Interim treatment selection using the normal approximation approach in clinical trials

We consider a study starting with two treatment groups and a control group with a planned interim analysis. The inferior treatment group will be dropped after the interim analysis, and only the winning treatment and the control will continue to the end of the study. This 'Two-Stage Winner Design' is based on the concepts of multiple comparison, adaptive design, and winner selection. In a study with such a design, there is less multiplicity, but more adaptability if the interim selection is performed at an early stage. If the interim selection is performed close to the end of the study, the situation becomes the conventional multiple comparison where Dunnett's method may be applied. The unconditional distribution of the final test statistic from the 'winner' treatment is no longer normal, the exact distribution of which is provided in this paper, but numerical integration is needed for its calculation. To avoid complex computations, we propose a normal approximation approach to calculate the type I error, the power, the point estimate, and the confidence intervals. Due to the well understood and attractive properties of the normal distribution, the 'Winner Design' can be easily planned and adequately executed, which is demonstrated by an example. We also provide detailed discussion on how the proposed design should be practically implemented by optimizing the timing of the interim look and the probability of winner selection.