Bioequivalence and Bioavailability Forum

Flaw in the GL? [Software]

posted by d_labes  – Berlin, Germany, 2013-01-08 12:44 (4502 d 19:16 ago) – Posting: # 9798
Views: 12,525

Dear Helmut,

❝ ... Transforms definitely into (II).

In contrast to you I'm not quite sure.

It is explicitly stated that way (< and not ≤) in

Hauschke, Steinijans, Pigeot
"Bioequivalence Studies in Drug Development"
Wiley, Chichester, 2007, page 90

... but I have 2 other minority reports for you (proof/evidence by authority: "Well, Lieschen Mueller says it's true, so it must be." )

Westlake, W.J.
"Symmetrical Confidence Intervals for Bioequivalence Trials"
Biometrics, 32, p 741-744 (1976)

stating the confidence interval inclusion rule explicitly with ≤ and

Diletti et.al.
"Sample size determination for bioequivalence assessment by means of confidence intervals"
Int. J. Clin. Pharm., Ther. and Tox., Vol.30, Supl. 1, p. S51-58 (192)

stating the two one-sided tests explicitly as
t1=(mT-mR-ln(Θ1))/(sD*sqrt(2/n)) ≥ t(1-α,df)
t2=(mT-mR-ln(Θ2))/(sD*sqrt(2/n)) ≤ -t(1-α,df)

Other papers state the interval inclusion rule as
I ⊂ (Θ1,Θ2)
subset sign: an U rotated 90° clockwise
where I is an appropriate confidence interval. I as an amateur are not able to figure out what is meant: The meaning A⊆B, when A is called a subset of B; A can be equal to B (i.e. borders included). Or A⊂B, then A is called a proper subset of B; A cannot equal B (i.e. at least one border excluded).
That time the "Theory of sets" was dealt with I have skipped school .

This is only an incomplete selection of findings which led to my uncertainness. As stated above: Using real numbers (not rounded) it will not make much a difference how we implement it, thus we can't empirical test it via simulations.
Any pro-statistician out there to enlighten this issue?

Complete thread:

• Rounding Helmut 2013-01-01 16:51 [Software] 
  • Rounding d_labes 2013-01-02 12:51
    • Rounding Helmut 2013-01-04 17:35
      • Rounding d_labes 2013-01-05 19:25
        • Rounding Helmut 2013-01-05 20:13
          • Sim’s are sim’s are sim’s d_labes 2013-01-05 20:57
        • Another vicious circle Helmut 2013-01-06 02:21
          • Where all these numbers came from? d_labes 2013-01-07 15:52
            • Flaw in the GL? Helmut 2013-01-07 17:29
              • Flaw in the GL?d_labes 2013-01-08 11:44
                • What a mess! Helmut 2013-01-08 19:08
                  • What a mess! d_labes 2013-01-09 10:33
                    • What a mess! Helmut 2013-01-09 15:18
  • Rounding ElMaestro 2013-01-02 16:12
    • Abandon rounding Helmut 2013-01-02 17:04
  • Rounding yjlee168 2013-01-05 23:15
    • Rounding Helmut 2013-01-06 03:29
    • Rounding Helmut 2013-01-06 15:34
      • Rounding yjlee168 2013-01-06 23:38