Bioequivalence and Bioavailability Forum

Hi komodo & balakotu,

❝ […] it will require semi or fully replicate design but to decide it better to perform a pilot study with 18 sub at least to have a meaningful results. as per literature sources ISCV >30%

>30% is correct; see this post: C_max ~200%, AUC ~300%!
Applying the EMA’s ABEL-method for C_max, CV 200%, GMR 0.90, power 80%, 4-period full replicate:

library(PowerTOST)
sampleN.scABEL(CV=2, theta0=0.9, targetpower=0.8,
               design="2x2x4", details=FALSE)

+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
---------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 2; CVw(R) = 2
Null (true) ratio = 0.9
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: EMA

Sample size
 n     power
156   0.8001

In Europe generally it is not acceptable to scale AUC. That would mean for a CV of 300%:

sampleN.TOST(CV=3, theta0=0.9, targetpower=0.8,
             design="2x2x4", details=FALSE)

+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  2x2x4 replicate crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.9,  CV = 3

Sample size (total)
 n     power
1028   0.800468

However, the MR-GL does allow reference-scaling for partial AUCs. I would not dare to walk that road without a scientific advice. Yet:

sampleN.scABEL(CV=3, theta0=0.9, targetpower=0.8,
               design="2x2x4", details=FALSE)

+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
---------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 3; CVw(R) = 3
Null (true) ratio = 0.9
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: EMA

Sample size
 n     power
224   0.8016

IMHO, a pilot study in 18 subjects is just a waste of time & money. For a product with such a high vari­ability you don’t get any meaningful information out of a small study. Let’s assume that the true CV is 300% and you run a 4-period full replicate in 18 subjects. The 95% CI of the CV is:

round(100*CVCL(CV=3, df=3*18-4, side="2-sided", alpha=0.05), 0)
lower CL upper CL
     203      565

Another issue is that the point estimate of HVDPs “jumps around” between studies. Let’s assume that you were extremely lucky and found a GMR of 1 in the pilot. You could calculate a 80% CI (i.e., accepting a 20% risk that the true value lies outside):

round(CI.BE(alpha=0.2, pe=1, CV=3, n=18, design="2x2x4"), 4)
 lower  upper
0.7382 1.3547

I’m asking myself whether it is possible to show BE for such a HVDP at all. Maybe therapeutic equi­valence is a better option?