Bioequivalence and Bioavailability Forum

Dear Ol'Simulant,

according to Julious¹⁾, log-transformed data, parallel group design with common variance, non-central t-approximation:

power = pt(-tcrit, df, delta2) - pt(tcrit, df, delta1)

with
df     = nT+nR-2           # unequal sizes of both groups allowed
tcrit  = qt(1-alpha, df)   # t-quantil, R function nomenclature       
delta1 = (log(GMR) - log(0.8))/SE
delta2 = (log(GMR) - log(1.25))/SE
and
SE  = sqrt((1/nT+1/nR)*mse)
mse = log(1.0 + CV^2).

If you prefer to think in total number n=nT+nR and have a balanced design with nT=nR=n/2 some of the formula reduce to:
df = n-2
SE = sqrt((4/n)*mse)

Note the design constant=4 in the last formulas (in terms of total n). Different from the 2 in your formulas for the classical 2x2x2 crossover.

If it comes to unequal CV's, variances: Duno exactly.

• One option would be simple pooling. mse = ((nT-1)*sT^2 + (nR-1)*sR^2)/(nT+nR-2).
  
• Another option is thinking in direction of Welch-t-test. But I'm absolutely not sure if the t-distribution does apply in this case. And non-integer df's are horror for me.

Hope I have complied all these stuff without typos.
The application of the 'shifted' central t-approximation is left to you .

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¹⁾ S.A. Julious
"TUTORIAL IN BIOSTATISTICS
Sample sizes for clinical trials with Normalal data"
Statistics in Medicine 2004; 23: 1921-1986
page 1970, formula 68