Bioequivalence and Bioavailability Forum

Dear d_labes,

now assume beman goes ahead with this study and he collects a bunch of data.
Subjects are dosed once with each treatment, so the logic that applies in 2,2,2-BE studies applies here as well, implying that we ignore the little issue of potentially correlated residuals due to intra-subject phenomena (subject as fixed, linear model).

Bottomline, from each subject we will have five (we hope) measurements, a period coding, a sequence coding, and a dose level coding. PROC GLM does the trick and yes we can throw sequence and period into the pot if we wish. We get LSMeans for all five treatment levels or just plain means. No big deal, but it should of course be specified in the protocol which one to use. And if someone makes a big fuss about using LSMeans or worries about imbalance then we just throw a little quote from the SAS manual back at them:
"(...)LS-means are, in effect, within-group means appropriately adjusted for the other effects in the model. More precisely, they estimate the marginal means for a balanced population(...)."

We can even beef the entire thing up with PROC MIXED to allow for intra-subject correlations and issues surrounding dropouts, I guess. In that case we will not have LSMeans but maximum likelihood effects extractable from the model's b-vector.

But having said that, I would also like to say that Dr_Dan's idea of just using three levels (lowest, middle, highest) also appeals a lot to me.

Dear d_labes,

ok then I will try and answer again more directly:

❝ Why do you favour a Williams design (balanced or not) BEman has in mind over a simpler Latin square design as I suggested or a much simpler incomplete block design with less periods than treatments which Helmut suggested as one possibility, which BTW addresses your concern "the risk of dropouts"?

I don't favour anything but practical solutions. There is nothing wrong with your suggestion, as I see it, as long as this does not become a discussion about avoiding imbalance or other stuff.

❝ Why do you think this is a "... big theoretical problem ..."? Because its more unusual and lesser known then what's called Williams design everybody who had some notation of BE studies can spell correctly?

I don't think it is a big theoretical problem; in fact I think the problems in the thread are of a more practical nature.

❝ Why even a cross-over at all if

❝ ❝ much of the info about linearity in current EU SPCs and US Prescr infos are based on simply descriptive stats from designs with parallel groups or xo.

Parallel would require 60 patients and most BE clinics cannot handle that in one go. 12, 16, 18 are typical magic numbers. 5 periods with 12 people is doable at most clinics. Besides, if I recall correctly, it is often cheaper to pay 12 subjects five periods each than to pay 60 subjects one period each. But I could be wrong here, as I often am.

❝ Take 5 groups with 3 subjects each (makes 15 in total ) treat them with the 5 doses and make your assessment of dose linearity via descriptive stats? Is this what you have in mind?

❝ Downright silly if two subjects from the same group drop out .

Thank you for this compliment . We agree. Dropout risks is a worry.
If there's a budget for 15 subjects then that's even better than 12, all other factors equal (no pun intended). Latin, Williams etc is simply not part of my consideration - in the grand scheme of things the whole theoretical discussion about imbalance and such is very low on my list of concerns.
Generate the data as best as you can, analyse them as best as you can. At the time the generic company enters the field they are applying mtethods that are likely to be 10 years newer and 10 times better than the methods applied by the originator and used for writing the SPC and prescr. info anyways. That in itself is also a kind of progress, even when the methodology has certain theoretical drawbacks.