Powering versus statistical significance in clinical trial design

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.

Applying the often used:

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.

Many thanks!

• Usually you don't "calculate" the minimum detactable effect size - rather you select such a size at the study design stage based on clinical considerations which are informed by prior research, etc. Commented Jul 5, 2019 at 1:36
• Yes but if I’m not designing the study but rather trying to infer what the sponsors of the trial selected would this be a reasonable approach? Commented Jul 6, 2019 at 4:12
• Why not ask the sponsors of the trial to disclose their choice of minimum detectable effect size? That information should not be a secret, unless something hanky-panky is going on. Commented Jul 6, 2019 at 18:36
• Because these disclosures are not always made and require contacting the sponsor? Can you please provide some insight into the mathematical approach here? Commented Jul 7, 2019 at 18:52
• I still maintain that you cannot "calculate" a minimally detactable effect size, but rather specify it based on subject matter considerations. As statisticians, we have to realize that there is a limit to what we can do - the clinical investigators we work with have a duty to step up to the plate and offer their expertise towards this specification. Specifying a minimally detectable effect size is not something that you should be expected to come up with, even under the best of circumstances. Maybe others here think differently, so I will let them wade in. Commented Jul 7, 2019 at 20:19