We have become masters of clinical trials. We design them beautifully, our protocols delineate objectives and categorize sharply e$cacy variables as primary or secondary, teams of investigators execute them e$ciently and then we analyse with the latest and most sophisticated statistical methods. Yet, all too often, they fail, being negative on the primary e$cacy variable and positive on a secondary endpoint. Positive and negative refer solely to attaining or not attaining statistical signi"cance. Statisticians try to interpret these trials. Some hold the position that the entire study is negative because the primary e$cacy variable does not achieve statistical signi"cance. For them, analyses of secondary variables are, at best, exploratory and no con"rmatory conclusions can be made. This position has the logic of adhering to a strict code of alpha spending. If the primary e$cacy variable is not signi"cant, then all the alpha has been spent and no further con"rmatory looks of the data are possible. Other statisticians oppose this stance as too rigid and argue to continue the analyses, and then judge the study as positive or negative depending on the importance of the signi"cant secondary variables and how the results of all the analyses "t together. Neither approach is satisfactory.
The deliberations of the Cardiovascular-Renal Advisory Committee of the Food and Drug Administration (FDA) of the drug Carvedilol for treating heart failure is an excellent example of the above [1,2]. The primary e$cacy variable related to exercise ability and was not statistically signi"cant, however, all-cause mortality was (p(0.001). In fact the Data and Safety Monitoring Committee stopped the study because of the mortality results. The FDA Advisory Committee's statistician, Lemuel MoyeH , took the position that the study was negative because the primary e$cacy variable was not signi"cant, and the mortality results could not be used to make the study positive. The sponsor's statistician, Lloyd Fisher, argued that mortality was so important that it could not be ignored, the results of other variables were consistent with the mortality results and lack of signi"cance on the exercise variable related to the appropriate decision to stop the trial because of the mortality results. This particular case was resolved by considering the above study in addition to supportive evidence from another independent positive study. Carvedilol was ultimately approved for the treatment of heart failure, interestingly without a mortality claim. This "nal FDA approval did not resolve the statistical issues.
In this issue of Statistics in Medicine, Professor Lemuel MoyeH o!ers another strategy for dealing with the conceptual problem of the negative primary variable and positive secondary variables. He calls it the prospective alpha allocation scheme (PAAS). It involves an a priori allocation of alpha at two levels; the usual allocation for primary variables (MoyeH calls this the