Bioequivalence and Bioavailability Forum

Hi Yura,

❝ How to calculate scABEL.ad (alpha = 0.05, CV = 0.3043689, design = "2x3x3", theta0 = 0.77058, regulator = "EMA", n = c (15,15,15)) if the point estimate is not in [0.80 ; 1.25] (SWR = 0.298 [0.79755; 1.25385])?

Note the error message thrown by scABEL.ad():

library(PowerTOST)
scABEL.ad(alpha=0.05, CV=0.3043689, design="2x3x3", theta0=0.77058,
          regulator="EMA", n=c(15,15,15))
Error in scABEL.ad(alpha = 0.05, CV = 0.3043689, design = "2x3x3", theta0 = 0.77058,  :
  theta0 must be within [theta1, theta2]

See the man-page of scABEL.ad():

theta0

‘True’ or assumed bioavailability ratio. Defaults to 0.90 if not given explicitly.

theta1

Conventional lower ABE limit to be applied in the mixed procedure if CVwR==CVswitch. Also lower limit for the point estimate constraint. Defaults to 0.80 if not given explicitly.

theta2

Conventional upper ABE limit to be applied in the mixed procedure if CVwR==CVswitch. Also upper limit for the point estimate constraint. Defaults to 1.25 if not given explicitly.

The purpose of scABEL.ad() is to iteratively adjust α to control the Type I Error either before the study (and see how power is affected with the argument details=TRUE) or post hoc when the T/R-ratio is already known. In both cases ABEL cannot be shown if theta0 would be outside the PE-constraints theta1, theta2 (0.80, 1.25). Hence, modifying your example the most extreme case (theta0=theta1=1/theta2) would be:

library(PowerTOST)
scABEL.ad(alpha=0.05, CV=0.3043689, design="2x3x3", theta0=0.8,
          regulator="EMA", n=c(15,15,15))

+++++++++++ 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 0.3044, n(i) 15|15|15 (N 45)
Nominal alpha                 : 0.05
True ratio                    : 0.8000
Regulatory settings           : EMA (ABEL)
Switching CVwR                : 0.3
Regulatory constant           : 0.76
Expanded limits               : 0.7975 ... 1.2538
Upper scaling cap             : CVwR > 0.5
PE constraints                : 0.8000 ... 1.2500
Empiric TIE for alpha 0.0500  : 0.06805
Power for theta0 0.8000       : 0.076
Iteratively adjusted alpha    : 0.03616
Empiric TIE for adjusted alpha: 0.05000
Power for theta0 0.8000       : 0.056