Bioequivalence and Bioavailability Forum

Hi Yura,

can you please explain what you mean by the abbreviations you used?

❝ Correction of alpha is carried out by CVWR and CVWT-R (nR and nT-R, GRMR and

❝ GRMT-R, respectively, for TRR / RTR / RRT) or only by CVWR? Since it is necessary to calculate CIT-R.

The inflation of the Type I Error depends on CV_wR (and to a minor extent on the sample size). CV_wT – which is indeed nice to know – is not accessible in the partial replicate design.
Examples of the TIE and adjusting α for an assumed true ratio of 0.9:

1. n = 48, balanced sequences
   library(PowerTOST)
scABEL.ad(CV=0.35, n=48, design="2x3x3")

+++++++++++ scaled (widened) ABEL ++++++++++++
         iteratively adjusted alpha
   (simulations based on ANOVA evaluation)
----------------------------------------------
Study design: 2x3x3 (TRR|RTR|RRT)
log-transformed data (multiplicative model)
1,000,000 studies in each iteration simulated.

CVwR 0.35, n(i) 16|16|16 (N 48)
Nominal alpha                 : 0.05
True ratio                    : 0.9000
Regulatory settings           : EMA (ABEL)
Switching CVwR                : 0.3
Regulatory constant           : 0.76
Expanded limits               : 0.7723 ... 1.2948
Upper scaling cap             : CVwR > 0.5
PE constraints                : 0.8000 ... 1.2500
Empiric TIE for alpha 0.0500  : 0.05663
Power for theta0 0.9000       : 0.801
Iteratively adjusted alpha    : 0.04405
Empiric TIE for adjusted alpha: 0.05000
Power for theta0 0.9000       : 0.785
   
   
2. Three dropouts
   scABEL.ad(CV=0.35, n=c(16, 14, 15), design="2x3x3")

+++++++++++ scaled (widened) ABEL ++++++++++++
         iteratively adjusted alpha
   (simulations based on ANOVA evaluation)
----------------------------------------------
Study design: 2x3x3 (TRR|RTR|RRT)
log-transformed data (multiplicative model)
1,000,000 studies in each iteration simulated.

CVwR 0.35, n(i) 16|14|15 (N 45)
Nominal alpha                 : 0.05
True ratio                    : 0.9000
Regulatory settings           : EMA (ABEL)
Switching CVwR                : 0.3
Regulatory constant           : 0.76
Expanded limits               : 0.7723 ... 1.2948
Upper scaling cap             : CVwR > 0.5
PE constraints                : 0.8000 ... 1.2500
Empiric TIE for alpha 0.0500  : 0.05634
Power for theta0 0.9000       : 0.779
Iteratively adjusted alpha    : 0.04420
Empiric TIE for adjusted alpha: 0.05000
Power for theta0 0.9000       : 0.762
   

Due to the smaller sample size in #2 the TIE is less inflated (0.05634 < 0.05663) and less adjustment is required (0.04420 > 0.4405) to preserve the patient’s risk. On the other hand the narrower CI (91.16% < 91.19%) cannot outweigh the loss in power (76.2% < 78.5%).