Alpha calculus in clinical trials: considerations and commentary for the new millennium

Regardless of whether a statistician believes in letting a data set speak for itself through nominal p-values or believes in strict alpha conservation, the interpretation of experiments which are negative for the primary endpoint but positive for secondary endpoints is the source of some angst. The purpose of this paper is to apply the notion of prospective alpha allocation in clinical trials to this difficult circumstance. An argument is presented for differentiating between the alpha for the experiment ('experimental alpha' or alpha(E)) and the alpha for the primary endpoint (primary alpha, or alpha(P)) and notation is presented which succinctly describes the findings of a clinical trial in terms of its conclusions. Capping alpha(E) at 0.10 and alpha(P) at 0.05 conserves sample size and preserves consistency with the strength of evidence for the primary endpoint of clinical trials. In addition, a case is presented for the well defined circumstances in which a trial which did not reject the null hypothesis for the primary endpoint but does reject the null hypothesis for at least one of the secondary endpoints may be considered positive in a manner consistent with conservative alpha management.