Methods for causal inference from gene perturbation experiments and validation

Abstract

Inferring causal effects from observational and interventional data is a highly desirable but ambitious goal. Many of the computational and statistical methods are plagued by fundamental identifiability issues, instability, and unreliable performance, especially for large-scale systems with many measured variables. We present software and provide some validation of a recently developed methodology based on an invariance principle, called invariant causal prediction (ICP). The ICP method quantifies confidence probabilities for inferring causal structures and thus leads to more reliable and confirmatory statements for causal relations and predictions of external intervention effects. We validate the ICP method and some other procedures using large-scale genome-wide gene perturbation experiments in Saccharomyces cerevisiae The results suggest that prediction and prioritization of future experimental interventions, such as gene deletions, can be improved by using our statistical inference techniques.

Keywords: genome database validation; graphical models; interventional–observational data; invariant causal prediction.

Fig. 1.

The activities of two pairs of genes. Observational data are shown as red crosses and interventional data as blue circles. A blue arrow marks the experiment where an intervention on gene YOL067C occurs (activity shown on the x axis in the left panel) and analogously in the right panel. The intervention on the Left is deemed not “strongly successful” [not fulfilling (i) in the definition of an SIE] as the activity of gene YPR089W (y axis) under the intervention is well within its usual range. The intervention on the Right is called strongly successful as the activity of YMR103C (y axis) under the intervention is outside of the previously seen range and likewise for the gene YMR104C on which the intervention occurs (strongly successful area is marked by the green box).

Fig. 2.

The average number of successful interventions (y axis) against the number of selected edges (x axis) for various methods.

Fig. 3.

The graph of estimated causal relations between the biochemical agents in the ref. data. Blue edges are found by an invariant prediction approach, whereas red edges are found if allowing hidden variables and feedback with invariant prediction. Purple edges are found with invariant prediction whether allowing for hidden variables or not. The solid edges (including the gray edges) are all relations that have been reported in either the consensus network according to ref. , or the newly reported edges in ref. , , or . See also SI Appendix, Table S1.