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. AVAILABILITY R-programs (R, 2005) to calculate asymptotically optimal designs are available on: http://statistics.msi.meduniwien.ac.at/index.php?page=ao2stage