Bioequivalence and Bioavailability Forum

Dear Someswara Rao,

I'm not in the mood to comment on any of your arguments.

Sorry, but I only can repeat Helmut's quote of Wolfgang Pauli:

That is not only not right, it is not even wrong!
(Das ist nicht nur nicht richtig, es ist nicht einmal falsch!)

You may find out the reasons why I'm repeating this if you study the posts in the forums category [Power / Sample size] and additionally if you study the literature on this topic in depth. Especially that about power/sample size for replicate crossover designs and for HVD(P)s.

Moreover I recommend Helmuts lectures / presentations. There are some about power / sample size.

Hi Sanketh Gupta (or Someswara Rao?),

first of all: Who are you? From the article and the registration e-mail of Sanketh Gupta I suppose that both of you are employees of the same company. Are you sharing an account? This is not acceptable and may lead to blocking Sanketh’s account (see the Forum’s Policy).
If you are in fact Someswara Rao please register to the forum and post with your own account.

❝ Please do not underestimate the article by looking at journal name.

I didn’t do so when I became aware of the article last October. I judged it based on its – rather doubtful – content.

❝ You all are requested to see the formulas mentioned to arrive at sample size estimations, since it is pure Mathematics. Please be noted that Mathematics is same throughout the globe.

THX for reminding me about the spatial validity of mathematics. Please note that a correct (though approximative) formula applied wrongly (e.g., to a false model) gives still a wrong result.

❝ You all believe following is the formula for sample size estiamtion?

I cannot speak for the others, but myself for 2×2×2 crossovers and ABE (!) as a last resort, yes. Note that the formula is based on the shifted central t-distribution which is an approximation of the noncentral t-distribution which itself approximates the exact method (Owen’s Q-function). Why not use a better method? But we are not discussing 2×2×2 crossovers here, right?

❝ Please be noted that the same formula used world wide for sample size estimation.

Hopefully not for reference-scaling! Due to the conditions of the frameworks (scaling applicable only if CV_wR >30%, GMR restriction of 0.8–1.25, different σ₀ for the FDA and the EMA, upper cap at CV_wR of 50% for the EMA) you must not simply plug the parameters you mentioned into any (‼) formula. Power and, therefore, sample sizes are not directly accessible – we need to perform Monte Carlo simulations! I suspect you did not understand the paper by Tóthfalusi and Endrényi. Quote:

Overall, the statistical properties of the methods proposed by EMA and FDA are rather complex as a result of the additional conditions and requirements (mixed procedure, GMR constraint, and (for EMA) a cap on the limits). Furthermore, the tests required by both EMA and FDA are dependent on each other which makes the theoretical treatment very complicated. Therefore, the required sample sizes were obtained by simulations.

Due to the slow convergence (example) one needs to simulate ≥10⁵ BE studies for any given GMR, CV, and target power. This should be taken into account if comparing results with the article of the two Lászlós (only 10,000 simulations; hence, power might have been not sufficiently stable).

❝ (In general 10% difference is considered. In case of highly variable drugs go for 5% difference of Generic Vs Innovator)

Exactly the opposite. In ABE and low to moderate CVs ≥5% can reasonably be considered. In the case of HVDs/HVDPs Tóthfalusi and Endrényi recommend 10%. A larger deviation than the one commonly used with drugs with low to moderate variability should be assumed regardless whether scaling is intended or not. It is an intrinsic property of HVD(P)s that the GMR varies between studies.

❝ We noted that the incomplete sentence in the article and suggested to delete the same before publishing, but unfortunately it was not deleted by the Editor.

Why the heck did you want to delete the truncated sentence? It should have been the other way ’round: Complete it. References 6–8 are not linked to anything in the article. So likely more text is missing.

❝ Moreover, we have validated obtained sample size estimations against the published article “Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs, J Pharm Pharmaceut Sci (www.cspsCanada.org) 15(1) 73 - 84, 2011”.

