Two-stage designs applying methods differing in costs

Motivation: Two-stage pilot and integrated designs are powerful tools for investigating large numbers of hypotheses. Asymptotically, optimal two-stage designs controlling the familywise error or false discovery rate are considered when costs and effect sizes per measurement differ between stages and total costs are constrained. Results: Depending on the cost and effect size ratios between the measurements, it is generally more powerful to apply two-stage procedures using one measurement method at both stages. For the practically relevant case that the same method is applied at both stages but designing the second-stage measurements raises extra costs, two-stage designs are more powerful than the single-stage design even for large costs ratios. The power of the optimal pilot and integrated two-stage designs generally are similar, however, the integrated approach is less sensitive even to severe design misspecifications in the planning phase.