
We can estimate the CVw with the R-package PowerTOST:

library(PowerTOST) round(100*CVfromCI(lower = 0.9625, upper = 1.2511,                    n = 41, design = "3x6x3"), 1)

and get

Unbalanced 3x6x3 design. n(i)= 7/7/7/7/7/6 assumed. [1] 36.8

Since this does not match what is given in the PAR, it is a strong hint that the 42.6% is the CVwR.
[Nonsense, not a Williams’ design! See ElMaestro’s post and the correction.]
If the expanded limits are given in the PAR, you can estimate the CVwR from the upper limit by the function CVwRfromU() to check. Example for 136.4%:

round(100 * CVwRfromU(136.4 / 100), 1) [1] 42.6

Although CVwT is not accessible in a partial replicate design, CVw < CVwR means that the test is less variable than the reference (since CVw is pooled from CVwR and CVwT).

I agree with Dan but want to add one point. In my experience the variability across studies (with the same clinical setup, bioanalytical method, ) tends to be more “stable” than the T/R-ratio. Hence, don’t fall into the trap of believing the nice 98.7% you observed in the pilot study. It might well have been pure chance. For HVD(P)s assuming a T/R-ratio of better than 90–111% is not a good idea (recommended by the two Lászlos* and therefore, the default in functions sampleN.scABEL() and sampleN.RSABE() of PowerTOST).

PS: Avoid sample size “calculation” if you don’t mind. Use “estimation” instead.
PPS: The partial replicate is a lousy design. If you want to have only three periods I suggest the 2×2×3 full replicate TRT|RTR instead. If you insist in the partial replicate (why?), use the function sampleN.scABEL.sdsims(). Slower than sampleN.scABEL() but more accurate. For a comparison see the vignette and scroll down to “Heterogenicity”.

• Tóthfalusi L, Endrényi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs. J Pharm Pharmaceut Sci. 2011;15(1):73–84. open access.

Dif-tor heh smusma 🖖
Helmut Schütz

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