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How should we measure proportionality on relative gene expression data?

Ionas Erb1,2, Cedric Notredame3,4

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Summary

Log-ratio analysis offers a normalization-free method for gene expression studies. This research introduces a symmetric proportionality coefficient to accurately identify proportional gene pairs, improving analysis sensitivity.

Keywords:
Co-expressionCompositional dataData normalizationGene networksLog-ratio analysisSpurious correlation

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Area of Science:

  • Bioinformatics
  • Computational Biology
  • Gene Expression Analysis

Background:

  • Correlation analysis in gene expression is widely used but often yields spurious results without proper normalization.
  • Normalization is crucial for accurate gene expression correlation, but can be bypassed using log-ratio analysis.
  • Log-ratio analysis identifies proportional gene pairs, whose correlation is reliable even in unnormalized data.

Purpose of the Study:

  • To analytically derive how spurious proportionality arises from scaling methods in gene expression analysis.
  • To introduce and analyze a symmetric proportionality coefficient for more robust identification of proportional gene pairs.
  • To investigate the impact of reference gene selection on proportionality detection and explore links to partial correlation.

Main Methods:

  • Analytical derivation of spurious proportionality introduced by scaling methods.
  • Development and application of a symmetric proportionality coefficient.
  • Exploration of the relationship between proportionality and partial correlation, deriving a partial proportionality coefficient.

Main Results:

  • Scaling methods can introduce spurious proportionality; a symmetric coefficient offers advantages over existing statistics.
  • The choice of reference gene significantly influences the identification of proportional gene pairs.
  • Using an unchanged gene as a reference enhances sensitivity in detecting proportional gene pairs.
  • Expressions for a partial proportionality coefficient were derived, linking proportionality to partial correlation.

Conclusions:

  • Log-ratio analysis provides a robust alternative to correlation for gene expression analysis, especially without normalization.
  • The proposed symmetric proportionality coefficient and careful reference gene selection improve the accuracy and sensitivity of identifying proportional gene pairs.
  • The study advances understanding of proportionality in gene expression data and its relationship with partial correlation.