You can’t be serious!
Example: Four-period full replicate design, GMR 0.90, target power ≥80%.
FDA Reference scaling according to progestrone guidance.
EMA Average Bioequivalence with Expanding Limits, Method A according to the Q&A document.
1 Rao et al. (2015)
2 R package PowerTOST (2016). Function sampleN.RSABE() for the FDA’s RSABE and sampleN.scABEL() for the EMA’s ABEL.
3 Tóthfálusi & Endrényi (2012)

         FDA          EMA   
     ──────────  ───────────
CV%   1   2   3    1   2   3
 30  41  32  30   41  34  35
 32  22  30   –   38  36   –
 34  21  28   –   35  34   –
 35  21  28  26   34  34  34
 36  20  26   –   33  34   –
 38  19  26   –   31  32   –
 40  19  24  24   29  30  31
 42  18  24   –   28  30   –
 44  18  24   –   27  28   –
 45  17  24  23   27  28  29
 46  17  24   –   27  28   –
 48  17  22   –   26  28   –
 50  17  22  22   25  28  28
 52  16  22   –   27  28   –
 54  16  22   –   29  28   –
 55  16  22  22   30  30  30
 56  16  22   –   31  30   –
 58  16  24   –   34  30   –
 60  16  24  23   36  32  32
 62  16  24   –   38  34   –
 64  16  24   –   41  36   –
 65  16  24  24   42  36  37
 66  16  24   –   43  36   –
 68  16  24   –   46  38   –
 70  16  26  24   48  40  40
 72  16  26   –   51  42   –
 74  16  26   –   54  44   –
 75  16  26  26   55  44  45
 76  16  28   –   57  46   –
 78  16  28   –   60  48   –
 80  16  28  29   63  50  50
 82  17  30   –   66  52   –
 84  16  30   –   69  54   –
 85  16  32   –   71  54   –
 86  16  32   –   72  54   –
 88  16  32   –   76  56   –
 90  16  34   –   79  58   –
 92  16  34   –   83  60   –
 94  16  36   –   86  62   –
 95  16  36   –   88  64   –
 96  16  36   –   90  64   –
 98  16  38   –   94  66   –
100  16  40   –   97  68   –
105  17  42   –  107  74   –
110  17  44   –  118  78   –

Note that PowerTOST always rounds up if necessary to give balanced sequences (formatted in red). n–1 would already achieve at least the target power.
Correlations of PowerTOST’s sample sizes with the ones of the two Lászlós are high (R² FDA 0.977, EMA 0.998) and close to the identity line. Can you please specify what you mean by “validated”?

Apart from the general disagreement, starting with a CV of 45% your sample sizes for RSABE become some kind of a “natural constant” (16–17). How do you explain that? With increasing CVs the likelihood of a PE with a large deviation from unity increases (pure chance!) and therefore, the GMR restriction to 0.8–1.25 will prevent demonstration of BE. Practically beyond 50% the GMR restriction is leading the decision; scaling itself becomes less important. You don’t even need a pocket calculator to check that. Pure reasoning. Tons of papers. This effect explains why with proper sample size estimation you will see a minimum at ~50% and increasing sample sizes beyond.

If companies follow your tables, studies would be

• either only unethical (too low sample sizes lacking sufficient power) or
  
• both unethical and economic questionable (too high sample sizes).

Scylla and Charybdis…

❝ The same article did not specify the sample size estimations beyond 60% ISCV and above.

Wrong again. All tables give sample sizes for up to 80% CV.

❝ […] I will make you understand.

How; what do you suggest? Brainwashing, waterboarding, hire a contract killer?

❝ […] please provide sample size estimation formula for scaled average bioequivalence studies from your end …

There is none.
If you hope that miraculously you will be able to derive an analytical solution, fantastic. Go ahead and submit it to a real journal. Become famous.

❝ … and educate the pharmaceutical world.

Mission accomplished.
@Someswara: I hope you have the guts to retract this article – if that’s possible at a predatory journal at all.

Since recentscientific.com and this site have the same PageRank (4) I hope that colleagues interested in sample size estimation for reference-scaling will find not only your article but this thread as well.

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Keywords: Highly Variable Drugs (HVDs) • Highly Variable Drug Products (HVDPs) • Reference-scaled Average Bioequivalence (RSABE) • Average Bioequivalence with Expanding Limits (ABEL) • Sample Size Estimation • Monte Carlo Simulation • Food and Drug Administration (FDA) • European Medicines Agency (EMA) • Progesterone Guidance • Power