Symmetry and Complexity in Gene Association Networks Using the Generalized Correlation Coefficient

High-dimensional gene expression data cause challenges for traditional statistical tools, particularly when dealing with non-linear relationships and outliers. The present study addresses these challenges by employing a generalized correlation coefficient (GCC) that incorporates a flexibility parameter, allowing it to adapt to varying levels of symmetry and asymmetry in the data distribution. This adaptability is crucial for analyzing gene association networks, where the GCC demonstrates advantages over traditional measures such as Kendall, Pearson, and Spearman coefficients. We introduce two novel adaptations of this metric, enhancing its precision and broadening its applicability in the context of complex gene interactions. By applying the GCC to relevance networks, we show how different levels of the flexibility parameter reveal distinct patterns in gene interactions, capturing both linear and non-linear relationships. The maximum likelihood and Spearman-based estimators of the GCC offer a refined approach for disentangling the complexity of biological networks, with potential implications for precision medicine. Our methodology provides a powerful tool for constructing and interpreting relevance networks in biomedicine, supporting advancements in the understanding of biological interactions and healthcare research.