Bioequivalence and Bioavailability Forum • No analytic solution!

No analytic solution! [Power / Sample Size]

posted by Helmut – Vienna, Austria, 2013-02-07 13:32 (4890 d 13:09 ago) – Posting: # 9985
Views: 13,035

Hi Anu,

❝ I have used the R-code as well that you have provided. In my data (CV=40%, Ratio=1.16), through R-code sample size came 39 and with ref to the Table A3, Sample-size is between (47-104).

As Detlew already pointed out there is no analytical solution for RSABE due to the GMR-restriction (+ the 50% CV cap for EMA). Either you use the tables or you set up your own simulations.

require(PowerTOST)

sigma0  <- 0.25 # FDA's

CVwr    <- 0.4

sigmawr <- CV2se(CVwr)

L       <- exp(-log(1.25)/sigma0*sigmawr)

U       <- exp(+log(1.25)/sigma0*sigmawr)

if(CVwr <= 0.3){L <- 0.8; U <-1.25} # no scaling

for(theta0 in seq(1.15, 1.20, by=0.05)){

  sampleN.TOST(CV=CVwr, theta0=theta0, theta1=L, theta2=U, design="2x3x3")

}



+++++++++++ Equivalence test - TOST +++++++++++

            Sample size estimation

-----------------------------------------------

Study design:  partial replicate (2x3x3)

log-transformed data (multiplicative model)



alpha = 0.05, target power = 0.8

BE margins        = 0.7090232 ... 1.410391

Null (true) ratio = 1.15,  CV = 0.4



Sample size (total)

 n     power

36   0.822516



+++++++++++ Equivalence test - TOST +++++++++++

            Sample size estimation

-----------------------------------------------

Study design:  partial replicate (2x3x3)

log-transformed data (multiplicative model)



alpha = 0.05, target power = 0.8

BE margins        = 0.7090232 ... 1.410391

Null (true) ratio = 1.2,  CV = 0.4



Sample size (total)

 n     power

54   0.803675

Table A3 (FDA method, 3-period, 80% power) for CV 40% gives 47 (GMR 1.15) and 104 (GMR 1.20) subjects. Sample sizes are substantially larger (especially for GMR 1.20) due to the [0.80–1.25] restriction.

Good news: For GMR 1.16 your 39 would be correct …
Bad news: … but only by ignoring the restriction.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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Complete thread:

Sample size for RSABE Anu 2013-02-01 07:01
- Sample size for RSABE d_labes 2013-02-01 09:46
  - Sample size for RSABE Anu 2013-02-07 06:58
    - No analytic solution!Helmut 2013-02-07 12:32
      - Coming soon ... d_labes 2013-02-08 11:57
        
        Wow! Helmut 2013-02-08 12:19
        
        Wow! Anu 2013-02-09 09:20
        
        read… Helmut 2013-02-09 09:35
        
        Bigamist d_labes 2013-02-09 18:11
        
        Some testing (Part I) Helmut 2013-02-10 18:35
        Some testing (Part II) Helmut 2013-02-11 01:00
        
        Power testing d_labes 2013-02-11 12:03
        
        the unknown x Helmut 2013-02-11 14:40
        
        Unequal CVs d_labes 2013-02-15 08:47
        
        Typo Helmut 2013-02-15 13:01