Detecting Pairwise Interactive Effects of Continuous Random Variables for Biomarker Identification with Small Sample Size

Aberrant changes to interactions among cellular components have been conjectured to be potential causes of abnormalities in cellular functions. By systematic analysis of high-throughput-omics data, researchers hope to detect potential associations among measured variables for better biomarker identification and phenotype prediction. In this paper, we focus on the methods to measure pairwise interactive effects among continuous random variables, representing molecular expressions, with respect to a given categorical outcome. Together with a comprehensive review on the existing measures, we further propose new measures that better estimate interactive effects, especially in small sample size scenarios. We first evaluate the performance of the existing and new methods for both small and large sample sizes based on simulated datasets that shows our proposed methods outperform previous methods in general. The best performing method for small sample size scenarios suggested by simulation experiments is then implemented to estimate interactive effects among genes with respect to the metastasis outcome in two breast cancer studies based on micro-array gene expression datasets. Our results further demonstrate that integrating detected interactive effects together with individual effects can help in finding more accurate biomarkers for breast cancer metastasis, which are indeed involved in important pathways related to cancer metastasis based on gene set enrichment analysis.