# Bioequivalence and Bioavailability Forum

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rajasekhar
Junior

India,
2017-01-20 08:54

Posting: # 16987
Views: 2,328

## Sample size justification [Power / Sample Size]

Hii,

for one study (two way crossover) based on sufficient CV, power and ratio we written protocol as 52 participants are sufficient to establish the bioequivalence however based on dropout/withdrawal rate (10%) we conducted study in 62 participants. But at end only 48 participants completed the study. but as per protocol 52 need to establish BE. study outcome is with in 90% CI. How can we justify for 48 participants. Please help me

Helmut
Hero

Vienna, Austria,
2017-01-20 10:59

@ rajasekhar
Posting: # 16989
Views: 1,950

## Post hoc sample size “justification”

Hi Raja,

» for one study (two way crossover) based on sufficient CV, power and ratio we written protocol as 52 participants are sufficient to establish the bioequivalence however based on dropout/withdrawal rate (10%) we conducted study in 62 participants.

That’s already doubtful. If you are with a CRO you were lucky that the sponsor lacked basic mathematical skills as well. If the required sample size is 52 and you expected a dropout-rate of 10% you should have dosed only 58 subjects (see this thread). With 62 you “adjusted” for a dropout-rate of 100(52–62)/62=16%.

The impact of dropouts on power is overrated by many. I don’t know which CV and GMR you assumed and what your target power was. If you have R, try this code:

```library(PowerTOST) plot(pa.ABE(CV=0.3, theta0=0.95,             targetpower=0.9, minpower=0.8), ratiolabel="GMR")```

If you would have dosed only 52 subjects (for 90% power) you could have had 13 dropouts (25%!) and still expect 80.6% power. IMHO, this “compensation” for loss of power due to dropouts by increasing the sample size is ethically doubtful (only making wealthy CROs richer by milking sponsors).

» But at end only 48 participants completed the study.

OK. With 23% the dropout rate was higher than you expected.

» but as per protocol 52 need to establish BE.

Are you asking whether this was a deviation from the protocol?

» study outcome is with in 90% CI.

Splendid. Open a bottle of champagne. If you are with a CRO ask your boss for a bonus selling the study to the sponsor with such a high sample size.

» How can we justify for 48 participants.

There is nothing to “justify”. Your sample size estimation was based on assumptions. Consider the example from above. The CV and GMR came out exactly as expected (30% and 95%). With 48 subjects power is still 87.9%. But the CV could have been higher and the GMR deviating more from 100% and you could still demonstrate BE. Extreme example: CV 30  35%, GMR 95  90%:

```library(PowerTOST) round(100*CI.BE(CV=0.35, pe=0.90, n=48), 2) round(100*power.TOST(CV=0.35, theta0=0.92, n=48), 1)```

You pass with 48 subjects (90% CI: 80.10–101.12%) although post hoc power is only 51%… This information only tells that assumptions were not correct and hence, the producer’s risk (β) was higher than desired. Nevertheless, you made it. Regulators are should be only interested in the patient’s risk (α) which is maintained at 0.05. ElMaestro once wrote “Being lucky is not a crime”.
No guideline asks for the irrelevant post hoc power. Only a few – inexperienced – assessors sometimes do. Send them a politely worded educational letter explaining that the outcome of a comparative BA-study is dichotomous:

Either bioequivalence was demonstrated or not.

Full stop.
Post hoc power (based on the actual CV, GMR, and sample size) does not play any role in this game.

Cheers,
Helmut Schütz

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