Multiple testing with discrete data: Proportion of true null hypotheses and two adaptive FDR procedures

Area of Science:

• Statistics
• Biostatistics
• Genomics

Background:

• Multiple testing is common in high-throughput studies.
• Controlling the false discovery rate (FDR) is crucial for reliable results.
• Existing methods struggle with discrete and heterogeneous null distributions of p-values.

Purpose of the Study:

• To develop a new, less biased estimator for the proportion of true null hypotheses.
• To introduce adaptive procedures for FDR control using the novel estimator.
• To evaluate the performance of these adaptive procedures compared to existing methods.

Main Methods:

• Proposed a novel estimator for the proportion of true null hypotheses.
• Developed adaptive Benjamini-Hochberg (aBH) and adaptive Benjamini-Hochberg-Heyse (aBHH) procedures.
• Conducted simulation studies and applied procedures to HIV vaccine efficacy data.

Main Results:

• The new estimator showed reduced upward bias compared to Storey's and other estimators.
• Adaptive procedures (aBH, aBHH) demonstrated increased power over nonadaptive counterparts.
• The aBHH procedure was generally more powerful than aBH and randomized p-value procedures.

Conclusions:

• The proposed adaptive procedures offer improved power for FDR control with discrete p-values.
• The novel estimator and adaptive methods are effective in identifying differentially polymorphic positions in genetic studies.
• These methods enhance the discovery potential in complex biological datasets while maintaining FDR control.