# Bioequivalence and Bioavailability Forum

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Yura
Regular

Belarus,
2017-12-08 08:48

Posting: # 18045
Views: 628

## alpha correction [RSABE / ABEL]

Hello everybody
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])?
with respect
Helmut
Hero

Vienna, Austria,
2017-12-08 12:33

@ Yura
Posting: # 18046
Views: 516

## theta0 within PE-constraints [theta1, theta2]

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```

Regards,
Helmut Schütz

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Yura
Regular

Belarus,
2017-12-08 12:55

@ Helmut
Posting: # 18047
Views: 502

## theta0 within PE-constraints [theta1, theta2]

Hi Helmut
yes, I did so at once
Regards
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