Effect size estimation for non-inferiority trial

[Niki Minckas]

Hi everyone,
I need your help calculating the estimated effect size for a non-inferiority hypothesis.
I have calculated de sample size for an efficacy hypothesis of a binary outcome using
power twoproportions 0.25, test(chi2) rrisk(0.85) power (0.90)

Based on that the sample size should be 2655 in each arm.
Now I have the secondary hypothesis that is a non-inferiority. I need to calculate the possible effect size on a different binary outcome considering that sample size (with a margin of 0)
Is it ok to do the following- considering a prevalence in the control group of 10% and a total sample size of 5310:

power twoproportions 0.10, test(chi2) effect(rrisk) power (0.90) n(5310)

I would appreciate any help possible.
Thank you very much,
Nicole

[Joseph Coveney]

I'm having--what I hope is a temporary--memory lapse: what is the effect size for a noninferiority hypothesis? Is it the chosen margin-of-noninferiority over some kind of SD of the difference of population parameters? The difference in posited true means over the pooled something-or-other?

[Niki Minckas]

Hi Joseph, most probably it’s not your memory but my confusion with this!!

I have calculated the required sample size for a superiority trial with a binary outcome (death). Now I need to calculate the minimum detectable difference for the secondary hypothesis that is a non-inferiority one to see the impact of the treatment on adverse effects, also binary (in this case, sepsis)- Null hypothesis: Standard treatment-New treatment<0; Alt hypothesis: Standard treatment- New treatment>=0
So my questions are actually 2:
1) is it ok to use the power twoproportions command to calculate the minimum detectable difference if it’s a non-inferiority hypothesis?
2) if I were to calculate a separate sample size for the non-inferiority hypothesis, could I still use the power twoproportions command or is there a different one for non-inferiority trials?

Hope I’m a bit more clear now!
Thanks in advance for any help.

[Joseph Coveney]

1) is it ok to use the power twoproportions command to calculate the minimum detectable difference if it’s a non-inferiority hypothesis?

I believe that you can use it, but it's tricky. You basically have to swap alpha and beta, and there's the problem with specifying the assumed true proportions in each group. You're better off with a dedicated command—Google blackwelder site:statalist.org for a user-written command for noninferiority study sample size estimation for proportions that's been posted to the forum as an attachment to a post. Try using it in conjunction with the official Stata minbound in order to find a so-called minimum detectable difference for a given Type I error rate, power and sample size and assumed true proportions.

2) if I were to calculate a separate sample size for the non-inferiority hypothesis, could I still use the power twoproportions command or is there a different one for non-inferiority trials?

Again, I suggest using the dedicated user-written command mentioned above. It uses the conventional Blackwelder formula for sample size estimation for noninferiority trials where proportion of success or failure is the outcome. You will find that sample sizes for a noninferiority study with anything like a conventional margin of noninferiority will be larger than the corresponding superiority study. Because of the relationship of the superiority hypothesis to the noninferiority hypothesis, most studies that I have run across that test both have based sample size on the latter (the margin of noninferiority ostensibly chosen solely on subject matter grounds, and the level of Type I error rate usually dictated as 0.025 by prevailing sentiment), and if that null hypothesis is rejected, have then gone ahead automatically to the corresponding superiority hypothesis without adjustment.