A consistency-adjusted alpha-adaptive strategy for sequential testing

In a clinical trial with two clinically important endpoints, each of which can fully characterize a treatment benefit to support an efficacy claim by itself, a minimum degree of consistency in the findings is expected; otherwise interpretation of study findings can be problematic. Clinical trial literature contains examples where lack of consistency in the findings of clinically relevant endpoints led to difficulties in interpreting study results. The aim of this paper is to introduce this consistency concept at the study design stage and investigate the consequences of its implementation in the statistical analysis plan. The proposed methodology allows testing of hierarchically ordered endpoints to proceed as long as a pre-specified consistency criterion is met. In addition, while an initial allocation of the alpha level is specified for the ordered endpoints at the design stage, the methodology allows the alpha level allocated to the second endpoint to be adaptive to the findings of the first endpoint. In addition, the methodology takes into account the correlation between the endpoints in calculating the significance level and the power of the test for the next endpoint. The proposed Consistency-Adjusted Alpha-Adaptive Strategy (CAAAS) is very general. Several of the well-known multiplicity adjustment approaches arise as special cases of this strategy by appropriate selection of the consistency level and the form of alpha-adaptation function. We discuss control of the Type I error rate as well as power of the proposed methodology and consider its application to clinical trial data.