## Output of sampleN.scABEL() [Power / Sample Size]

Hi Divyen,

❝ But why the 90% BE range is still 80.00-125.00% where you know that you can apply the HVD concept to widen the boundary?

Seemingly the output of the function sampleN.scABEL() is not clear enough. It gives:

ABE limits / PE constraint = 0.8 ... 1.25 EMA regulatory settings - CVswitch            = 0.3 - cap on scABEL if CVw(R) > 0.5 - regulatory constant = 0.76 - pe constraint applied

What does it mean? The sample size is based on simulations (by default 100,000 studies; see this article). In a certain fraction of the simulated studies $$\small{CV_\textrm{wR}\le30\%}$$ and hence, ABE has to applied, where the conventional limits are 80.00–125.00%. Only if $$\small{CV_\textrm{wR}>30\%}$$, ABEL can be applied but additionally to assessing whether the 90% CI lies within the now expanded limits, the point estimate has to lie within 80.00–125.00%.
See this article for the decision scheme.

In coding the function sampleN.scABEL.ad() I tried to be more specific (see also my post below) and it gives for $$\small{CV_\textrm{wT}=CV_\textrm{wR}=0.3532}$$:

Regulatory settings: EMA (ABEL) Switching CVwR     : 0.3 Regulatory constant: 0.76 Expanded limits    : 0.7706 ... 1.2977 Upper scaling cap  : CVwR > 0.5 PE constraints     : 0.8000 ... 1.2500

If you use the function with a substantially lower $$\small{CV_\textrm{wR}}$$ you would get:

Regulatory settings: EMA (ABE) Switching CVwR     : 0.3 BE limits          : 0.8000 ... 1.2500 Upper scaling cap  : CVwR > 0.5 PE constraints     : 0.8000 ... 1.2500

Note that the sample size tables of the ‘The Two Lászlós’* don’t reach below $$\small{CV_\textrm{wR}=30\%}$$. They state:

»In view of the consequences of the mixed approach, it could be judicious to consider larger numbers of sub­jects at variations fairly close to 30%.«

You could assess at which $$\small{CV_\textrm{wR}}$$ (on the average) we will switch in the simulations.

library(PowerTOST) fun <- function(x) {   n.1 <- sampleN.TOST(CV = x, theta0 = theta0,                       targetpower = target,                       design = design, details = FALSE,                       print = FALSE)[["Sample size"]]   n.2 <- sampleN.scABEL(CV = x, theta0 = theta0,                         targetpower = target,                         design = design, details = FALSE,                         print = FALSE)[["Sample size"]]   return(n.1 - n.2) } theta0 <- 0.90 target <- 0.80 design <- "2x3x3" cat(design, "design:",     sprintf("Equal sample sizes for ABE and ABEL at CV = %.2f%%.",             100 * uniroot(fun, interval = c(0.3, 0.4), extendInt = "yes")\$root), "\n") 2x3x3 design: Equal sample sizes for ABE and ABEL at CV = 27.90%.

• Tóthfalusi L, Endrényi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs. J Pharm Phar­ma­ceut Sci. 2011; 15(1): 73–84. doi:10.18433/j3z88f. Open access.

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