Bioequivalence and Bioavailability Forum

❝ My questions are: (1) is it necessary to do so? regulatory or statistical basis? and (2) if yes, what 90% CIs will you recommend (Anderson-Huack's, Westlake's, Locke' exact CI, Fixed Fieller's, Mandallaz-Mau's, etc.)? Thanks.

Hi,
In a sense, the basis is empirical. It seems to work well, that's pretty much the present reason behind it. The standard way is the classic (shortest) CI. Look it up in Chow & Liu's book (Ch. 4.2.1 in the 2000 version).
When regulators have 5 minutes to assess a BE dossier then the CI is the primary thing they look at (very often 5 minutes is a reality, for reasons that go beyond the scope of this question). The anova test for treatment effect is neglected; obviously it is not problematic per se if two formulations are different. It is only problematic if they are different in a clinically significant way, and that is what the CI empirically addresses.

So I think the answer to (1) is yes, a CI is necessary, and (2) shortest.

EM.

Dear Yung-yin

❝ [...] Usually, we talk about 90% CIs in data analysis of a BE study, but we do not mention what 90% CIs we calculate.

This is partly due to the fact that we implicitly assume that we talk about classical confidence intervals and therefore there is no need to mention the sort of variation by their name.

❝ to add various 90% confidence interval (CI) calculations into bear for R.

❝ My questions are: (1) is it necessary to do so? regulatory or statistical basis? and (2) if yes, what 90% CIs will you recommend (Anderson-Hauck's, Westlake's, Locke' exact CI, Fixed Fieller's, Mandallaz-Mau's, etc.)?

As always it depends. On the purpose which bear shall be used for.

Is it a tool for evaluation of ABE studies which have to be submitted to regulatory authorities?
Then my recommendation is:
(1) It is not necessary to implement some sort of other CI's.
To borrow a sentence of Helmut (I hope with his permission): There can only be one!

Imagine some variants of other CIs implemented and all used and submitted by "naive" users (and, without bothering someone personally, there are such out there, too on this forum ).
  Method1 -> bioequivalent
  Method2 -> not bioequivalent
  Method3 -> bioequivalent
and so on. What do you think about regulator's view of that?
Especially if they take five minutes as ElMaestro mentioned. Although I think the right time span is in mathematically notation < 5 min .

Since the standard method is the classical CI, leave it as is.
If mentioned at all guidelines recommend this approach.

There is one exception: If you are not willing to assume a log-normal distribution for a specific pharmacokinetic target but rather a normal distribution (and this can be a reasonable strategy for such metrics as HVD, Swing, PTF or others), but need the CI for the ratio, the Locke/Fieller CI for the untransformed values may be helpful.
But I have not seen many cases where such PK metrics are used as primary targets with the need of calculating a CI as BE test.

But if bear is a tool for academic interest, implement other CIs for educational purposes. Most of your mentioned variants under (2) of your question are historical milestones in BE testing and certainly have interest in education. Which to implement you, as university staff, know better then I.

Dear Yung-jin,

I agree with ElMaestro. BTW, Westlake’s CI should never be used and thrown into the statistical garbage collection because it obscures information about the location of the difference (I have not the slightest idea why it’s still used in WinNonlin).
Example from a study with low variability (CV_intra 8.63%, n=12):

Shortest CI:   100.54% – 113.52% (PE 106.84%)
Westlake’s CI:  88.06% – 111.94%

According to the original paper of Westlake* the CI would be stated as ±11.94%… You have no clue that the BA of the test formulation is statistically significant (though not clinically relevant) higher than the reference’s.

---

• Westlake WJ. Symmetrical Confidence Intervals for Bioequivalence Trials. Biometrics. 1976;32(4):741–4. doi:10.2307/2529259.