Ranking analysis of correlation coefficients in gene expressions

Development of statistical methods has become very necessary for large-scale correlation analysis in the current “omic” data. We propose ranking analysis of correlation coefficients (RAC) based on transforming correlation matrix into correlation vector and conducting a “locally ranking” strategy that significantly reduces computational complexity and load. RAC gives estimation of null correlation distribution and an estimator of false discovery rate (FDR) for finding gene pairs of being correlated in expressions obtained by comparison between the ranked observed correlation coefficients and the ranked estimated ones at a given threshold level. The simulated and real data show that the estimated null correlation distribution is exactly the same with the true one and the FDR estimator works well in various scenarios. By applying our RAC, in the null dataset, no gene pairs were found but, in the human cancer dataset, 837 gene pairs were found to have positively correlated expression variations at FDR ≤ 5%. RAC performs well in multiple conditions (classes), each with 3 or more replicate observations.