Bioequivalence and Bioavailability Forum

Dear Helmut / All,

You raised an interesting question and yes the TSD from Potvin et al appears to have astonishing design features. The classical GSD or the adaptive two-stage design according to the inverse normal method rely on a formal statistical framework: mathematical theorems including proofs are available on why they work, what properties they have and how they should be applied. This is nice. For the Potvin approach we only have simulations for certain scenarios at hand. Even though it appears to be good, it is not clear if this is always the case. More information on that topic with some more elaborations contains for example the article from Kieser and Rauch (2015).

❝ In a TSD one would opt for a stage 1 sample size of ~75% of the fixed sample design.

Reference? Some software packages give an inflation factor that helps determining the study size… Anyhow, I think such a rule of thumb is too strict and inflexible.

Consider for example two alternative scenarios:

• Pre-planned n1 = 52 and final N = 78 (i.e. n2 = 26). The average sample number (ASN) is smaller than for the Potvin TSD. Power is higher up until a certain point where the CV gets too high.
  
• Pre-planned n1 = 48, n2 = 48. ASN comparable, Power similarly as above.

Two further comments on the comparison:

• For some reason the variable alpha and iuse for bounds() should be 1-dimensional to get the correct values. IMHO alpha is then 1-pnorm(bnds$upper.bounds), i.e. do not multiply by 2.
  
• As Detlew already pointed out, the comparison using the overall N from the classical GSD to the average sample number from the TSD is not fair, one should use the ASN in both cases.

Therefore, I think the GSD has some charme and can be useful in situations with uncertainty. Moreover, the advantage is that we do not have to rely on only simulation results from certain parameter settings (So I disagree with ElMaestro on that GSDs are a relic from the past with inferior properties).

Best regards,
Ben

Ref:
Kieser M, Rauch G
Two-stage designs for cross-over bioequivalence trials
Stat Med (Epub ahead of print 24 March 2015)
doi 10.1002/sim.6487