An efficient method for accommodating potentially underpowered primary endpoints

If a trial is adequately powered for two clinically important endpoints, A and B, each of which can fully characterize a treatment benefit to support a regulatory claim by itself, then both endpoints are usually labeled primary, and the trial is deemed positive if either endpoint is statistically significant after a multiplicity adjustment. However, if only A is adequately powered, then should B be designated a secondary endpoint, or should it be retained in the primary family despite being (potentially) underpowered? The former option can lead to a negative trial if A is not statistically significant, no matter how positive the results are for B, since no familywise type I error rate (FWER) is allocated to B, while the latter can reduce the likelihood of a positive trial if an inefficient multiplicity adjustment is used. We underscore this contemporary problem with real examples and offer a novel and intuitively appealing solution for accommodating clinically important but potentially underpowered endpoint(s) in the primary family. In our proposal, for the above scenario with two endpoints, A is tested at a prespecified level alpha(1)=alpha-epsilon (e.g. epsilon=0.01 when alpha=0.05), and B at an 'adaptive' level alpha(2) (