A new p-value based multiple testing procedure for generalized linear models.

Area of Science:

• Statistics
• Statistical Modeling
• Computational Statistics

Background:

• Generalized linear models (GLMs) are widely used but face challenges in multiple testing due to heterogeneous variances and parameter dependencies.
• Existing methods struggle to control the false discovery rate (FDR) when test statistics are arbitrarily dependent.

Purpose of the Study:

• To develop a novel p-value-based multiple testing approach for GLMs.
• To address the challenge of controlling the FDR under arbitrary dependency structures.
• To provide a versatile statistical framework with efficient computational algorithms.

Main Methods:

• Development of a p-value-based multiple testing framework for GLMs.
• Integration of tools for model matrix construction, including random row permutations and Model-X knockoffs.
• Efficient algorithms to solve quadratic matrix equations for constructing paired p-values, suitable for a two-step testing procedure.

Main Results:

• The proposed approach effectively controls the false discovery rate (FDR) at a specified level.
• Theoretical analysis confirms the desirable properties of the new methodology.
• Empirical evaluations demonstrate strong performance across various simulation scenarios.

Conclusions:

• The novel p-value-based method offers a robust solution for multiple testing in generalized linear models.
• The developed framework and algorithms enhance the applicability of FDR control in complex statistical settings.
• This approach provides a valuable tool for researchers working with dependent test statistics in GLMs.