Bioequivalence and Bioavailability Forum

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...

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 n_i 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 n_i, 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.

❝ 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

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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]