Bioequivalence and Bioavailability Forum

Hi BE-proff,

Out of curiosity: what is the reason not to use the detailed Helmut's answer to your previous similar question here?

Dear BE-proff,

❝ I have the following data:

❝ n=20

❝ CV=0.18 (for Cmax and AUC)

❝ GMR1 = 0.97

❝ GMR2=1.19

❝

❝ If to calculate size based on GMR1 I think it's better to use a script:

❝ (...) if to use GMR = 1.19 we see something terrible:

❝ (...) What to do in such situations?

If your product has a true GMR of 1.19 for a primary ratio, then 166 may be a sample that meets your power requirement size.
However, bear in mind that such calculations involve models with assumptions, notably a Normal distribution on the log scale. Your GMR from the trial is an estimate and not a true value; a good guess is that there is 50% chance the true GMR is worse.

In this paper, the author tried to look into the various options for situations like yours: How to use the result from one trial in the planning of the next?
The answer was: You have several options, but you do not get any easy solution that allows high power and low sample size if you try to make use of the observed GMR (and that, by the way, is also why pilot trials are not good approaches for telling if candidate formulations are so promising that a pivotal trial is merited). And if you gamble and use a GMR for planning that is closer to 1.0 than what you observed previously then you are also easily screwing yourself.

Dear BE-proff, dear All,

❝ Let's say I want to calculate sample size based on results of a previous study.

❝

❝ I have the following data:

❝ n=20

❝ CV=0.18 (for Cmax and AUC)

❝ GMR1 = 0.97

❝ GMR2=1.19

Taking into account that CV and GMR's of such a previous (pilot) trial are not the true values but estimates with uncertainty, as ElMaestro already pointed out. One answer to such a goal is using the so-called "expected power" implemented in PowerTOST::exppower.TOST() and expsampleN.TOST().

Let's play with your numbers step by step:
1. Taking into account uncertainty of CV, but assuming a known (true) GMR =0.95
expsampleN.TOST(CV=0.18, theta0=0.95, prior.parm = list(m=20, design="2x2"), prior.type="CV")
++++++++++++ Equivalence test - TOST ++++++++++++
       Sample size est. with uncertain CV
-------------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins = 0.8 ... 1.25
Ratio = 0.95
CV = 0.18 with 18 df

Sample size (ntotal)
 n   exp. power
18   0.823287
Not so much more than using the conventional power assuming GMR and CV known.

2. Taking into account uncertainty of CV, but assuming a true GMR =1.19
expsampleN.TOST(CV=0.18, theta0=1.19, prior.parm = list(m=20, design="2x2"), prior.type="CV")
++++++++++++ Equivalence test - TOST ++++++++++++
       Sample size est. with uncertain CV
-------------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins = 0.8 ... 1.25
Ratio = 1.19
CV = 0.18 with 18 df

Sample size (ntotal)
 n   exp. power
180   0.801466
Again slightly higher than using the conventional power.

3. Now taking into account uncertainty of CV and GMR =1.19
expsampleN.TOST(CV=0.18, theta0=1.19, prior.parm = list(m=20, design="2x2"), prior.type="both")

++++++++++++ Equivalence test - TOST ++++++++++++
  Sample size est. with uncertain CV and theta0
-------------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

Design characteristics:
df = n-2, design const. = 2, step = 2

alpha = 0.05, target power = 0.8
BE margins = 0.8 ... 1.25
Ratio = 1.19 with 18 df
CV = 0.18 with 18 df

Upper bound of expected power = 0.802418

Sample size search (ntotal)
 n   exp. power
Search for improved starting value based on nct approximation for conditional power:
4130   0.769089
4146   0.769157
4162   0.769219
4194   0.769354
4258   0.769619
4386   0.770131
...
619480   0.800000
Final search:
619480   0.800000
619478   0.800000
619476   0.800000

3 iterations
619478   0.800000

That result (!) should everyone convince that using the GMR from pilot studies with small number of subjects (or likewise from usually small stage 1 of a TSD) is not a good idea, as our captain already stated in his post above.
It results mainly from "... there is 50% chance the true GMR is worse." And power is heavily influenced by deviations in the GMR as we already know from the power analysis functions f.i. pa.ABE()

BTW: Don't ask me for the theory behind expected power. It is something Bayesian.
If you are interested you may find a short tractatus at
https://github.com/Detlew/PowerTOST/tree/master/inst/doc
written by Ben (Benjamin Lang) who is also responsible for the implementation.

Hi all,

Just curiosity, but does anyone here had questions on sample size from regulators?

I'm asking that since in Portugal I never saw a question from regulators or ethics committees regarding sample size. They just assume we did it right