Optimized multi-stage designs controlling the false discovery or the family-wise error rate

Area of Science:

• Statistical methodology
• Biostatistics
• Experimental design

Background:

• Investigating numerous hypotheses necessitates efficient allocation of limited observations.
• Single-stage designs distribute observations equally, potentially underpowering promising hypotheses.
• Sequential approaches offer a way to optimize resource allocation in hypothesis testing.

Purpose of the Study:

• To propose and evaluate multi-stage trial designs for hypothesis testing.
• To control for family-wise error rate (FWER) or false discovery rate (FDR).
• To optimize power through sequential sample size allocation and stopping boundaries.

Main Methods:

• Development of multi-stage procedures for FWER and FDR control.
• Derivation of asymptotically optimal stopping boundaries and sample size allocations.
• Comparison of optimized multi-stage designs with classical single-stage designs.
• Evaluation of integrated versus pilot designs and the impact of the number of stages.

Main Results:

• Optimized multi-stage designs significantly increase statistical power compared to single-stage designs.
• Increasing the number of stages (up to four) further enhances power, with diminishing returns.
• Integrated and pilot designs show similar power, but integrated FDR-controlling designs are more robust.
• The power difference between FWER and FDR control diminishes with more stages.

Conclusions:

• Sequential testing, by dropping non-promising hypotheses early, is the most critical factor for increasing trial power.
• Multi-stage designs offer substantial power gains over single-stage approaches.
• The choice between integrated and pilot designs has less impact on power than the sequential nature of the trial.