Capturing heterogeneity in gene expression studies by surrogate variable analysis

Abstract

It has unambiguously been shown that genetic, environmental, demographic, and technical factors may have substantial effects on gene expression levels. In addition to the measured variable(s) of interest, there will tend to be sources of signal due to factors that are unknown, unmeasured, or too complicated to capture through simple models. We show that failing to incorporate these sources of heterogeneity into an analysis can have widespread and detrimental effects on the study. Not only can this reduce power or induce unwanted dependence across genes, but it can also introduce sources of spurious signal to many genes. This phenomenon is true even for well-designed, randomized studies. We introduce "surrogate variable analysis" (SVA) to overcome the problems caused by heterogeneity in expression studies. SVA can be applied in conjunction with standard analysis techniques to accurately capture the relationship between expression and any modeled variables of interest. We apply SVA to disease class, time course, and genetics of gene expression studies. We show that SVA increases the biological accuracy and reproducibility of analyses in genome-wide expression studies.

Conflict of interest statement

Competing interests. The authors have declared that no competing interests exist.

Figures

Figure 1. Impact of Expression Heterogeneity

One thousand gene expression datasets containing EH were simulated, tested, and ranked for differential expression as detailed in Simulated Examples. (A) A boxplot of the standard deviation of the ranks of each gene for differential expression over repeated simulated studies. Results are shown for analyses that ignore expression heterogeneity (Unadjusted), take expression heterogeneity into account by SVA (Adjusted), and for simulated data unaffected by expression heterogeneity (Ideal). (B) For each simulated dataset, a Kolmogorov-Smirnov test was employed to assess whether the p-values of null genes followed the correct null Uniform distribution (Text S1). A quantile–quantile plot of the 1,000 Kolmogorov-Smirnov p-values are shown for the SVA-adjusted analysis (solid line) and the unadjusted analysis (dashed line). It can be seen that the SVA-adjusted analysis provides correctly distributed null p-values, whereas the unadjusted analysis does not due to EH. (C) A plot of expected true positives versus FDR for the SVA-adjusted (solid) and -unadjusted (dashed) analyses. The SVA-adjusted analysis shows increased power to detect true differential expression.

Figure 2. Example of Expression Heterogeneity

(A) A heatmap of a simulated microarray study consisting of 1,000 genes measured on 20 arrays. (B) Genes 1–300 in this simulated study are differentially expressed between two hypothetical treatment groups; here the two groups are shown as an indicator variable for each array. (C) Genes 201–500 in each simulated study are affected by an independent factor that causes EH. This factor is distinct from, but possibly correlated with, the group variable. Here, the factor is shown as a quantitative variable, but it could also be an indicator variable or some linear or nonlinear function of the covariates.

Figure 3. SVA Captures EH Due to Genotype

(A) A plot of significant linkage peaks (p-value < 1e−7) for expression QTL in the Brem et al. [10,21] study by marker location (x-axis) and expression trait location (y-axis). (B) Significant linkage peaks (p-value < 1e−7) after adjusting for surrogate variables. Large trans-linkage peaks on Chromosomes II, III, VII, XII, XIV, and XV have been eliminated without reducing cis-linkage peaks.

Figure 4. Surrogate Variables from Human Studies

(A) A plot of the top surrogate variable estimated from the breast cancer data [22]. The BRCA1 group is relatively homogeneous (triangles), but the BRCA2 group shows substantial heterogeneity (pluses). (B) A plot of tissue type versus array for the Rodwell et al. [7] study (dotted line) and the top surrogate variable estimated from the expression data when tissue was ignored (dashed line). There is strong correlation between the top surrogate variable and the tissue type variable.

Figure 5. Null p-Values under Heterogeneity

A histogram of the null p-values from a single simulated experiment affected by heterogeneity. The distribution of these p-values appears identical to a complete set of p-values from an experiment that is not subject to heterogeneity. Therefore, it is not possible to identify and account for heterogeneity by analyzing one-dimensional p-values or test-statistics (see also Text S1).