Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
With respect to power, we have performed power calculations aimed at testing the sample size needed to identify differences between treatment arms. We assumed a baseline control-group registration rate of 2%, which was the average registration rate across all three of our pilot studies.
We believe that in our main study, the sample size of 125,000 people, with 25,000 in control, should allow us to detect a minimum treatment effect of .28 percentage points. Comparing the control to any one of the treatment arms (each of which included 25,000 people) will allow us to detect a minimum treatment effect of .35 percentage points. These minimal detectable effects are substantially smaller than the effects we saw in our pilot studies.
In our second study, with a total of 35,708 individuals equally split between treatment and control, we should be able to detect a minimum treatment effect of .41 percentage points.