Bioequivalence and Bioavailability Forum

Dear EM,

❝ The evaluation with a simple (one-stage) parallel study is a normal linear model with a single factor (treatment) of two levels (Test or Ref). For stage two we need to calculate sample size, and here I am not so sure what to do. For evaluation at stage 2, I imagine -and I'd really love to hear your opinion- that the factors are treatment (two levels) + stage (two levels) + stage x treatment.

I'm not sure if you really need the stage x treatment interaction in stage 2 model. If you apply the same prerequisite like Potvin et.al. "... Does not require poolability criteria (or at least should know whether results from both stages are poolable before sample analysis, i.e. base poolability on study conduct such as subject demographics, temporal considerations, use of same protocol, use of same site, etc., rather than a statistical test of poolability)." then IMHO the model with treatment + stage is sufficient.

❝ ... In a parallel two-stage evaluation, stage is also a between-subject factor, and hence it does affect the residual. Should one therefore take that fact into consideration when calculating sample size for stage 2? If yes, any idea how?

Since you don't know how the stage effect affects your residual variance in stage 2 the only thing you can do is to use the residual variance from stage 1 in your sample size adaptation. Regardless of a significant or insignificant stage effect in stage 2 evaluation your assumption is that the residual variance from stage 1 or stage 2 measure the same variability and will be used in calculating the (1-2*alpha_stage)-confidence intervals as a test of BE in both stages.

The only way you can consider the stage effect is the use of the degrees of freedom for stage 2 ANOVA in your sample size calculation after stage 1 data are obtained. This is also done by Potvin et.al. for the 2x2 crossover.
But I don't think this will make a great difference.

❝ ... But on the other hand, if the anova after stage 2 comes out with a significant p-value for stage as a factor, would this then be bad?

Like you I would consider stage as nuisance effect and thus would not worry about it's significance.

Hope this helps.