Bioequivalence and Bioavailability Forum

Dear Outlaw Torn,

❝ I must first admit that I am statistically challenge.

Welcome to the club. Search the forum for 'statistical amateur', 'bloody amateur' or 'bloody raw recruit in statistics' .

❝ Let's say we want to conduct an equivalency study, with 80% power and confidence margins of 10%. The primary outcome we want to measure, depending on what criteria is used, occurs at a rate of either 5% or 10%. My brain is telling me that if we chose a primary outcome that will occur at an expected rate of 5%, we would need a significantly higher sample size than if we chose a primary endpoint that occurs at a rate of 10%.

This is a question that is somehow beyond the horizon of us doing mainly BE studies all of our working time.
Without really understanding what I did, I fired up PASS2008 [1]. Choosing the module
Equivalence of proportion/Two independent proportions/Specify using differences
I got:
PR     N (per group)
0.05  236
0.1   155
I set target power to 80%, alpha=0.05, equivalence margin (for the risk difference P_T-P_R) +10% and 'true' difference = zero. The power/sample size was calculated based on the simplest test in this respect, the unpooled Z-test.

If the sample size for the 5% rate is significantly higher then for the 10% rate is left to you .

❝ But I'm told that this is not actually the case ...

So what? Show the results of my sample size estimation to your statistical consultant and ask him to comment.

❝ The bit between 50% and 100% makes perfect sense to me. But the bit below 50% does not.

The binomial is 'symmetric' about 50%. If this makes sense for you or not .
Look at the sample size:
PR     N (per group)
0.9   155
0.95  236
Again with 'true' risk difference = zero.

BTW: The binomial is always good for a surprise. Have a look onto the sample size if 'true' risk difference is set to 0.01 instead of zero:
PR     N
0.05  209
0.1   179
In case of the 5% outcome the sample size decreases! Somehow counter intuitive for me. But as said above: Didn't really understood what I'm doing here .

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[1] Hintze, J. (2008)
PASS2008, NCSS
LLC. Kaysville, Utah