Bioequivalence and Bioavailability Forum

Hi Jamesmartinn!

❝ […] I'm going to take it upon myself to read up on BA-BE trials, now that I have free time.

Does that mean you didn’t get the job? Maybe not the worst which could happen with a boss asking such questions. Let’s have a look:

❝ The intra-subject variability, expressed as CV% (coefficient of variation) of a measured response is expected to be 35%.

So far, so good. It should be noted that in a conventional 2×2×2 (2 sequence, 2 period, 2 treatment design or TR|RT) CV_intra (aka CV_W) is actually pooled from CV_WR and CV_WT – the within (=intra) subject variabilities of the Test and Reference treatments. We need a replicate design (like the one you mentioned in your first post: TRTR|RTRT) in order to estimate them.

❝ The intra-subject variability is defined as the variability of the response within the same subject from one occasion to another.

Almost. Correct only if the same treatment is administered. Since in a 2×2×2 we cannot estimate CV_WR and CV_WT separately, in the common model we have to assume that they are identical.

❝ The intention is to design a study as a 2-way, crossover, replicate administration of the same treatment to estimate the intra-subject variability.

Oops. This disqualifies your (still potential?) boss. If we administer only the same treatment twice, it’s not a cross-over (I was trapped myself). Although scientifically valid (e.g., RR as ElMaestro assumed above) regulators do not accept such an approach as a ‘proof’ of high variability (USA & Canada: ≥30%, EU: >30%). The only reason we want to show high variability is that the conventional acceptance range for bioequivalence (80–125%) may be widened (or more technical: scaled to s²_WR). Regulators want to see CV>30% demonstrated in the same study (Reference and Test); CV>30% in another study is irrelevant. Why plan a study which will not be accepted?

❝ What will be the appropriate sample size (number of subjects) in order to have at least 80% confidence that the estimated CV% is larger than 30%?

This is weird. Chow & Liu (Chapter 7.3.2; see below) give a method based on χ² – but only for cross-overs. If we assume CV 35% (s²=ln[0.35²+1]=0.11556) and use df=n-1 instead of n₁+n₂-2:
  n  ν   SSE=s²·ν  χ²0.8,ν   SSE/χ²   CLlower
————————————————————————————————————————————
 10   9  1.0400    12.242    0.08495  29.78%
 11  10  1.1556    13.442    0.08597  29.96%
 12  11  1.2711    14.631    0.08688  30.13% bingo?
 13  12  1.3867    15.812    0.08770  30.28%
 14  13  1.5023    16.985    0.08845  30.41%
Take it with a pinch of salt – maybe it’s total crap!

❝ The results of a clinical trial are:

❝

❝ What was the power of the study to detect a 20% difference between treatments?[

What was the study’s target: A vs. placebo, B vs. placebo, A vs. B (including ‘internal validation’, i.e., superiority of A and B against placebo)? As an exercise you can get the weighted variances and calculate the pooled (=total) variance, but IMHO that’s the end of the story. For a power calculation you would need both α and Δ. BTW, retrospective (aka a posteriori, post hoc) power is futile ( search the forum) and should go straight to the statistical garbage bin.

❝ Would you mind recommending one for someone who knows absolutely nothing about the area? For example, defining what Cmax and AUC are and where they come from?

See this post. I would start with Hauschke et al. (2007) and continue with the 3^rd ed. of Chow & Liu (2009). For some background I recommend David Bourne’s online course on Biopharmaceutics and Pharmacokinetics.