Bioequivalence and Bioavailability Forum

Dear Ben!

❝ From your given example, let's say we plan with the primary/reasonable assumption CV=20% and start with n1=24. The fixed design would require a sample size of 20 (sampleN.TOST(CV=0.2, alpha=0.05, targetpower=0.8)), correct?

Yes; power 83.5%.

❝ What do you mean by "total sample sizes 10-20% higher"?

The full quote from the end of Potvin’s discussion section:

There is some cost to using a two-stage design when the a priori variance assumption is correct. If the initial sample size, n₁, is too small for the actual CV, the average total sample size for the two-stage design will be about 20% higher than that for the single stage design with a correct choice of CV for determining the sample size.

Since the grid (sample size multiples of 12 and CVs multiples of 10%) was too coarse for my taste I repeated the simulations with a narrower grid (exact power instead of the shifted t). Potvin’s target (besides maintaining the patient’s risk) was to keep power >80% within the entire framework – which they almost met. See slide 61: With the exception of combinations of small n₁ and high CV in the upper left corner power was >80%. For n₁ 24 and 20% power is 88.1%.

❝ In case the CV turns out to be different and we have to go to stage two …

Power will be higher than the 83.5% in fixed design, because in 8.6% of cases we proceed to the second stage and are able to show BE then. So we pay a penalty but gain power (88.1%).

❝ … or compared to the case where we stop after stage 1? In the former, doesn't it depend on the different CV?

I’m not sure whether I understand you here. If the CV turns out to be ≤20%, we have to distinguish between Method B and C – I will concentrate on B here. If CV is 20% the study has to be evaluated for BE at 0.0294 (remember we planned like a fixed design with 0.05). Whether it passes/fails here is difficult to predict: We have some headroom because the fixed sample design with 0.0294 in 24 gives 83.6% power. Also the PE may be closer to 1. If we pass and the PE is 0.95 the penalty is 20% (24/20). If the CV is lower, the penalty is higher (but this is also the case in a fixed design – we pass and have wasted money).

❝ E.g. CV=30% as you said, then we would require sampleN.TOST(alpha=0.0294, CV=0.3)-24 = 24 additional subjects and hence it's 100% higher …

Yes, that’s how it works. But it doesn’t make sense to say “it's 100% higher”. If in the fixed design (assumed 20%) the CV is 30% and you run the study in 24, power will be only 55.8% (power.TOST(CV=0.3, n=24)).

❝ … (or using the mean total n from Table II: 39.9/24 = 1.6625). In the latter case we would have 20% (24/20 = 1.2) but is it reasonable to talk about "total" here?

Here again we are in the trap of comparing one particular study to the average of 10⁶ simulated ones. Also you are comparing the wrong row of the table. You should stay at n₁ 24 and CV 20%. The simulations were run with T/R 0.95 and the given CVs with lognormal error. So with a target of 20%, for sure there were a few studies with only 5% and some with 50%. Average n_total was 24.6 (5^th, 50^th, 95^th percentiles: 24, 24, 28). On the average for this scenario the penalty is 24.6/24 = +2.5%. Only in 5% of cases the penalty was +16.7%. For an overview of penalties see slide 63. On the average (!) it’s not that bad.

See also this goody:



Funny, isn’t it?