Two-stage designs applying methods differing in costs.

Area of Science:

• Statistical methodology
• Biostatistics
• Hypothesis testing

Background:

• Two-stage pilot and integrated designs are effective for investigating numerous hypotheses.
• Asymptotically optimal designs are considered under differing costs and effect sizes across stages with constrained total costs.

Purpose of the Study:

• To evaluate the power and sensitivity of two-stage designs compared to single-stage designs.
• To determine optimal two-stage procedures when measurement costs and effect sizes vary.

Main Methods:

• Asymptotic optimality criteria were used to derive two-stage designs.
• Familywise error rate and false discovery rate were controlled.
• R programs are available for calculating optimal designs.

Main Results:

• Two-stage procedures using a single measurement method at both stages are generally more powerful.
• Even with increased second-stage costs, two-stage designs outperform single-stage designs.
• Integrated two-stage designs show similar power to pilot designs but are more robust to planning errors.

Conclusions:

• Two-stage designs are advantageous for hypothesis testing, particularly when measurement costs differ.
• The integrated two-stage approach offers enhanced robustness against design misspecifications.