CECIF
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Colombia,
2017-10-11 20:18
(2182 d 22:16 ago)

Posting: # 17887
Views: 4,777

## T/R ratio and the content of the active compound in each product [Power / Sample Size]

Hello,
I have been following the tutorial in biostatistics by SA Julious (2004, DOI:10.1002/sim.1783). There, he mentions that it is possible to expect a priory a T/R ratio different to the unity (in a extent 0.8 to 1.20). However it is not clear to me, what criteria or in which cases can I assume an apriori ratio as big as 0.8 or 1.20, if knowingly I am trying to demonstrate bioequivalence and then I should be expecting a T/R ratio of 1.00.

In a particular case I happen to have a test product with content of the active compound that is above 110% of the content of the reference product. Could this product be evaluated for bioequivalence, by designing a study with an apriori T/R ratio of 1.10?

Edit: Category changed; I think this one fits better (was “Design Issues”). [Helmut]
Helmut
★★★  Vienna, Austria,
2017-10-11 21:18
(2182 d 21:16 ago)

@ CECIF
Posting: # 17888
Views: 3,925

## assumed (!) T/R ratio

Hi CECIF,

❝ […] it is possible to expect a priory a T/R ratio different to the unity (in a extent 0.8 to 1.20).

Sure. Note that in BE we are using a multiplicative model (or an additive on log-transformed data). Hence, a maximum accepted Δ of 20% translates into a BE-range of 0.80–1.25 in the raw domain (not 0.80–1.20).

❝ However it is not clear to me, what criteria or in which cases can I assume an apriori ratio as big as 0.8 or 1.20, if knowingly I am trying to demonstrate bioequivalence and then I should be expecting a T/R ratio of 1.00.

If you would expect a T/R-ratio exactly at one of the BE-boundaries, power would equal the Type I Error – which is the nominal level of the test or lower.
Anything else within the BE-range is fine, although T/R-ratios deviating a lot from unity could require extremely large sample sizes.

❝ In a particular case I happen to have a test product with content of the active compound that is above 110% of the content of the reference product.

I would try to get a batch of the reference which is closer to the test. F.i., according to the EMA’s BE-GL contents should not differ more than 5%. Only if you could prove (!) that it was impossible to find a better matching batch, a content correction is acceptable if stated in the protocol.

❝ Could this product be evaluated for bioequivalence, by designing a study with an apriori T/R ratio of 1.10?

In principle, yes. But think twice before going there. I suggest to get the package PowerTOST for the statistical system (open source). Then you can perform all needed estimations yourself. Example:

library(PowerTOST) sampleN.TOST(CV=0.2, theta0=1.10, targetpower=0.8, design="2x2")

Gives

+++++++++++ Equivalence test - TOST +++++++++++             Sample size estimation ----------------------------------------------- Study design:  2x2 crossover log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.8 ... 1.25 True ratio = 1.1,  CV = 0.2 Sample size (total)  n     power 32   0.810068

Even if you will perform a content-correction don’t assume a T/R-ratio of 1.
1. No analytical method is perfectly accurate and precise. Ask your analysts and you will be surprised. A method with an inaccuracy if 2% is already excellent.
2. The method was validated for the test. You can only hope that it “works” equally good for the reference. Asking the originator for the CoA of the batch is futile. Dif-tor heh smusma 🖖🏼 Довге життя Україна! Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮
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CECIF
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Colombia,
2017-10-11 22:35
(2182 d 20:00 ago)

@ Helmut
Posting: # 17889
Views: 3,901

## assumed (!) T/R ratio

Thank you very much.  Ing. Helmut Schütz 