## Strange result [Regulatives / Guidelines]

Hi John,

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

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*🖖🏼 Довге життя Україна!_{}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