False discovery rate control for high dimensional networks of quantile associations conditioning on covariates

Motivated by gene coexpression pattern analysis, we propose a novel sample quantile contingency (SQUAC) statistic to infer quantile associations conditioning on covariates. It features enhanced flexibility in handling variables with both arbitrary distributions and complex association patterns conditioning on covariates. We first derive its asymptotic null distribution, and then develop a multiple-testing procedure based on the SQUAC statistic to test simultaneously the independence between one pair of variables conditioning on covariates for all p(p-1)/2 pairs. Here, p is the length of the outcomes and could exceed the sample size. The testing procedure does not require resampling or perturbation and thus is computationally efficient. We prove by theory and numerical experiments that this testing method asymptotically controls the false discovery rate. It outperforms all alternative methods when the complex association patterns exist. Applied to a gastric cancer data set, this testing method successfully inferred the gene coexpression networks of early and late stage patients. It identified more changes in the networks which are associated with cancer survivals. We extend our method to the case that both the length of the outcomes and the length of covariates exceed the sample size, and show that the asymptotic theory still holds.