Bioequivalence and Bioavailability Forum

Hi Someswara,

❝ Simulation with ≥10⁵ BE studies is not possible with us […]

Too bad that simulations are the only possible approach.
Your article is a slap in the face of the ones devoting a lot of time and efforts into developing fast algorithms and setting up simulations. When in 2010 the FDA’s draft progesterone guidance and the EMA’s BE-GL were published statisticians were desperate because it became immediately evident (though still not to you, obviously) that common methods for sample size estimation cannot be applied.
It was a big relief when the two Lászlós published their paper in 2011 and that since Feb. 2013 package PowerTOST allows simulations for any expected θ₀, CV_wR, and desired power.
R and package PowerTOST come free of costs and are licensed under GPL-3. What do you mean by “not possible with us”?

❝ In general sample size calculations are done using 80% power requirements; however, the post hoc power is not at all important, as long as you bioequivalence limits are within the acceptance range.

Splendid! In the following a comparison of part of your tables with results obtained by simulations.
n1 Sample size for ≥80% power.
n2 Sample size for ≥90% power.
β  Producer’s risk (1 – power). β larger than desired (= underpowered) formatted in red.

• FDA (RSABE)
  
              RRT | RTR | TRR        
      Rao    Sim’s    Rao    Sim’s
CV  n1  β   n1  β   n2  β   n2  β  
30% 62 11.1 45 19.7 86  4.8 65  9.9
50% 26 25.1 30 19.8 35 15.3 45  9.9
80% 24 31.8 41 20.0 32 24.3 88 10.0

              RTRT | TRTR          
      Rao    Sim’s    Rao    Sim’s
CV  n1  β   n1  β   n2  β   n2  β  
30% 41 11.6 31 19.4 57  5.1 44 10.0
50% 17 30.1 22 19.7 23 21.3 32  9.7
80% 16 35.1 28 19.9 21 25.9 60  9.9
  
  
• EMA (ABEL)
  
              RRT | RTR | TRR         
      Rao    Sim’s    Rao     Sim’s
CV  n1  β   n1  β    n2  β   n2  β  
30% 62 14.1 52 19.5  86 6.3  73  9.8
50% 38 20.3 39 19.2  53 9.5  52  9.9
80% 95 11.3 75 19.7 131 5.3 100 10.0

              RTRT | TRTR          
      Rao    Sim’s    Rao    Sim’s
CV  n1  β   n1  β   n2  β   n2  β  
30% 41 14.1 34 19.7 57 14.4 48 10.0
50% 25 23.1 27 19.9 35 11.3 37 10.0
80% 63 11.4 49 19.5 87  5.9 68  9.8

  

In many cases studies designed according to your tables will be (extremely) underpowered (i.e., producer’s risk larger than desired). Hence, the chances to fail are higher than expected as well. If you are working with a CRO and the sponsor seeks a second opinion by a learned statistician, you will loose a client.

However, sometimes you’ll make a lucky strike (producer’s risk substantially smaller than targeted). Study overpowered, more subjects than required treated. Fortunately HVD(P)s are safe; low chances of AEs. But any intervention possesses risks. As a member of an IEC I would never accept the protocol. Anyhow: Study performed and easily passes BE. Cross you fingers that the sponsor is so happy with the outcome that he does not seek a second opinion. If he does, he would ask himself why he spent more money than necessary. Probably he will hire another CRO the next time.

Almost needless to say that in the simulations β is always as close as possible to the desired level.

❝ In general, a generic player will always try to match innovator. To reserve the resources and to ensure the probability of success (to pass the study), a 10% difference can be considered low to moderate variable drugs as it demand less sample size and a 5% difference is always appropriate for highly variable drugs as it demands more sample size due high variability.

Whereof one cannot speak,
thereof one must be silent.    Ludwig Wittgenstein

❝ We have compared the obtained sample size by using our method with Tóthfálusi & Endrényi (2012) method and it was identified that the obtained sample size did not differed significantly using EMA approach. However it was differed using FDA method. This difference is expected as our approach is the formula based one as the calculations are different here due to change in the regulatory constants.

Did you bother to look at the table and plots in my previous post? If you don’t see differences likely you are .

❝ I am confident that the formula used will definitely works, […] and the same formula know to everyone in the pharmaceutical industry.

Old beliefs die hard
even when demonstrably false.    E. O. Wilson

❝ I am not bothered about the ranking of journals …

In earnest? If you were so confident that you discovered the “philosopher’s stone” – everybody is desperately seeking for so long – why didn’t you submit the manuscript to a reputable journal (free of costs, BTW)? Or were you in private afraid that it will fail to survive any serious peer-review?