Classes of Multiple Decision Functions Strongly Controlling FWER and FDR.

Area of Science:

• Statistics
• Statistical methodology
• Data analysis

Background:

• Multiple decision functions are crucial for controlling error rates in statistical testing.
• Existing methods like the Benjamini-Hochberg (BH) procedure control the false discovery rate (FDR).
• There is a need for methods that optimize Type II error criteria, such as the missed discovery rate (MDR), while controlling Type I error rates.

Purpose of the Study:

• To describe two general classes of multiple decision functions.
• To explore the potential for finding optimal functions that control family-wise error rate (FWER) or false discovery rate (FDR) while minimizing the missed discovery rate (MDR).
• To evaluate the performance of these new functions against established methods.

Main Methods:

• Description of two classes of multiple decision functions.
• Simulation study using gamma-distributed data.
• Comparison of a novel FDR-controlling procedure with the Benjamini-Hochberg (BH) procedure.

Main Results:

• The proposed FDR-controlling procedure demonstrated a gain in missed discovery rate (MDR) compared to the Benjamini-Hochberg (BH) procedure.
• The developed functions offer the possibility of optimizing Type II error control under FWER or FDR constraints.
• Simulation results indicate improved performance in specific data scenarios.

Conclusions:

• The described multiple decision functions provide a framework for enhanced error rate control in multiple testing.
• These methods show potential for improved efficiency in detecting true effects, particularly in high-dimensional datasets.
• The findings suggest broader applicability in statistical analysis, especially for complex data structures.