mittyri
★★

Russia,
2014-03-20 20:55

Posting: # 12681
Views: 5,946

FDC Power [Power / Sample Size]

Dear All,

I would like to discuss some issues in FDC studies design.
For examle, we have FDC with 2 APIs. Let's say we know that no PK interaction is expected and the intraCVs in the pilot study were similar to the single dosage forms.
If we calculate the sample size for the first API (ABC) and the second API (XYZ) with a power 80%, we'll get some values.
So... We have only 80% of probability to prove BEQ for ABC (20% of II type error) and 80% for XYZ.
Final probability is 80%*80%=64%!
Should we use another power for calculations (89%*89%=80%)?

Can someone correct or comment my statistical calculations?

Kind regards,
Mittyri
Helmut
★★★

Vienna, Austria,
2014-03-20 21:49

@ mittyri
Posting: # 12682
Views: 5,150

FDC Power

Hi Mittyri,

» I would like to discuss some issues in FDC studies design.
» So... We have only 80% of probability to prove BEQ for ABC (20% of II type error) and 80% for XYZ.
» Final probability is 80%*80%=64%!
» Should we use another power for calculations (89%*89%=80%)?

You are thinking into the right direction. See also this thread. The question is: Are the two tests independent?

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
mittyri
★★

Russia,
2014-03-26 19:47

@ Helmut
Posting: # 12719
Views: 5,005

FDC Power

Hi Helmut,

» The question is: Are the two tests independent?

I think two tests aren't independent. Let's say we calculated the II type errors for both APIs, ABC and XYZ - 15% and 20% accordingly.
There is an information that API XYZ is bioequivalent. What is the likelihood of the bioequvalence for ABC? I think more than 85%.

In such a circumstance should I use Bonferroni-correction? (according to the CPMP’s ’Points to Consider on Multiplicity Issues in Clinical Trials’)

By the way I cannot find a prime example in EPAR where both APIs would have same ISV. Isn't it a keypoint? See below...

In this case (Irbesartan/Hydrochlorothiazide) Irbesartan and Hydrochlorothiazide had ISVs 20.13% and 15.31% accordingly.
The requiring sample size for Irbesartan (with Ratio 92%) is calculated as 27=>28 (the power 81.85%, II type error 18.15%). With 28 subjects the power for Hydrochlorothiazide is 95.54%, (II type error 4.46%). So overall power would be 77.39%...

Kind regards,
Mittyri
d_labes
★★★

Berlin, Germany,
2014-03-27 08:47

@ mittyri
Posting: # 12723
Views: 4,997

Power for Testing Multiple Instances of TOST

Dear mittyri,

have a look at:

Kem Philips
"Power for Testing Multiple Instances of the Two One-sided Tests Procedure"
The International Journal of Biostatistics
Band 5, Heft 1, ISSN (Online) 1557-4679, DOI: 10.2202/1557-4679.1169, May 2009

Contains R-code to play with, but unfortunately only for 2 instances of TOST.
Eventually this helps, at least for FDC with two active moieties and one PK metric only .

As Helmut already pointed out, the power of the combined TOST's depends crucial on the assumptions about independence of the tests instances aka correlation of the data. Just to cite from the abstract of the paper:
"The power of testing two or more equivalence hypotheses simultaneously is less than the power to test any one hypothesis separately, and depends on the correlations of the measurements."

Regards,

Detlew
fno
☆

Belgium,
2014-03-27 11:59

@ mittyri
Posting: # 12725
Views: 4,993

FDC Power

Dear Mittiry,

The results of both compounds are certainly not fully independent, but considering them as such allows to remain on the most conservative side for the sake of sample size estimation.

Most of the time, the counterpart to pay (additional subjects to include to account for duplicity) is not so high.

Taking the post-hoc estimates of the Irbesartan/Hydrochlorothiazide example you shared, the sample size is driven by irbesartan (higher variability and ratio more deviating from unity than hydrochlorothiazide):

Ratio=1.0793, GCV=0.2013, (25 =>) 26 subjects to reach a power of 80%: actual power = 82.6%.

For hydrochlorothiazide (ratio=0.9534 and GCV=0.1531), power = 99.2% with 26 subjects.

So assuming independence, the combined power with N=26 = 0.826 * 0.992 = 81.9%
=> no need to include any additional subject to adjust for the multiplicity issue.

The impact would become more relevant if both compounds have a ratio far from unity and/or high variability.
For instance, for a ratio of 0.85 and a GCV of 0.3, you would need 292 subjects to reach a power of 80% to demonstrate the classical (single-compound) bioequivalence, but (395 =>) 396 subjects (104 additional subjects) for the combined bioequivalence.
Anyway, we are here quite far away from realistic BE scenarios

Kind regards,
Fabrice
d_labes
★★★

Berlin, Germany,
2014-03-27 13:27

@ fno
Posting: # 12727
Views: 4,958

FDC Power

Dear Fabrice,

» The impact would become more relevant if both compounds have a ratio far from unity and/or high variability.

The impact is also relevant if you don't think extremes. Lets assume CV=0.2 for both ingredients and GMR=0.95 also for both. That gives:
Sample size n=20 with actual power = 0.834680 for each. That lets to an overall power (assuming independence) of only 0.6966907 ~ 70%.

We have to plan for a power of 90% to assure overall power around 80%, which gives n=26, a 30% increase. Not so small IMHO.

Regards,

Detlew
fno
☆

Belgium,
2014-03-27 15:41

@ d_labes
Posting: # 12730
Views: 4,952

FDC Power

Dear Detlew,

» The impact is also relevant if you don't think extremes.

I fully agree with you that the loss of power due to multiplicity should not be neglected, even in less extreme scenarios.
What I meant is that, in a usual (i.e. not too extreme) BE context, the absolute price (€ or \$) to pay is not that high.

» We have to plan for a power of 90% to assure overall power around 80%, which gives n=26, a 30% increase. Not so small IMHO.

According to my calculation (SAS Proc Power), 24 subjects would be enough:
"single" power = 89.7% => "combined" power = 81.9%.
Moreover, just to nuance the impact of double testing on the sample size: in the design of a classical single-product BE study, increasing from 20 to 24 subjects would correspond to consider a CV of 23% instead of 20%.

Kind regards,
Fabrice