Statistical Methods for Detecting Nonlinear Relationships in Gene Expression and Omics Data: A Review.

Area of Science:

• Omics data analysis
• Bioinformatics
• Computational biology

Background:

• High-throughput technologies like RNA-seq and single-cell transcriptomics produce large, high-dimensional gene expression datasets.
• These datasets often exhibit complex nonlinear dependence structures that classical linear methods may miss.
• Existing nonlinear dependence measures are diverse but lack consistent comparative evaluations, leading to a fragmented field.

Purpose of the Study:

• To systematically review and organize various nonlinear dependence methods.
• To critically compare their statistical behavior, strengths, limitations, and failure modes.
• To provide scenario-based guidance for method selection in transcriptomics and functional genomics.

Main Methods:

• Categorization of nonlinear dependence methods into major families (e.g., information-theoretic, kernel-based, copula-based).
• Critical comparison of statistical properties, advantages, disadvantages, and typical failure patterns.
• Identification of trade-offs between flexibility, robustness, interpretability, and computational scalability.

Main Results:

• The review organizes diverse nonlinear methods into coherent methodological families.
• It provides a comparative analysis of their performance characteristics and failure modes.
• Key trade-offs influencing method selection are identified.

Conclusions:

• Method selection for nonlinear dependence in omics data requires matching inferential goals with method assumptions and constraints.
• Understanding method-specific limitations and trade-offs is crucial for reliable analysis.
• This work aims to support principled, application-specific use of nonlinear methods in modern omics research.