## Strange result [Regulatives / Guidelines]

Hi John,

» […] I read some report […] and the one sided 90% CI was reported as lower = -18.33%, upper = -6.36%; T/R Ratio = 93.86, n=24. I found it strange to report CI in such a way so I was wondering if the reporting was based on some old rules.

Strange!

As the name tells, TOST are interval (significance) tests giving two

Coming back to your case. I’ve never seen results reported in such a way.

If we would report the CI as usual we would give (93.86 – 18.33)% = 75.53% and (93.86 – 6.36)% = 87.53% and the study failed (like nobody assumed). But then we have another problem with the reported T/R-ratio which transforms to (93.86 – 100)% = –6.14%. Then –18.33% < –6.14% < –6.36%, or what? Based on 100√0.7553 × 0.8753 we get 81.29% ≠ 93.86%.

Or are the boundaries given relative to 100%? Bizarre. However, then the study would pass since (100 – 18.33)% = 81.67% and (100 – 6.36)% = 93.64%. Note that the reported PE is

» […] (dated 1990; the synopsis only)

Was the study performed for Health Canada? In the 1989 draft 80–120% (untransformed data) were recommended and changed to 80–125% (log-transformed) in 1991.

Then the study would have passed again cause –18.33% > –20% and –6.36% < +20%. However, the problem with the PE persists cause 100(–0.1833 + (–0.0636)) / 2 = –12.35% ≠ –6.14%. I don’t get it.

» […] I read some report […] and the one sided 90% CI was reported as lower = -18.33%, upper = -6.36%; T/R Ratio = 93.86, n=24. I found it strange to report CI in such a way so I was wondering if the reporting was based on some old rules.

Strange!

As the name tells, TOST are interval (significance) tests giving two

*p*-values – one for the 1^{st}(left) test where*H*_{01}: *PE* < ln(1–0.2)

*H*_{11}: *PE* ≥ ln(1–0.2)

^{nd}(right) test where*H*_{02}: *PE* > ln(1+0.2)

*H*_{12}: *PE* ≤ ln(1+0.2).

*both**H*_{01}*and**H*_{02}are rejected at the level α, BE is concluded. In my entire career I haven’t seen a single report where this was done^{1}– though most claim that**TO**ST was applied. The confidence interval inclusion test is*two*-sided (though**OT**ST is difficult to pronounce) and “operationally equivalent” to TOST. Some call that just “an algebraic coincidence”.^{2}There is*no*CI in TOST.^{3}The FDA’s 1992 guidance^{4}mixes both approaches up:`The two one-sided hypotheses at the α = 0.05 level of`

significance should be tested for AUC and C_{max} by con-

structing the 90% confidence interval for the ratio

between the test and reference averages.

Coming back to your case. I’ve never seen results reported in such a way.

If we would report the CI as usual we would give (93.86 – 18.33)% = 75.53% and (93.86 – 6.36)% = 87.53% and the study failed (like nobody assumed). But then we have another problem with the reported T/R-ratio which transforms to (93.86 – 100)% = –6.14%. Then –18.33% < –6.14% < –6.36%, or what? Based on 100√0.7553 × 0.8753 we get 81.29% ≠ 93.86%.

Or are the boundaries given relative to 100%? Bizarre. However, then the study would pass since (100 – 18.33)% = 81.67% and (100 – 6.36)% = 93.64%. Note that the reported PE is

*outside*the CI…» […] (dated 1990; the synopsis only)

Was the study performed for Health Canada? In the 1989 draft 80–120% (untransformed data) were recommended and changed to 80–125% (log-transformed) in 1991.

Then the study would have passed again cause –18.33% > –20% and –6.36% < +20%. However, the problem with the PE persists cause 100(–0.1833 + (–0.0636)) / 2 = –12.35% ≠ –6.14%. I don’t get it.

- I did it myself in a few studies upon sponsor’s wish. In all cases assessors asked for the 90% CI later…

For ages I do it the other way ’round. Describe the confidence interval inclusion approach according to the guidelines and – to make newbies happy – state that it is “operationally equivalent” to TOST.

- Brown LD, Casella G, Hwang JTG.
*Optimal Confidence Sets, Bioequivalence, and the Limaçon of Pascal.*J Amer Statist Assoc. 1995;90(431):880–9. doi:10.1080/01621459.1995.10476587. free resource.

- Schuirmann DJ.
*A comparison of the Two One-Sided Tests Procedure and the Power Approach for Assessing the Equivalence of Average Bioavailability.*J Pharmacokin Biopharm. 1987;15(6):657–80. doi:10.1007/BF01068419.

- FDA/CDER.
*Guidance for Industry. Statistical Procedures for Bioequivalence Studies Using a Standard Two-Treatment Crossover Design.*Jul 1992. Internet Archive.

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- History lessons - FDA BE 90% CI jag009 2019-02-25 22:03 [Regulatives / Guidelines]
- History lessons - FDA BE 90% CI nobody 2019-02-25 22:39
- History lessons - FDA BE 90% CI Helmut 2019-02-26 00:44
- History lessons - FDA BE 90% CI jag009 2019-02-26 15:19
- History lessons - FDA BE 90% CI nobody 2019-02-26 16:07
- Strange resultHelmut 2019-02-28 12:03
- Strange result nobody 2019-03-01 08:50
- Pandora's box? jag009 2019-03-01 17:40
- Confusing Helmut 2019-03-02 15:37

- Pandora's box? jag009 2019-03-01 17:40
- Strange result jag009 2019-03-01 17:44
- Transformation, acceptance range Helmut 2019-03-02 15:09
- Transformation, acceptance range nobody 2019-03-02 16:42

- Transformation, acceptance range Helmut 2019-03-02 15:09

- Strange result nobody 2019-03-01 08:50

- History lessons - FDA BE 90% CI jag009 2019-02-26 15:19

- History lessons - FDA BE 90% CI Helmut 2019-02-26 00:44

- History lessons - FDA BE 90% CI nobody 2019-02-25 22:39