Some optimal and non-optimal two-stage designs using an alpha-spending function

While designing a group sequential clinical trial in the pharmaceutical industry setting, we often face a problem of determining the time for an interim analysis. For a two-stage trial we compute the sample sizes n and N per treatment group for the interim and final analyses, respectively, that minimize the average trial size for a specified overall power. We consider this optimization when we monitor the trial using a Lan-DeMets alpha-spending function. Two additional problems considered in this context are (i) finding the sample sizes that maximize the overall power for a specified average trial size, and (ii) finding the sample sizes that achieve specified powers at the interim and final analyses.