Model-free latent confounder-adjusted feature selection with FDR control

Omics-wide association analysis is an important tool for investigating medical and human health. Unobserved confounders can cause adverse effects to association analysis, thence adjusting for latent confounders is very crucial. However, the existing latent confounder-adjusted analysis methods lack effective false discovery rate (FDR) control and rely on some specific model assumptions. Motivated by this, the paper firstly proposes a novel latent confounding single index model for omics data. It is model-free in performance of allowing the connections between the response and covariates can be connected by any unknown monotonic link function, and the model's random errors can follow any unknown distribution. Utilizing the proposed model, the paper further employs the data splitting approach to develop a model-free and latent confounder-adjusted feature selection method with FDR control. The theoretical results demonstrate asymptotic FDR control properties of the new method and the numerical analysis results show it can control FDR for no-confounding, sparse confounding and dense confounding scenarios. The analysis of the actual gene expression data demonstrates that it can detect the co-expression genes interacting with the target genes in the presence of latent confounding. Such findings can help to comprehend the connects between pediatric small round blue cell cancers and gene network.