Estimating the proportion of true null hypotheses when the statistics are discrete

Area of Science:

• Biostatistics
• Bioinformatics
• Statistical Genetics

Background:

• Estimating π0 (proportion of true null hypotheses) is crucial in high-dimensional testing.
• Discrete test statistics present challenges due to non-uniform null distributions, unlike continuous ones.
• Existing π0 estimators may falter with discrete data, necessitating new approaches.

Purpose of the Study:

• To introduce novel π0 estimators suitable for discrete test statistics.
• To evaluate the performance of existing methods adapted for discrete testing.
• To demonstrate the application of these estimators in biological data analysis.

Main Methods:

• Development and implementation of regression and 'T' methods for π0 estimation.
• Assessment of existing continuous test statistic methods on discrete data.
• R software implementation for practical application.

Main Results:

• The proposed regression and 'T' methods show strong performance with discrete test statistics.
• Established methods adapted from continuous tests exhibit variable performance on discrete data.
• Successful application of new estimators to RNA-seq and SNP data analysis.

Conclusions:

• Novel π0 estimators provide reliable estimates for discrete testing scenarios.
• These methods enhance the analysis of complex, high-throughput biological datasets.
• The R package facilitates the application of these advanced statistical techniques.