# Bioequivalence and Bioavailability Forum

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Yura
Regular

Belarus,
2017-01-17 08:30

Posting: # 16963
Views: 4,531

## The formula of a CI for TRR|RTR|RRT [RSABE / ABEL]

Dear all
For calculation of a confidence interval of a difference of test and reference pharmaceuticals for two sequences (RT|TR) the formula is used:

What formula is used for calculation of a confidence interval of a difference of test and reference pharmaceuticals for three sequences (TRR|RTR|RRT)?
Kindest regards
BE-proff
Senior

Russia,
2017-01-17 11:33

@ Yura
Posting: # 16965
Views: 4,102

## The formula of a CI for TRR|RTR|RRT

Hi Yura,

Certainly I am not an expert in math but it seems that your formula uses arithmetic means while BE operates with geometric means...
Yura
Regular

Belarus,
2017-01-17 13:13

@ BE-proff
Posting: # 16966
Views: 4,028

## The formula of a CI for TRR|RTR|RRT

It is clear that log transformation becomes.
I'm interested in the boundaries of the interval.
d_labes
Hero

Berlin, Germany,
2017-01-18 13:36

@ BE-proff
Posting: # 16974
Views: 3,928

## Geometric, Arithmetic, Harmonic, Disharmonic …

Dear BE-proff!

» Certainly I am not an expert in math ...

Whereof one cannot speak,
thereof one must be silent.
Ludwig Wittgenstein

SCRN.

Regards,

Detlew
d_labes
Hero

Berlin, Germany,
2017-01-18 13:30

@ Yura
Posting: # 16973
Views: 4,049

## The formula of a CI for TRR|RTR|RRT

Dear Yura!

» For calculation of a confidence interval of a difference of test and reference pharmaceuticals for two sequences (RT|TR) the formula is used:
»

what you have delivered here is not the formula for a 2x2 design , but the formula for a parallel group design with 2 groups.

Replace σ2 with 0.5*σ2 and you get the correct formula.

» What formula is used for calculation of a confidence interval of a difference of test and reference pharmaceuticals for three sequences (TRR|RTR|RRT)?

The formula for the partial replicate is very similar to the above formula:
Replace σ2 with (1/6)σ2 and use (1/n1+1/n2+1/n3) under the square-root and you got it . The ni are the number of subjects in the 3 sequence groups.

Check out the function CI.BE() in package PowerTOST which can do the calculations for you. Given you have the ni, the point estimate in the original scale (i.e. sloppy spoken the GMR) and the residual CV.

The formula for (TRR|RTR|RRT) clearly depends on the statistical model. I gave you the one which is obtained if the same model for replicate studies is used as in case of a 2x2 crossover: all effects fixed, data without missings. That way is what the EMA wants us to go.
A mixed model analysis is a different cattle of fish .

Moreover I strongly recommend not to use an explicit formula for the CI but let the software do that job. Most if not all statistical software has tools for that. For instance `estimate` statement in SAS `Proc GLM` or `confint()` function in `R` just to name two of them. Doing so circumvents all the bells and whistles with missing data, un-balancedness and so on.

Hope this helps.

Regards,

Detlew
Yura
Regular

Belarus,
2017-01-19 04:43

@ d_labes
Posting: # 16976
Views: 3,814

## The formula of a CI for TRR|RTR|RRT

Dear d_labes
thank you very much
opened their eyes
Regards
Mahmoud
Junior

Jordan,
2017-01-19 06:01

@ Yura
Posting: # 16977
Views: 3,825

## The formula of a CI for TRR|RTR|RRT

» What formula is used for calculation of a confidence interval of a difference of test and reference pharmaceuticals for three sequences (TRR|RTR|RRT)?

Dear Sir
=====

Lower= EXP(Mean(T)-Mean(R)-SQRT(var(intra)*1/6(1/n1+1/n2+1/n3)))

Upper= EXP(Mean(T)-Mean(R)+ SQRT(var(intra)*1/6(1/n1+1/n2+1/n3)))

Mahmoud Abdel-Mohsen Ph.D

Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5! [Helmut]
Yura
Regular

Belarus,
2017-01-19 07:16

@ Mahmoud
Posting: # 16978
Views: 3,793

Dear Mahmoud
Where tst?
Mahmoud
Junior

Jordan,
2017-01-19 07:55

@ Yura
Posting: # 16979
Views: 3,784

## The formula of a CI for TRR|RTR|RRT

» Where tst?

Dear Sir
=====
This is the exact formula for find the CIs for this design
Yura
Regular

Belarus,
2017-01-20 05:28

@ Mahmoud
Posting: # 16984
Views: 3,673

## The formula of a CI for TRR|RTR|RRT

Dear Mahmoud
Using a formula in an example of the working group of EMA, results don't turn out.
Regards
Mahmoud
Junior

Jordan,
2017-01-20 08:11

@ Yura
Posting: # 16986
Views: 3,709

## The formula of a CI for TRR|RTR|RRT

Dear Sir
=====

Lower= EXP(Mean(T)-Mean(R)- t(.05,2(n1+n2+n3)-3)*SQRT(var(intra)*1/6(1/n1+1/n2+1/n3)))

Upper= EXP(Mean(T)-Mean(R)+ t(.05,2(n1+n2+n3)-3)*SQRT(var(intra)*1/6(1/n1+1/n2+1/n3)))

Yesterday I even deleted a post of yours which contained only a lengthy quote of yourself (i.e., without any additional text). First warning posted on the 16th. Since you repeatedly did not follow the Forum’s Policy, I blocked your account for three weeks. [Helmut]
Yura
Regular

Belarus,
2017-01-20 10:33

@ Mahmoud
Posting: # 16988
Views: 3,659

## The formula of a CI for TRR|RTR|RRT

Dear Mahmoud
now yes
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