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

Regardless of whether a statistician believes in letting a data set speak f or itself through nominal p-values or believes in strict alpha conservation , the interpretation of experiments which are negative for the primary endp oint but positive for secondary endpoints is the source of some angst. The purpose of this paper is to apply the notion of prospective alpha allocatio n in clinical trials to this difficult circumstance. An argument is present ed 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 findi ngs 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 wit h 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 bu t does reject the null hypothesis for at least one of the secondary endpoin ts may be considered positive in a manner consistent with conservative alph a management. Copyright (C) 2000 John Wiley & Sons, Ltd.