Using probabilistic estimation of expression residuals (PEER) to obtain increased power and interpretability of gene expression analyses

Abstract

We present PEER (probabilistic estimation of expression residuals), a software package implementing statistical models that improve the sensitivity and interpretability of genetic associations in population-scale expression data. This approach builds on factor analysis methods that infer broad variance components in the measurements. PEER takes as input transcript profiles and covariates from a set of individuals, and then outputs hidden factors that explain much of the expression variability. Optionally, these factors can be interpreted as pathway or transcription factor activations by providing prior information about which genes are involved in the pathway or targeted by the factor. The inferred factors are used in genetic association analyses. First, they are treated as additional covariates, and are included in the model to increase detection power for mapping expression traits. Second, they are analyzed as phenotypes themselves to understand the causes of global expression variability. PEER extends previous related surrogate variable models and can be implemented within hours on a desktop computer.

Figure 1

Protocol alternatives for applying PEER to analyses of expression QTL studies. PEER infers hidden factors (red triangles), their weights (red star) and a residual gene expression matrix (red square) from a set of gene expression levels (orange squares). If available, experimental confounders (blue triangles) or prior information on groups of genes affected by a factor (blue star) can be included. (a) Results of PEER are processed in downstream QTL analysis on the residual data set. (b,c) Alternatively, the inferred factors can be used (b) as additional covariates or (c) as phenotypes themselves. Orange shapes denote experimental measurements; blue shapes denote prior information including covariates; and the red shapes denote PEER results. Similar shapes of the figures denote similar matrix dimensions. Dashed arrows indicate dependencies that optionally can be taken into account.

Figure 2

Illustrative analysis results of the application of PEER. Data are from Smith and Kruglyak. (a) The number of significant associations between locus genotype and probe expression levels is expected to increase upon the application of PEER (orange line) compared with the standard model (light blue line) for a range of LOD score cutoffs (FDR threshold of 5% shown as dashed line). (b) Diagnostic plot of the factor relevance (ARD parameters). PEER deactivates all but the first three factors in this data set.

Figure 3

Illustrative analysis results of the application of PEER in supervised mode. Data are from Smith and Kruglyak. (a) Density of the genetic associations between genetic markers and genes (per-gene FDR < 5%). (b) When PEER is used to infer transcription factor activations, the resulting variables are themselves influenced by genotype, which are demonstrated here by linkage plots of YAP5 (orange), PHO4 (light blue) and PDR3 (black) factors. Inferred factors capture some of the eQTL hotspots from standard eQTLs.