Multiple Testing of General Dependence by Quantile-Based Contingency Tables with an Application in Identifying Gene Co-expression Network Change Associated with Cancer Survival

Gene co-expression networks describe the interactions among a set of regulators and other substances in the cell to govern the gene expression levels of mRNA and proteins. One popular way to estimate them is to infer the network between gene expression levels, which can be formulated as a high dimensional network estimation/testing problem. The existing methods focus on networks measuring linear dependence or rank association, which cannot always represent gene regulatory mechanisms. Without parametric assumptions on the marginal distributions of continuous random variables and their dependence structure, we propose a test statistic to test whether the expression levels of two genes are independent. Based on the test statistic, we further propose a multiple testing procedure that can simultaneously test independence among all pairs of variables conditioning on other covariates. The numerical experiments show that the performance of our method significantly outperforms other methods when complex dependence structures exist. Even when non-linear or non-rank-associated dependence exists, the proposed method performs much better in both validity and efficiency. Theoretically, we prove that the proposed method can control false discovery rate (FDR) under the desired level. We apply this method on a gastric cancer data set to investigate the change in gene co-expression networks of patients with early or late stages, and show that our method can identify more changes that relate to the survival of the patients.