Bioequivalence and Bioavailability Forum

Hi Astea,

❝ I've noted that sample size, estimated with the help of PowerTOST's scABEL, depends on the difference between CV_T and CV_R.

Correct.

❝ Suppose we have a HVD with unknown CV (or CV is known in literature but it ranges widely through the studies). There could be a situation when CV_T and CV_R do not coincides.

Correct as well.

❝ Do I undestand correctly? If it so then there are always exist a miserable possibility that calculated by scABEL with CV_T=CV_R sample size would be insufficient?

Yes. Shit might happen.

• CV_wT < CV_wR: Test “better” in terms of the variability; incentive in the sample size.
  
  library(PowerTOST)
sampleN.scABEL(CV=c(0.3, 0.4), design="2x2x4",
               details=F, print=F)[["Sample size"]]
[1] 24
  
  
• CV_wT = CV_wR: Test’s variability equals the one of the Reference.
  
  sampleN.scABEL(CV=rep(0.3, 2), design="2x2x4",
               details=F, print=F)[["Sample size"]]
[1] 34
  
  
• CV_wT > CV_wR: Test “worse” in terms of the variability; penalty in the sample size.
  
  sampleN.scABEL(CV=c(0.4, 0.3), design="2x2x4",
               details=F, print=F)[["Sample size"]]
[1] 48

Let’s go back to conventional (unscaled) ABE in a 2×2×2 crossover. In this design we have no means to estimate the intrasubject CV separately for Test and Reference (CV_wT, CV_wR). We get only CV_intra pooled from both. If CV_wT < CV_wR (in many cases…) the higher variability of R will lead to a wider CI (compared to the one with CV_wT = CV_wR) and the “good” T is penalized by the “bad” R.
Note that ABE is bijective (more about that later):

If T = R → R = T ∧ if T ≠ R → R ≠ T.

The original idea of reference-scaling goes back to a proposal by Boddy et al.¹ for the 2×2×2 design and at a workshop² dedicated to HVD(P)s two recommendations were given, namely

For some highly variable drugs and drug products, the bioequivalence standard should be modified by changing the bioequivalence limits while maintaining the current confidence interval at 90%
and
the bioequivalence limits should be determined based in part upon the intrasubject variability for the reference product.

(my emphases)
These suggestions lead to the reference-scaling model:

ln(0.80) / σ_w0 ≤ [ln(μ_T) – ln(μ_R)] / σ_wR ≤ ln(1.25) / σ_w0

where the switching variability σ_w0 is a fixed constant (specific for the agency).
Note that RSABE is not bijective like ABE. There is nothing like “test-scaled” ABE. Only if σ_wT ≡ σ_wR, you could switch from to [ln(μ_T) – ln(μ_R)] to [ln(μ_R) – ln(μ_T)] and get the same outcome. Statistically dissatisfying but it still makes sense: Only the Reference product has a documented history of safety and efficacy (phase III/IV).

Seen and Grieve³ argued that is not reasonable to assume heterogenicity in bioequivalence:

Why would an investigator plan a trial with the object of proving equality of two formulations if the variances were believed different?

I’m not so sure. Sometimes the originator is well aware that changing the manufacturing process would require a very expensive BE-study (even by applying RSABE; see this post for an example) and prefers to keep the manufacturing line “alive” as long as possible (“If it ain't broke, don't fix it”). Generic companies for ages are facing the problem to manufacture a product which is “equally bad” as the reference. Generally they don’t have last century’s machinery. Remember some PPIs (omeprazole, pantoprazole, lansoprazole)? The enteric coating of the originators’ products was lousy; some ABE-studies with extreme sample sized passed only by luck (subjects after R with very low concentrations and erratic profiles → extremely high CVi_ntra → inflated CI), many studies failed, some companies simply gave up.

Coming back to your question:

• If you have good reasons (pilot study!) to assume that CV_wT < CV_wR, perfect.
  
• If you have no idea, I would assume that the CVs are equal.
  
• If you believe (!) that your product will be worse than the Reference in terms of variability, you should add more subjects to be on the safe side since scaling is based on CV_wR but the 90% CI still on the (pooled) CV_intra.

Whenever you assume a CV_wR keep the (maybe counterintuitive) behavior of power in ABEL in mind. Try this goody:

library(PowerTOST)
pa.scABE(CV=0.3, design="2x2x4")

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1. Boddy AW, Snikeris FC, Kringle RO, Wei GCG, Opperman JA, Midha KK. An Approach for Widening the Bioequivalence Acceptance Limits in the Case of Highly Variable Drugs. Pharm Res. 1995;12(12):1865–8. doi:10.1023/A:1016219317744
   
2. Shah VP, Yacobi A, Barr WH, Benet LZ, Breimer D, Dobrinska MR, Endrényi L, Fairweather W, Gillespie W, Gonzalez MA, Hooper J, Jackson A, Lesko LJ, Midha KK, Noonan PK, Patnaik R, Williams RL. Evaluation of Orally Administered Highly Variable Drugs and Drug Formulations. Pharm Res. 1996;13(11):1590–4. doi:10.1023/A:1016468018478
   
3. Senn S, Grieve AP. A Comment on Optimal Allocations for Bioequivalence Studies. Biometrics. 1999;55(4):1314–5. doi:10.1111/j.0006-341X.1999.01314.x