Bioequivalence and Bioavailability Forum

Dear Yung-jin,

❝ ... I just wonder if there is any way to

❝ VALIDATE (or how to validate) this method

Unfortunately Julious has not given worked examples in his book considering the case of uncertain variance.
But he has given Inflation factors (factors to multiply the classical "carved in stone" sample sizes) on page 115.
Here an excerpt with the usual powers:

         ------- alpha ---------
  m beta 0.010 0.025 0.050 0.100
--------------------------------
  5 0.10 2.167 2.068 1.980 1.875
    0.20 1.776 1.711 1.652 1.581
 10 0.10 1.463 1.425 1.392 1.353
    0.20 1.328 1.301 1.276 1.248
 25 0.10 1.163 1.150 1.139 1.125
    0.20 1.119 1.109 1.101 1.091
 50 0.10 1.078 1.072 1.067 1.060
    0.20 1.058 1.053 1.049 1.044
 75 0.10 1.052 1.047 1.044 1.040
    0.20 1.038 1.035 1.032 1.029
100 0.10 1.038 1.035 1.033 1.030
    0.20 1.029 1.026 1.024 1.022

But they are only for the case that the assumed true ratio is 1.

❝ ... imprecise/uncertain CV (how imprecise can it be allowed?) ...

As you can see up to df(=m) around 75 there is still approximately a 5% higher sample size compared to the classical calculation depending on alpha, beta. How big this excess is for the true ratio assumed !=1 can be answered using the code supplied above.
Note also the nearly doubling of the sample size for df=5 corresponding roughly to a CV from a pilot with 6 subjects!

❝ ... But I'll late. I was thinking the possibility to solve

❝ this using Bayesian inference approach recently.

"He who comes too late will be punished by life."
(Michail Gorbatschow in 1989 to Erich Honnecker shortly before the opening of the Berlin Wall)

Julious has not given much details, not to say nearly nothing, about the theory behind his formulas. But I think its sort of Bayesian reasoning. Expected power (aka some sort of average) seems the power averaged over the distribution of the variability namely a chi-squared distribution we (Helmut) up to now used in sensitivity analysis aka upper confidence limit.