It's fairly easy to write a simulation procedure to calculate, for any given global type 1 error rate, adjusted local "stopping" alphas for interim "looks" in a sequential design, for any sort of significance test. Basically I simulate the observations, and do the tests as I would in a real experiment by continually adding observations until I get a significant outcome at an interim look or reach the final look.
My problem and the question is: How can I correct effect sizes, p values, and CIs, in a way that is generalizable to any conventional significance test? I'd guess it should again be some sort of simulation procedure, but of course I'd just as well welcome any other solution.
I do have a vague idea for correcting standardized effect sizes: having obtained, in my real experiment, the given effect size and p value, I could simulate again a bunch of effect size variations to find the "true" (simulated) effect size with which it is most likely that, in my sequential analysis, I end up with the obtained effect size and/or p value. However, even in that case I would not know what specific data characteristic contributed to the effect size difference, i.e., for example, in case of a t-test, I wouldn't know whether in the real standardized effect size (Cohen's d) the variance is smaller or the mean difference is larger. But maybe that's simply impossible to tell?
As for adjusting p values, my intuition is that I could repeat the simulation procedure with the obtained p value as local alpha at the given "look", and leaving all other settings unchanged. Then the resulting global type 1 error rate could be the adjusted p value. (The CI could then also be derived in a similar manner.) But I'm really not sure whether this would be correct.
(Note: I'm aware that there are solutions for certain basic parametric tests, like t-tests, in rpact, gsDesign, etc., but I want the procedure to be generalizable to any sort of statistical significance test.)
