Bioequivalence and Bioavailability Forum

Dear AB,

❝ But according to Table 1 “Average Bioequivalence Estimated Numbers of Subjects D=0.05” Results for two-period designs use method of Diletti et al. (Diletti 1991) from FDA’s Statistical Approaches to Establishing Bioequivalence (page 28 of guidance) Sample size of 2 period with CV of 50 and D=0.05 and power 80% is given as 108 and 75% & 50% of the same is 81 & 54.

The cited table, as very clearly depicted in the heading (!), is sample size for common average bioequivalence.
Further it is detailed not for any CV but for the standard deviations (square root of variance) of variability decomposed into within-subject variance (assuming equal variances for Test and Reference) and the so-called subject by formulation variance sigma_D.
Additionally this table seems to be obtained using an point estimator of theta₀=1.05 whereas conventionally 0.95 is used because the power is some amount smaller there.
A third difference is the usage of the degrees of freedom = N-seq (called 'robust' df in PowerTOST).

You could obtain the sample sizes of this table considering according to Wang and Chow⁽¹⁾ the formulas relating the intra-subject variance and the subject-by-formulation variance to the variance of the treatment differences (mixed model analysis):
for 2x2 cross-over
var1=var(µT-µR)=0.5*(s2D + s2WT + s2WR)

for 4-period repl. cross-over
var2=var(µT-µR)=s2D + 0.5(s2WT + s2WR)

CV1 or 2=sqrt(exp(var1 or 2)-1)
and then using CV's for sample size estimation f.i. in PowerTOST.

Here some R-code to play with:
require(PowerTOST)
tp  <- 0.8    # target power
sD  <- 0.01
sWT <- 0.5
sWR <- 0.5
var1 <- 0.5*(sD*sD + sWT*sWT + sWR*sWR)
var2 <- sD*sD + 0.5*(sWT*sWT + sWR*sWR)
CV1  <- sqrt(exp(var1)-1)
CV2  <- sqrt(exp(var2)-1)
sampleN.TOST(CV=CV1, theta0=1.05, targetpower=tp, design="2x2")
sampleN.TOST(CV=CV2, theta0=1.05, targetpower=tp, design="2x2x4", robust=TRUE).

This will give you n=108 for design="2x2" and n=54 for design="2x2x4", the numbers shown in Table 1 of the FDA guidance. Note CV1 / CV2 ~0.533 (53.3%).
All other entries of Table 1 can also reproduced with this code (with some minor deviations for power 90%). Try it .

❝ and when i check the sample size @ 50% CV , 80% power & GMR 0.95 given in the document article ...why these figures are very different in the guideline, article to the calculation

The sample size tables of your linked document deals with scaled average bioequivalence evaluated via the methods recommended by EMA (widened acceptance limits) or FDA (95% CI of the scaled ABE criterion).
These methods are completely different from the conventional ABE and can't therefore compared directly .

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(1)Hansheng Wang and Shein-Chung Chow (2002)
"On Statistical Power for Average Bioequivalence Testing under Replicated Crossover Designs"
J. BIOPHARM. STAT. Vol. 12, No. 3, pp. 295–309, 2002