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[Helmut Schütz]

Dear all,

now for the second part. According to FDA's data ~one third of drugs/drug products are highly variable, i.e., show an intra-subject CV of >30%. Although not covered in FDA's general and statistical guidance on BE, in the last couple of years FDA published API-specific guidances allowing the application of RSABE (Reference Scaled Average Bioequivalence). In these guidances FDA refers to a paper by
Haidar et al.
Bioequivalence Approaches for Highly Variable Drugs and Drug Products
Pharm. Res. 25:237-241(2008).

But I will concentrate on the European GL here. If no safety reasons come into play, EMA allows widening of the conventional acceptance range (AR) of 80%-125% (C_max only), if CV_intra >30% of the reference was demonstrated in a replicate design study. The method is called ABEL (Average Bioequivalence with Expanding Limits). For details see:
Tothfalusi L, Endrenyi L and A Garcia Arieta
Evaluation of Bioequivalence for Highly Variable Drugs with Scaled Average Bioequivalence
Clin Pharmacokinet 48/11, 725-743 (2009)
online resource
The GL allows for widening of AR based on the reference; starting at CV=30% and limited to CV=50% (i.e., if the reference procuct shows a CV of >50%, the maximum AR for CV=50 is applied). Like in the US, an additional constraint is set on the GMR (within 80-125%).
The method consists of following steps:
The regulatory standardized variation sigma₀ is calculated according to sqrt(log(0.3)²+1). Use the value in full precison (not 0.294!). The scaling factor theta_S=log(1.25)/sigma₀. Again, use full precison (not 0.760).
The scaled AR [L, U] is calculated according to:
L, U = exp(±theta_S*sqrt(log(CV_WR²+1))), where CV_WR is the intra-subject CV of the reference formulation.
Example: at CV 40%, the scaled AR is [74.61%,134.02%] and at 50% [69.83%,143.20%].

Now fire up Phoenix, import Data 2x4.CSV. BE as usual, reference = Capsule (imagine AUClast = C_max, because no scaling for AUC in the EU...).
I got (PHX 6.1 on XP Pro SP3):

Failed to show average bioequivalence for confidence=90.00 and percent=20.0.

Rounding to two decimal places (91.61, 125.78) would be nice - but that's another story. Close shave, but not BE.
Ratio within of 80%-125%, so let's see whether the study qualifies for scaling. If I understood the manual, the variance of test and reference are

Var(Period*Formulation*Subject)_21     0.167256
Var(Period*Formulation*Subject)_22     0.191084

CV_WR 45.89% (pocket calculator - no output from PHX/WNL). Scaled AR [U, L] is 71.73%, 139.41%. Now we are easily BE.

If you want a nice output, you could enter in the Options tab at 'Percent of Reference to Detect' 1-L (that's 28.2710725), but PHX/WNL only accept two decimal places! Caution: if you paste the value from somewhere, it is truncated, not rounded (25.009 ends up as 25.00).
@Pharsight: Calls for a fix!

At 'Anderson-Hauck Lower and Upper Limit' enter 0.717289275, 1.394137672 (here full precison is possible). Update, and:

Average bioequivalence shown for confidence=90.00 and percent=28.3.

Anybody out there to write a routine for the workflow?

BTW: Sometimes it's clear from a replicate study that neither test nor reference are highly variable. In such a case (lower blood loss, fewer drop outs, etc.) it may make sense to continue with conventional 2×2 studies. Since the conventional model assumes IDD, we would need a (pooled?) CV_intra for sample size estimation – any ideas how to get the value? Naïvely I would say it's sqrt(log((sigma_WR+sigma_WT)/2)+1), but is that correct?