Bioequivalence and Bioavailability Forum

1–2α CI and TOST at α 0.05 [General Statistics]

posted by Helmut – Vienna, Austria, 2017-03-28 01:47 (2580 d 11:09 ago) – Posting: # 17189
Views: 9,002

Hi GM,

❝ If the 90%CI is one side of hundred, i.e. either (85.00-98.00) or (102.00-119.00) then there should be significant treatment effect. Is this statement correct...?

Absolutely.

❝ And why we are generally checking the treatment effect at 5% level of significance...?

The inclusion of a 100(1–2α) confidence interval within the common acceptance range [L, U] of 80–125% is operationally equivalent to Two One-Sided t-Tests (TOST). One t-test is for ≤80% and the other one for ≥125%, both at a level of α 0.05. Null and alternative hypotheses:

Inclusion of the 100(1–2α) CI:

[image]

TOST at α 0.05:

[image]

In BE the Null is inequivalence.

Extreme example:

library(PowerTOST) lower <- 0.80 upper <- 1.25 pe <- sqrt(lower*upper) n <- 24 alpha <- 0.05 CV <- CVfromCI(lower=lower, upper=upper, n=n, alpha=alpha, design="2x2") p <- pvalues.TOST(pe=pe, CV=CV, n=n, design="2x2") cat(sprintf("%g%% %s %.2f–%.2f%%", 100*(1-2*alpha), "CI:", 100*lower, 100*upper), "\n"); print(p) # 90% CI: 80.00–125.00% # p.left p.right # 0.05 0.05

Although the treatment-effect (and its p-value) is part of the standard output of most software packages, it is not relevant for the BE-decision. Statistical significant ≠ clinically relevant…
I don’t know why you are checking it – I don’t.

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

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Science Quotes

Complete thread:

Relationship between calculated 90% CI and sign. treatment effect in BE GM 2017-03-27 19:40
- 1–2α CI and TOST at α 0.05Helmut 2017-03-27 23:47
  - 1–2α CI and TOST at α 0.05 GM 2017-03-28 06:50
    - 1–2α CI and TOST at α 0.05 DavidManteigas 2017-03-28 11:48
      - 1–2α CI and TOST at α 0.05 ElMaestro 2017-03-28 13:12
        
        alpha TOST is not alpha 2-sided d_labes 2017-03-28 15:12
        
        Interesting! ElMaestro 2017-03-28 21:10
        
        Google has the answer d_labes 2017-03-29 08:20
        Interesting! DavidManteigas 2017-03-29 11:16
        
        Interesting! ElMaestro 2017-03-29 11:20
        
        Interesting! DavidManteigas 2017-03-29 12:28
        
        95% CI for a test on difference d_labes 2017-03-29 14:24
        Interesting! GM 2017-03-29 20:06
        
        Interesting! nobody 2017-03-30 08:24
      - Relationship between calculated 90% CI and sign. treatment effect in BE GM 2017-03-29 12:11
        
        Relationship between calculated 90% CI and sign. treatment effect in BE DavidManteigas 2017-03-29 12:30

1–2α CI and TOST at α 0.05 [General Sta­tis­tics]

Complete thread:

1–2α CI and TOST at α 0.05 [General Statistics]