## Confidence Interval [General Sta­tis­tics]

Dear MGR!

❝ According to the guidelines the 90% Confidence Interval are 80-125%, my doubt is how

they fixed these limits.

  ^^^^ who?

❝ Is there any references or websites regarding this?

Oh my goodness, you want me digging out the real old ones…
There are some rumors (sometimes quoted by Leslie Z. Benet) that the 20% originated in an internal survey at the FDA about the acceptable difference – but nobody ever come up with a reference.
Another rumor (the one I like personally, because it gives a nice impression about the atmosphere of the late 1970s) is this one:
Wilfred J Westlake (a statistician at Smith, Kline & French Labs in Philadelphia and one of the ‘fathers’ of BE testing) once went out of his office and asked some of his friends in the department of clinical pharmacology:

‘What do you think would be an acceptable difference between test and reference in a comparative bioavailability study?’

… And the 20% were born. Also note he questioned about a ‘difference’, since in the early days thinking about (or believing in?) normal distributed data was the rule.

❝ And in genral if it is 100% if we fix a 20% deviation then the limits become 80-120% (is it correct?)

Yes, if you want to stay with the rules of the 1980s.

❝ If so then why the limits has taken as 80-125%?

In the first Bio-International (Toronto 1989) there was a survey on the application of log-transformation in bioequivalence.
⅓ of participants opted for “never” (=acceptance range 80%-120%), ⅓ for “always” (AR 80%–125%), and ⅓ for data-driven decisions (normality testing).
If we are dealing with biological variables, log-normal distribution is the rule (just search the forum, or have a look at this post) – and the statistical model is multiplicate rather than additive. In the log scale the acceptance range is symmetrical around zero [ln(0.8)=-0.2231, ln(1.25)=+0.2231]. Just think about the way we talk:

Q: What’s the opposite of ‘one half’ of something?
A: ‘Twice’ of something.

Or in more mathematical terms: 1/½=2.
Once we have accepted the lower limit as 100%–20% = 0.80, the upper limit is 1/0.80=1.25.
Of course this is a convention. There was a – just minor – debate in the mid 1980s why we are not using 100%+20%, and a lower limit of 1/1.20=0.83, but empirically the limits of 80%–125% right now are established for many years without any reported failures in clinical practice.

If you are in doubt which model to use, just listen to the way we talk.
Everybody would say ‘The maximum concentration is ~85% of the reference!’ and not ‘… 37.4 ng/mL lower!’ – that's a multiplicate statement (→ transform your data).
On the other hand we would say ‘The time of the peak occurred one hour later.’ – that’s an additive statement (→ no transformation).

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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