Similar approaches have previously been shown to improve power for eQTL mapping (Leek and Storey 2007; Choy et al. 2008; Kang et al. 2008; Listgarten et al. 2010; Pickrell et al. 2010; Stegle et al. 2010). Compared to the linear mixed model analyses (Kang et al. 2008; Listgarten et al. 2010), our approach is more similar to surrogate variable analysis (SVA) (Leek and Storey 2007) or to the Bayesian factor analysis model (VBQTL) used by Stegle et al. (2010) and Pickrell et al. (2010), in that the unobserved confounders are modeled explicitly. Our analysis differs from these principal component analysis (PCA) or VBQTL models in their control of model complexity. For genome-wide eQTL analysis, SVA chooses significant PCs based on permutation based P-value without involving SNP information. Stegle et al. (2010) uses automatic relevance detection (ARD) prior to switching off unused factors, and Pickrell et al. (2010) chooses the number of PCs that gives the largest number of eQTLs. Our approach selects the number of PCs that gives the largest number of local-eQTLs (defined as a SNP within 1 Mb
