  When designing confirmatory Phase 3 studies, one usually evaluates one or
more efficacious and safe treatment option(s) based on data from previous
studies. However, several retrospective research articles reported the
phenomenon of ``diminished treatment effect in Phase 3'' based on many case
studies. Even under basic assumptions, it was shown that the commonly used
estimator could substantially overestimate the efficacy of selected group(s).
As alternatives, we propose a class of computational methods to reduce
estimation bias and mean squared error (MSE) with a broader scope of multiple
treatment groups and flexibility to accommodate summary results by group as
input. Based on simulation studies and a real data example, we provide
practical implementation guidance for this class of methods under different
scenarios. For more complicated problems, our framework can serve as a starting
point with additional layers built in. Proposed methods can also be widely
applied to other selection problems.
