Estimating the null distribution to adjust observed confidence levels for genome-scale screening

Area of Science:

• Statistics
• Bioinformatics
• Genomics

Background:

• The multiple testing problem is significant in analyzing large biological datasets.
• Estimating null distributions offers a novel approach to address this challenge.
• Existing methods can be improved by incorporating estimated null distributions.

Purpose of the Study:

• To evaluate the utility of estimating null distributions for multiple-comparison procedures (MCPs).
• To introduce and assess a confidence-posterior MCP (CPMCP) framework.
• To develop an information-theoretic score for guiding the use of estimated null distributions.

Main Methods:

• Formulating estimators for test statistic or p-value distributions under a null hypothesis.
• Applying an MCP based on minimizing expected loss with respect to a confidence posterior.
• Conducting simulation studies using generic and gene expression data.
• Developing an information-theoretic score based on ancillarity and inferential relevance.

Main Results:

• Estimating null distributions can improve various MCPs, including the proposed CPMCP.
• Conditional inference is markedly improved by using estimated null distributions as ancillary statistics.
• However, estimating null distributions can worsen conservative bias with heavy-tailed data.
• The information-theoretic score provides a quantitative measure for decision-making.

Conclusions:

• Estimating null distributions is a valuable tool for multiple testing in large-scale biological data analysis.
• The CPMCP offers a flexible framework, particularly for genomic screening.
• Researchers can use the proposed score to judiciously apply estimated null distributions.
• The methods are demonstrated on gene expression microarray data.