Bioequivalence and Bioavailability Forum

Hi Martin,

❝ First of all – thank you very much for your input. Here is the „situation“ in more detail. There are k test lots, one reference and one negative control lot. From each lot k>3 samples are drawn (i.e. 3 vials) each analyzed seperately with a specific assay. For this reason, I assume that the replicates independent within each lot.

I agree, proper sampling this way can be considered independent within each lot.

❝ I suppose that the focus is on individual lots (i.e. „showing“ that each lot is „comparable“ to the reference lot and that each lot is superior to the negative control lot).

Comparative lots: Sounds to me just like standard parallel bioequivalence then. R's simple t.test with a 90% CI comes to mind here. Might need to omit the log step depending on residual considerations. And I am sure Helmut will chirp in with a comment about Welch-Satterthwaite.
But on the other hand, with three replicates per lot a CI-approach seems quite meaningless.

❝ Based on your suggestions I think that here only PE estimates may be used. What do you think about a figure showing ratios of means for individual lots relative to the mean of the negative control for “showing” superiority and another figure showing ratios of means for individual lots relative to the reference for “showing equivalence” similar like forest plot in meta analysis (y-axis = lots; x-axis = ratio of means).

Sounds completely fine and intuitive to me.

❝ For an overall statement (i.e. all lots combined) a CI for the ratio (package mratios) can be calculated using an ANOVA model that models the lot effect (i.e. replicates within each lot) with a contrast matrix that gives the estimated mean over all lots versus the estimated mean of the reference lot. In this model, the potential day effect can be included to adjust for a potential day effect.

❝

❝ What do you think?

Apart from my comment above, I am afraid I can only produce completely flat brain waves here. I am unfortunately unfamiliar with mratios. A closer look at your code is needed and I feel neither competent nor worthy. It does, however, not sound readily intuitive to me if you say the lot effect is the replicates of units within lots. But that's probably just a matter of semantics.