Bioequivalence and Bioavailability Forum

Dear BEQool!

❝ So the values of reference treatment in period 3 are irrelevant for estimating the treatment effect (and therefore for calculating PE and 90% CI)?

Yes - for PE under the standard fixed effects model with period (any systematic shift in period 3, R is absorbed by the period 3 effect)
No - for CI (see residual MS and residual df)

❝ If I understand correctly, the model assumes that these "lower" values of reference treatment in period 3 are a " consequence" of the period (period effect) rather than the reference product itself? Consequently, the model assumes that if. e.g. the values of reference treatment are about 50% lower in period 3, the values of test treatment would also be about 50% lower if administered in the same period 3? Therefore, the PE remains unchanged?

Yes, if period 3 R values are lower and period 3 contains only R, then the model can only represent that systematic shift through the period 3 coefficient (if period term is included in the model, see below)

❝ What does one then even gain with this design (with additional 3rd period) - I assume this design is more powerful than 2x2x2 design and therefore the 90% CIs should be narrower compared to 2x2x2?

Some CI tightening via more df/different MSE, but that’s typically not the reason to choose the design. It allows reference-scaled BE - that's the only real gain we can guess. Although more affordable designs exist (TRT|RTR, TRR|RRT|RTR)

❝ I am a little confused about what this means exactly. Here in our example we have period effect - does that mean that the calculated PE is biased?

With the model including period, treatment estimate is not biased in the way you are worried about, because the period 3 shift is absorbed by the period term, and the contrast is identified from where both treatments occur.
The bias warnings mainly target analysis without period term included (i.e. assuming no period effect). So there's a trade-off: include period term and get PE driven by periods 1-2 or omit period term and assume no period effect at all.

❝ Or is PE (treatment effect) biased only if we exclude factor period (i.e. using ANOVA model with treatment, sequence and subject(sequence)) in the presence of period effect (as is the case here)? Namely if we exclude factor period from the ANOVA model, I think it would then also take into account reference data in period 3 for the calculation of treatment effect (PE) and the results would differ from that based on the first 2 periods? Therefore, would ANOVA model without factor period (i.e. ANOVA model of treatment, sequence and subject(sequence) also suffice if there is no period effect?

Correct. But no period effect is a strong assumption you typically cannot justify. I guess this is the reason why extra-reference design is widely discouraged