Sample size calculation in non-inferiority trials with binary endpoint: scale matters
It is becoming increasingly difficult to justify testing the efficacy of a new treatments against placebo. Instead, active controlled trials are being used to test whether the new treatment has not much worse efficacy than an already known effective treatment. Choosing the margin defining ‘not much worse’ is a pivotal step in designing such non-inferiority trials. It is well known that the size of the margin strongly influences the required sample size. What is largely ignored however, is that also the scale of the margin (for binary endpoints absolute risk difference, risk ratio or odds ratio) strongly influences the power of the trial and thus the required sample size.
Using the same margin for the minimum allowed success proportion in the trial arm receiving the new treatment, but a different choice of the parameter used for evaluating the distance between this proportion and the success proportion in the active control arm could easily require two times larger sample size.
By exploring the exact size of the power differences in various scenarios, I will show in what kind of trials this scale choice is particularly influential for sample size requirement. Also I will show which parameter choice has highest power in which situation. Alongside, I will discuss other considerations than power when choosing between risk difference, risk ratio and odds ratio as primary estimand in a non-inferiority trial.