Log in
RegisterOperationally equivalent… [General Statistics]
posted by Helmut 
– Vienna, Austria, 2012-12-11 15:54 (4938 d 18:59 ago) – Posting: # 9711
Views: 10,319
Dear Detlew!
No, I don’t. Only in less than a handful of studies 25 years ago – upon sponsor’s wish (“Hey, that’s new = fashionable and suggested by an FDA guy!”) – I applied TOST, i.e., reported a result like:
When I started in the early 1980s (without knowing any literature at all) I naïvely calculated a two-sided 95% CI. Later I adapted for the 90% CI, though the term “operationally equivalent” to TOST gave me headaches. I wouldn’t go that far calling it just “an algebraic coincidence”1 but I don’t get the point why the straightforward confidence interval inclusion (one H0 and H1)
$$H_0:\frac{\mu_T}{\mu_R}\notin [\theta_1,\theta_2]\;\mathit{vs.}\;H_1:\theta_1<\frac{\mu_T}{\mu_R}<\theta_2$$
should be replaced by a {set} of two Nulls and Alternatives,
$$H_{0L}:\frac{\mu_T}{\mu_R}\leq \theta_1\;{vs.}\;H_{1L}:\frac{\mu_T}{\mu_R}>\theta_1$$
$$H_{0U}:\frac{\mu_T}{\mu_R}\geq \theta_1\;{vs.}\;H_{1U}:\frac{\mu_T}{\mu_R}<\theta_1$$
tested on the same body of data.
For an overview see Berger & Hsu (including comments by Hauck, Anderson, Meredith, Heise, Liu, Chow, Schuirmann, and Hwang).2
❝ ❝ To be honest my brain works two-sided only. […]
❝
❝ One of best justification of a two-sided test/CI ... I have ever seen 
.
❝ And this from a guy which works nearly all the days with TOST.
No, I don’t. Only in less than a handful of studies 25 years ago – upon sponsor’s wish (“Hey, that’s new = fashionable and suggested by an FDA guy!”) – I applied TOST, i.e., reported a result like:
p(<0.8) 0.0014 ʌ p(>1.25) 0.0034 ![[image]](img/uploaded/image28.png)
When I started in the early 1980s (without knowing any literature at all) I naïvely calculated a two-sided 95% CI. Later I adapted for the 90% CI, though the term “operationally equivalent” to TOST gave me headaches. I wouldn’t go that far calling it just “an algebraic coincidence”1 but I don’t get the point why the straightforward confidence interval inclusion (one H0 and H1)
$$H_0:\frac{\mu_T}{\mu_R}\notin [\theta_1,\theta_2]\;\mathit{vs.}\;H_1:\theta_1<\frac{\mu_T}{\mu_R}<\theta_2$$
should be replaced by a {set} of two Nulls and Alternatives,
$$H_{0L}:\frac{\mu_T}{\mu_R}\leq \theta_1\;{vs.}\;H_{1L}:\frac{\mu_T}{\mu_R}>\theta_1$$
$$H_{0U}:\frac{\mu_T}{\mu_R}\geq \theta_1\;{vs.}\;H_{1U}:\frac{\mu_T}{\mu_R}<\theta_1$$
tested on the same body of data.
For an overview see Berger & Hsu (including comments by Hauck, Anderson, Meredith, Heise, Liu, Chow, Schuirmann, and Hwang).2
- 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.
![[image]](https://static.bebac.at/img/free_icon.png)
free resource.
- Berger RL, Hsu JC. Bioequivalence Trials, Intersection–Union Tests and Equivalence Con fidence Sets. Stat Sci. 1996;11(4):283–319. doi:10.1214/ss/1032280304. free resource.
—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!![[image]](https://static.bebac.at/pics/Blue_and_yellow_ribbon_UA.png)
Helmut Schütz
![[image]](https://static.bebac.at/img/CC by.png)
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:
- CV point estimate outside CI d_labes 2012-12-05 12:13
![[Mix]](https://static.bebac.at/img/mix.png "open in Mix view")
- What the heck? Helmut 2012-12-05 18:41
- Code validated d_labes 2012-12-06 09:21
- PE outside its CI?! Helmut 2012-12-06 11:14
- PE outside its CI?! Jack 2012-12-06 13:20
- PE outside its CI?! Helmut 2012-12-07 15:51
- PE outside its CI! d_labes 2012-12-06 15:04
- PE outside its CI! Helmut 2012-12-07 15:40
- PE outside its CI! ElMaestro 2012-12-07 22:40
- CV of log-normal data d_labes 2012-12-09 16:20
- Two-sided brain d_labes 2012-12-10 08:25
- Operationally equivalent…Helmut 2012-12-11 14:54
- Austrian logic? ElMaestro 2012-12-11 15:41
- Fuzzy logic Helmut 2012-12-11 16:12
- PE outside its CI! ElMaestro 2012-12-07 22:40
- PE outside its CI! Helmut 2012-12-07 15:40
- PE outside its CI?! Jack 2012-12-06 13:20
- PE outside its CI?! Helmut 2012-12-06 11:14
- Code validated d_labes 2012-12-06 09:21
- What the heck? Helmut 2012-12-05 18:41
Ing. Helmut Schütz