A Stepwise Approach of Finding Dependent Variables via Coefficient of Intrinsic Dependence.

The coefficient of intrinsic dependence (CID) is capable of determining associations among variables without making distributional or functional assumptions regarding random variables. In this study, we developed the partial coefficient of intrinsic dependence (pCID) to facilitate the step-by-step selection of variables that are relevant to a target variable. The strategy of selecting relevant variables using the CID along with the pCID can eliminate interference from other relevant variables. From simulation results, we observed that the proposed method is more sensitive to curvilinearity and more specific to linearity than the combination of Pearsons correlation coefficient and the partial correlation coefficient (PCC/pPCC). This property may provide the opportunity to index different levels of curvilinearity according to CID/pCID outcomes. In practice trials conducted using publicly available microarray data, the CID/pCID procedure successfully identified cold-responsive genes related to three C-repeat binding factors, and was especially effective at identifying some sample-specific gene-gene interactions. Therefore, the proposed strategy may be beneficial in meta-analysis to distinguish general forms of relationships from the noise.