Multiple-input multiple-output causal strategies for gene selection

Abstract

Background: Traditional strategies for selecting variables in high dimensional classification problems aim to find sets of maximally relevant variables able to explain the target variations. If these techniques may be effective in generalization accuracy they often do not reveal direct causes. The latter is essentially related to the fact that high correlation (or relevance) does not imply causation. In this study, we show how to efficiently incorporate causal information into gene selection by moving from a single-input single-output to a multiple-input multiple-output setting.

Results: We show in synthetic case study that a better prioritization of causal variables can be obtained by considering a relevance score which incorporates a causal term. In addition we show, in a meta-analysis study of six publicly available breast cancer microarray datasets, that the improvement occurs also in terms of accuracy. The biological interpretation of the results confirms the potential of a causal approach to gene selection.

Conclusions: Integrating causal information into gene selection algorithms is effective both in terms of prediction accuracy and biological interpretation.

Figure 1

Single-output case with different causal patterns: (i) common effect or explaining away effect configuration involving x₁, x₂ and y₁; (ii) spouse configuration involving x₅ and y₁; (iii) common cause configuration involving y₁, x₃, x₄; and (iv) causal chain configuration involving x₁, y₁, x₄.

Figure 2

Two-output case with different causal patterns: (i) common effect configuration involving x₃, y₁ and y₂; (ii) spouse configuration involving y₂ and x₆; (iii) common cause configuration involving x₁, y₁ and y₂; and (iv) causal chain configuration involving x₁, y₂ and x₇.

Figure 3

Two-inputs two-outputs causal pattern.

Figure 4

Bayesian causal network used for synthetic experiment. The green node 9 denotes the non observable variable. The three red nodes denote the targets of the multiple-output classification problem. The isolated node (30-40) represents a set of 11 independent variables.

Figure 5

Synthetic data experiment: average ranking of direct causes for different values of λ as a function of the noise standard deviation. Dotted lines are used to denote the 90% confidence interval estimated on the basis of 150 trials.

Figure 6

Synthetic data experiment: probability of selecting a direct cause among the first 5 ranked variables for different values of λ as a function of the noise standard deviation. Dotted lines are used to denote the 90% confidence interval estimated on the basis of 150 trials.

Figure 7

Most enriched GO terms with respect to λ according to a pre-ranked gene set enrichment analysis (GSEA): (A) GO terms enriched in the conventional ranking and having a high degree of causality for tumorigenesis; (B) GO terms increasingly enriched with respect to larger λ, suggesting they are putative causes for tumorigenesis; (C) GO terms decreasingly enriched with respect to larger λ, suggesting they are putative effects for tumorigenesis. The normalized enrichment score (NES) depends on the genome-ranking of the genes, which in turn depends on λ. Larger the NES of a GO term, stronger the association of this gene set with survival; the sign of NES reflects the direction of association of the GO term with survival, a positive score meaning that over-expression of the genes implies worst survival and inversely.