Bioequivalence and Bioavailability Forum

Dear Yung-jin,

❝ Guess many other colleagues are looking for the answers of your QUESTION now. I don't know if I can really help here. But allow me to try first.

Thanx.

❝ To calculate intra-individual variabilities and means seems not a problem for the guy like you.

Of course not . One part of the output of the Proc MIXED code contains the intra-subject variabilities for Test and Reference and the between-subject variability also. They have therefore what they request.
But it seems they do not belief in the results of the REML estimates from that Proc MIXED
That's where my confusion comes from. And means make no sense within the category if intra-subject variance.

❝ Or see Hauschke D., et al., "Bioequivalence Studies in Drug Development - Methods and Applications", 2007, pp. 258-9.

Cannot find anything about intra-subject variabilities on that pages.

❝ [...] [BTW, where to get it? Is this drug2-replicate program (SAS macros) freely available?]

Sorry. But its the property of the company I am working in.

Old Sailor and Pirate!

❝ Separate tables with descriptive stats (mean, median, sd, min, max, sem) for:

❝ T-T in TRTR and RTRT

❝ R-R in TRTR and RTRT

❝ ...and then a table or the pooled stuff at the end.

Is it because an Old pirate always knows from where the wind blows?
Or had you also such a question in your career?

Thanks for acknowledging my own guess.
I must say my second thought.

First I guessed they would have a 'conventional' evaluation ignoring the replicate nature (same as for a 2x2 cross-over). But this seemed too silly.

Now I will go with intra-individual variability calculated from the contrasts T-T or R-R. This is sometimes called "Method of moments" (MoM) I think.
But looking on the formulas in Chapter 9.4 of Chow, Liu "Design and analysis of bioavailability and bioequivalence studies" I cannot see why they call this simple .
All the stuff in calculation stratified over sequence groups to account for the different period effects in the contrasts ... My implementation in SAS is currently getting longer and longer compared to the approximate 6-8 lines with Proc MIXED.

And if our guess is what the assessor wants to see the question remains why.
The MoM estimation is only another estimation method with its pros and cons.
Just to cite Patterson and Jones¹⁾: "Variance estimates are of less concern in ABE testing, but in alternative criteria where estimates are important to interpretation (i.e., for IBE and PBE) method-of-moments estimates should be viewed cautiously. Method-of-moment estimation, as expected, yields unbiased estimates in complete data sets, but results in positively biased sigma²_D in some sample with missing data. Bias in method-of-moment sigma²_D (with certain patterns of missing data) and constrained REML procedures increases as drugs become more highly variable and decreases with increasing sample size..."
(sigma²_D is the subject by treatment interaction term)

Is the Proc MIXED result with REML estimates to complicated to understand?
Or why do they not trust them?
Or is it because the French do not love Americans?
Of course I know that one cannot ask why an regulator has a question.
But maybe I overlooked something here.

BTW: Why did you suggest all the summary statistics above? The only relevant is the variance I think, because it is well known that T-T or R-R have the expectation 2*sigma²_within for test or reference.

1) Patterson, Jones
"Replicated Designs and Average, Individual, and Population Bioequivalence"
GlaxoSmithKline BDS Technical Report 2002-05, 11 December 2002, page 55

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Edit: Online resource added. [Helmut]