Combining Benjamini-Hochberg with statistical power calculations

Suppose I am investigating a question which involves e.g., many statistical T-tests. The normal Benjamini-Hochberg procedures tells me how to control the false discovery rate. However, suppose that some or many of these tests do not have sufficient statistical power i.e., it falls below 0.8. (Recall that statistical power depends on three things: sufficient effect size, sufficient number of records and sufficiently low variance.)

What is the procedure for combining these? First use BH and then abandon cases which fail statistical power? Would it be acceptable to replace those failing statistical power with others which pass?

Any thoughts appreciated.

Thank you much.


Not a robit
Why did they have low statistical power. If you were planning on conducting the test but then they had low power it doesnt matter. You still need to pledge allegiance to your original plan otherwise you are fishing!
Some of them have low power because the tests are unconditioned. So you would say, perform all the tests, filter according to the BH procedure, then throw out tests that turn out not to be sufficiently powerful at the end of the pipeline?