Considering dependence among genes and markers for false discovery control in eQTL mapping

Abstract

Motivation: Multiple comparison adjustment is a significant and challenging statistical issue in large-scale biological studies. In previous studies, dependence among genes is largely ignored. However, such dependence may be strong for some genomic-scale studies such as genetical genomics [also called expression quantitative trait loci (eQTL) mapping] in which thousands of genes are treated as quantitative traits and mapped to different genetical markers. Besides the dependence among markers, the dependence among the expression levels of genes can also have a significant impact on data analysis and interpretation.

Results: In this article, we propose to consider both the mean as well as the variance of false discovery number for multiple comparison adjustment to handle dependence among hypotheses. This is achieved by developing a variance estimator for false discovery number, and using the upper bound of false discovery proportion (uFDP) for false discovery control. More importantly, we introduce a weighted version of uFDP (wuFDP) control to improve the statistical power of eQTL identification. In addition, the wuFDP approach can better control false positives than false discovery rate (FDR) and uFDP approaches when markers are in linkage disequilibrium. The relative performance of uFDP control and wuFDP control is illustrated through simulation studies and real data analysis.

Supplementary information: Supplementary figures, tables and appendices are available at Bioinformatics online.

Fig. 1.

Boxplots of FDP or weighted FDP among 1000 simulations for FDR, uFDP and wuFDP controls. The differential signal β=0.5. The threshold for FDR, uFDP and wuFDP is 0.1. z_1−α is 1.65. The number of correlated non-differentially expressed genes (nc) varies from 0 to 200. The correlation among these genes (c) varies from 0.6 to 0.9.

Fig. 2.

Statistical power for different differential signal (0.3–0.9). The number of correlated non-differentially expressed genes varies from 50 to 200. The correlation among these genes varies from 0.6 to 0.9. The threshold for uFDP and wuFDP is 0.1. z_1−α is 1.65. Triangle symbol line is for wuFDP control and cross symbol line is for uFDP control.

Fig. 3.

ROC curves for FDR, uFDP and wuFDP controls. The differential signal β=0.4. Two hundred non-differentially expressed gene are correlated with correlation 0.7. z_1−α is 1.65 to control Pr(V/R≥uFDP) and Pr(∑w_iv_i/∑w_ir_i≥wuFDP) less than or equal to 0.05. Triangle symbol line is for wuFDP control, cross symbol line is for uFDP control and circle symbol line is for FDR.