Principal component of explained variance: An efficient and optimal data dimension reduction framework for association studies

Abstract

The genomics era has led to an increase in the dimensionality of data collected in the investigation of biological questions. In this context, dimension-reduction techniques can be used to summarise high-dimensional signals into low-dimensional ones, to further test for association with one or more covariates of interest. This paper revisits one such approach, previously known as principal component of heritability and renamed here as principal component of explained variance (PCEV). As its name suggests, the PCEV seeks a linear combination of outcomes in an optimal manner, by maximising the proportion of variance explained by one or several covariates of interest. By construction, this method optimises power; however, due to its computational complexity, it has unfortunately received little attention in the past. Here, we propose a general analytical PCEV framework that builds on the assets of the original method, i.e. conceptually simple and free of tuning parameters. Moreover, our framework extends the range of applications of the original procedure by providing a computationally simple strategy for high-dimensional outcomes, along with exact and asymptotic testing procedures that drastically reduce its computational cost. We investigate the merits of the PCEV using an extensive set of simulations. Furthermore, the use of the PCEV approach is illustrated using three examples taken from the fields of epigenetics and brain imaging.

Whole-genome bisulfite sequencing in systemic sclerosis provides novel targets to understand disease pathogenesis

“…Simultaneously, within each CpG-based DMR, we first regressed out the effect of age and obtained residual methylation level on each CpG dinucleotide. We then used a multivariate method (PCEV [24]) to test associations between residual methylation levels and the binary disease status. We followed this by examining the PCEV-derived variable importance measures to identify the dinucleotide most strongly associated with disease status in the DMR.…”

Application of novel and existing methods to identify genes with evidence of epigenetic association: results from GAW20

“…To analyze unrelated individuals, Zhao et al used PCEV [ 25 ], which seeks to identify the linear combination of outcomes that maximizes the proportion of the variance being explained by the covariate. They contrasted the method using the VC-score test [ 26 ], which reduces significantly the model degrees of freedom compared to standard multivariate regression models.…”

“…Zhao et al restricted their analysis to genes on chromosomes 11 and 19 and employed 2 multimarker approaches, SKAT and PCEV [ 25 ], described in Theme 1. There was some overlap in the top results of the SKAT and PCEV approaches: OR8H3 was in the top 5 genes associated with change in HDL-C for both methods, and P2RX3 was in the top 5 genes associated with change in TG for both methods.…”

“…Methylation data on chromosomes 11 and 19 were grouped into 1484 and 1698 genes, respectively, and transformed using the logit function. The principal components of explained variance (PCEV [ 25 ]) and a variance component (VC) score test [ 26 ] were used to analyze the unrelated individuals. Family data were analyzed via an extension of a VC-score test [ 26 ].…”