Bioequivalence and Bioavailability Forum

Hi Antigoni,

❝ Noticed that a letter is missing below, which would not let me run the code

Oops! I corrected it.

However, much easier with the function sampleN.scABEL.ad(), which was implemented in version 1.3-3 (2016-01-15) of PowerTOST.

library(PowerTOST)
CV     <- 0.4
target <- 0.9
design <- "2x2x4"
sampleN.scABEL(CV = CV, targetpower = target, design = design, details = TRUE)
# theta0 = 0.9 is the default in the HVD reference-scaling functions

+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
   (simulation based on ANOVA evaluation)
---------------------------------------------
Study design: 2x2x4 (4 period full replicate)
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.9
CVw(T) = 0.4; CVw(R) = 0.4
True ratio = 0.9
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


Sample size search
 n     power
36   0.8630
38   0.8782
40   0.8924
42   0.9032

sampleN.scABEL.ad(CV = CV, targetpower = target, design = design, details = TRUE)
# using the values of above

+++++++++++ scaled (widened) ABEL ++++++++++++
            Sample size estimation
        for iteratively adjusted alpha
   (simulations based on ANOVA evaluation)
----------------------------------------------
Study design: 2x2x4 (4 period full replicate)
log-transformed data (multiplicative model)
1,000,000 studies in each iteration simulated.

Assumed CVwR 0.4, CVwT 0.4
Nominal alpha      : 0.05
True ratio         : 0.9000
Target power       : 0.9
Regulatory settings: EMA (ABEL)
Switching CVwR     : 0.3
Regulatory constant: 0.76
Expanded limits    : 0.7462 ... 1.3402
Upper scaling cap  : CVwR > 0.5
PE constraints     : 0.8000 ... 1.2500

n  42, nomin. alpha: 0.05000 (power 0.9032), TIE: 0.0557

Sample size search and iteratively adjusting alpha
n  42,   adj. alpha: 0.04256 (power 0.8914), rel. impact on power: -1.31%
n  44,   adj. alpha: 0.04326 (power 0.9052), TIE: 0.05000
Compared to nominal alpha's sample size increase of 4.8% (~study costs).

Runtime    : 12.7 seconds
Simulations: 16,400,000

To get only the sample size use

sampleN.scABEL.ad(CV = CV, targetpower = target, design = design,
                  print = FALSE)[["Sample size"]]


I leave it to you to loop over the target power, CV_wR, and designs to get the plots…

For examples and more elaborated -scripts see this article.