False discovery rate control for multiple testing based on discrete p-values

Area of Science:

• Biostatistics
• Statistical Genetics
• Clinical Trials

Background:

• Multiple testing with discrete p-values presents challenges for traditional false discovery rate (FDR) control.
• Existing methods like the Benjamini-Hochberg (BH) procedure may lack power or applicability to certain p-value distributions.

Purpose of the Study:

• To propose and validate a novel, conservative FDR procedure (BH+) for discrete p-values.
• To demonstrate the enhanced power of BH+ compared to the BH procedure, particularly with mid-p-values.
• To introduce an adaptive version of BH+ and evaluate its performance.

Main Methods:

• Development of the BH+ FDR procedure for discrete p-values.
• Theoretical analysis of BH+ conservativeness and power relative to the BH procedure.
• Application of BH+ to real-world datasets from methylation, HIV, and clinical safety studies.
• Simulation studies to assess the performance of an adaptive BH+ procedure.

Main Results:

• BH+ is proven to be conservative for discrete p-values.
• BH+ demonstrates at least equal power to the BH procedure for superuniform p-values.
• BH+ shows increased power when applied to mid-p-values compared to conventional p-values.
• BH+ yielded considerably more discoveries than the BH procedure in methylation, HIV, and clinical safety studies.
• An adaptive BH+ procedure shows excellent performance in simulations.

Conclusions:

• BH+ is a powerful and conservative FDR procedure applicable to discrete p-values, including mid-p-values and general distributions.
• BH+ offers improved discovery rates in practical applications compared to the standard BH procedure.
• The adaptive BH+ procedure represents a promising advancement for FDR control in complex biological and clinical research.