I think I have a simple question that I have not seen directly answered elsewhere, and as a stats beginner, I'm wary to translate answers that are not directly answering this question - apologies if it is viewed as duplicate.
My question is this - clinical trials are generally powered at 80% to show some level of treatment effect, but how can you calculate the minimum detectable treatment effect that would yield statistical significance?
For example let's say that a trial is 80% powered to show a treatment effect delta of 2.2 (e.g., the difference between treatment and control on a specific metric is 2.2)
Furthermore, we initially target an N of 210 for the entire trial and each arm is 1:1 randomized (105 per arm).
The standard deviation is assumed to be 8.05, statistical significance is defined as having a p-value < 0.05.
We can solve for the treatment effect (the difference of the means) based on changing the other variables - specifically:
Since we cannot change n, or Z(1-a) we can only reduce Z(1-b) and presumably assume a lower standard deviation.
Does this mean then that the true minimal difference that would be considered statistically significant, and thus a trial success, would be:
In other words, simply letting Z(1-b) equal 0 for a powering of 50%?
Thus, on one hand, based on the example a minimum treatment effect could be 2.2 or 1.54 which could be a major difference in the likelihood of the trial being viewed as "successful" (showing stat sig) or not.