Bioequivalence and Bioavailability Forum

Hi simulators!

I stumbled upon another goodie. A presentation at last years “AAPS Workshop on Facilitating Oral Product Development and Reducing Regulatory Burden through Novel Approaches to Assess Bioavailability / Bioequivalence”:

Alfredo García-Arieta
Current Issues in BE Evaluation in the European Union
23 October, Washington

The views expressed in this
presentation are the personal views of
the author and may not be
understood or quoted as being made
on behalf or reflecting the position of
the Spanish Agency for Medicines
and Health Care Products or the
European Medicines Agency or one
of its committees or working parties

Two-stage design

• The first stage is an interim analysis and
  
• The second stage is the analysis of the full data set
    • The 2^nd data set cannot be analyzed separately.
  
• To preserve the overall type I error the significance level needs to be adjusted to obtain a coverage probability higher than 90%
    • It is not acceptable to perform
      • a 90% CI at the interim analysis and
      • a 95% CI in the final analysis with the full data set.

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• How alpha is spent must be pre-defined in
  the protocol
  
• The same or a different amount alpha can be spent in each analysis
    • If the same alpha is spent in both stages the
      Bonferroni rule (95% confidence interval in both
      analyses) is too conservative and
    • 94.12% confidence interval can be used
    • It is also possible to distribute the alpha differently
        • A extreme case it is acceptable to design no alpha
          expenditure in the interim analysis when designed to
          obtain information of formulation differences and intra-
          subject variability and 90% CI are not estimated at the
          interim stage.

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• Even if the final sample size is going to be
  decided based on the intra-subject variability
  estimated in the interim analysis, a proposal
  for a final sample size must be included in the
  protocol.
  
• This proposed final sample size should be
  recruited if the estimation obtained from the
  interim analysis were lower than the one predefined
  in the protocol in order to keep the
  consumer risk.
  
• A term for the stage in the ANOVA model.

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What puzzles me here is the “proposed final sample size”. I don’t understand why performing the stage in a smaller sample size should violate the consumer’s risk. The contrary was already demonstrated by Potvin et al. with Method B. Furthermore how would a sponsor derive the final sample size? This idea smells of the original work of Pocock, which would require for one interim analysis the first stage to be ½ of the final size. In my understanding (corrections welcome) the framework might look like this:

I’ve performed some simulations for CV 20% (see at the end of the post).

I wonder why so many new “methods” popped up in the last years (remember this one?) without any [sic] published evidence that they maintain the patient’s risk.

Example: α_adj 0.0294, CV 20%, GMR 0.95, target power 80%, n₁ 12 (n_p 24), 10⁶ simulations, exact sample size estimation (Owen’s Q)
                 αemp        1–βemp   ntot   5%  50%  95%  % in stage 2
Method B     :  0.046293    0.841332  20.6  12   18   40    56.3795
Pseudo Pocock:  0.050903*   0.896622  21.9  12   24   40    58.6798
* significantly >0.05 (limit 0.05036).

Such a method would require simulations for every single study – in order to come up with a proposed final sample size and a suitable α_adj. It don’t expect 0.0294 to be applicable. Imagine a situation where the proposed sample size was 48 (n₁ 24), and the expected CV 20%. Actually it was 25%. Instead of running the second stage in ten subjects (n_est–n₁=34–24) we would have to dose another 24 subjects. Of course we could set the proposed size just a little bit larger than n₁ (would go with n_est most of the time) – but this is not even “intended Pocock” any more and we end up with Method B without power. Patient’s risk? No idea, again. Show me simulations, please.
Why do we have to waste our time assessing all this “methods”? I would prefer that their inventors do their job. If they have done it already – which I doubt –, they should publish it.

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Patient’s risk significantly inflated with n₁ 12 – although within Potvin’s maximum acceptable inflation (0.052); less conservative than Method B (especially at higher sample sizes in the first stage) where α_emp asymptotically approaches α_adj of 0.0294.


Higher power than Method B because studies proceeding to the second stage with n_est < n_prop have to be performed in n_prop – n₁ subjects (instead of in only n_est – n₁).