Bioequivalence and Bioavailability Forum

Hi Lucas,

welcome to the forum.

❝ ANVISA […] is now studying the possibility of accepting EMA's method for scaling the BE acceptance interval based on the variability of the reference medication.

Interesting.

❝ So we […] did not manage to reproduce the results of PowerTOST calculations for RSABE. Is a whole different calculus?

Yes, since the method is aggregate (scaling for CV_WR >30% with a 50% cap, ratio with 80–125%) you cannot estimate the sample size directly, but have to use simulations – for some background see the paper* by the two Lászlós. Therefore, PASS (or NQuery Advisor as well) cannot do the job.

❝ […] when I try to calculate a sample size for a full replicate crossover design (TRTR, RTRT) considering a true ratio of 0.95, a target power of 80% and a reference ISCV of 63%, in PASS I got 28 subjects (considering the equivalence limits of 69.84%–143.19%) and in PowerTOST I got 22 subjects.

In PowerTOST (EMA’s method) you have to use the function sampleN.scABEL(), not sampleN.TOST() with the scaled acceptance range.

require(PowerTOST)
sampleN.scABEL(theta0=0.95, CV=0.63, targetpower=0.8, design="2x2x4")
+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
---------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.63; CVw(R) = 0.63
Null (true) ratio = 0.95
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: EMA
- CVswitch =  0.3, cap on ABEL if CVw(R) > 0.5
- Regulatory constant = 0.76

Sample size search
 n    power
22   0.7312
24   0.7773
26   0.8167

László’s Table A2 gives for CV_WR 65% a sample size of 28.
HVDs/HVDPs are also nasty when it comes to the ratio. I would not suggest to assume a ratio of 95% (it jumps around between studies like crazy). I generally use 90%, which in your case would mean 34 sub­jects.

❝ Should I throw away my PASS?

When it comes to reference-scaling, yes.

PS: Where does your 63% come from? If you have done a fully replicated pilot study (RTRT|TRTR or just three periods RTR|TRT) calculate CV_WT as well. Sometimes the reference is an awful product and the test is substantially better. You’ll get a reward for that (the CI will be narrower). In PowerTOST you can give both CVs as a vector (test’s first). Let’s say CV_WT 45% and CV_WR 63%.

sampleN.scABEL(theta0=0.95, CV=c(0.45, 0.63), targetpower=0.8, design="2x2x4")
+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
---------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.45; CVw(R) = 0.63
Null (true) ratio = 0.95
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: EMA
- CVswitch =  0.3, cap on ABEL if CVw(R) > 0.5
- Regulatory constant = 0.76

Sample size search
 n    power
16   0.6787
18   0.7496
20   0.8038

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• Tóthfalusi L, Endrényi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs J Pharm Pharmaceut Sci. 2011; 15(1): 73–84. online

Hi Lucas!

❝ ANVISA (Brazil's regulatory agency) is now studying the possibility of accepting EMA's method for scaling the BE acceptance interval based on the variability of the reference medication.

Fine for you. That minimizes the burden for you in case of HVD/HVDP.

❝ So we are struggling a little bit in the sample size calculation, since it is very new to us. We have always used PASS for sample size calculation, for the standard BE studies, and did not manage to reproduce the results of PowerTOST calculations for RSABE. Is a whole different calculus? For example, when I try to calculate a sample size for a full replicate crossover design (TRTR, RTRT) considering a true ratio of 0.95, a target power of 80% and a reference ISCV of 63%, in PASS I got 28 subjects (considering the equivalence limits of 69.84%-143.19%) and in PowerTOST I got 22 subjects.

Unfortunately I can't reproduce your numbers. Could you please post the code (function calls) you have use with PowerTOST?

You are right in guessing that PowerTOST and PASS uses different calculus.
In case of 'usual' power for replicate studies the difference is that PowerTOST uses by default exact calculation of the power via Owen's Q-function. PASS uses here an approximation via shifted central t-distribution. For the 2x2x4 design the PASS calculations are moreover based on a model including carry-over. In today's time no one will use such an model.

For reference scaled ABE PASS don't has a module AFAIK. At least the versions I have seen so far.

The use of the usual power calculation with simply plugging in the widened BE acceptance ranges from the EMA guidance is only a very rough approximation to the problem.

The respective functions in PowerTOST dealing with scaled ABE (sampleN.scABEL() for the EMA approach, sampleN.RSABE() for the FDA) tackle the problem by an other way: power calculation via simulations. See the PDF "Implementation details of the power calculations via simulations for scaled ABE" in the doc sub-directory of the R-package for more details.

Moreover I highly recommend you the search function of the forum. We had some discussions here concerning that problem.

❝ Should I throw away my PASS?

When it comes to reference-scaling, yes.
When it comes to replicate designs, also yes if you are interested in an exact solution.

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Ups. Helmut was faster than me, as always .