## assumed (!) T/R ratio [Power / Sample Size]

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 nomnal 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

Even if you will perform a content-correction

» […] 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 nomnal 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 **R**(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")

`+++++++++++ 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.- 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.

- 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.

—

All the best,

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼

Science Quotes

All the best,

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼

Science Quotes

### Complete thread:

- T/R ratio and the content of the active compound in each product - CECIF, 2017-10-11 18:18 [Power / Sample Size]
- assumed (!) T/R ratio - Helmut, 2017-10-11 19:18
- assumed (!) T/R ratio - CECIF, 2017-10-11 20:35

- assumed (!) T/R ratio - Helmut, 2017-10-11 19:18