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 largescale 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.interventional-observational data | invariant causal prediction | genome database validation | graphical models I n this article, we discuss statistical methods for causal inference from perturbation experiments. As this is a rather general topic, we focus on the following problem: based on data from observational and perturbation settings, we want to predict the effect and outcome of an unseen and new intervention or perturbation. Taking applications in genomics as an example, a typical task is as follows: based on observational data from wild-type organisms and interventional data from gene knockout or knockdown experiments, we want to predict the effect of a new gene knockout or knockdown on a phenotype of interest. For example, the organism is the model plant Arabidopsis thaliana, the gene knockouts correspond to mutant plants, and the phenotype of interest is the time it takes until the plant is flowering (1).From a methodological viewpoint, the prediction of unseen future interventions belongs to the area of causal inference where one aims to quantify presence and strength of causal effects among various variables. Loosely speaking, a causal effect is the effect of an external intervention (or say the response to a "What if I do?" question). The corresponding theory, e.g., using Pearl's do-operator (2), provides a link between causal effects and perturbations or randomized experiments. We mostly assume here that all of the variables in the causal model (for inferring causal effects) are observed: the case with hidden variables is mentioned only briefly in a later section, although it is an important theme in causal inference (due to the problem of hidden confounding variables) (cf. refs. 2 and 3).A popular and powerful route for causal modeling is given by structural equation models (SEMs) (2, 4). We consider a set of random variables X 1 , . . . , X p , X p+1 , and we often denote by Y = X 1 , emphasizing that Y is our response variable of interest (e.g., a phenotype of interest). The main building blocks of a SEM...

Causal Inference by using Invariant Prediction: Identification and Confidence Intervals

“…We obtain rather different results which are in reasonable agreement with the speculated ‘ground truth’ in Sachs (); see Meinshausen et al . ().…”

Identifiability and experimental design in perturbation studies

“…to reduce the effect of noise, incorporate heterogeneous data sets, or allow for the analysis of single cell data (Greenfield et al, 2013;Santra et al, 2018;Klinger and Blüthgen, 2018;Santra et al, 2013;Kang et al, 2015;Dorel et al, 2018) and have thus become a standard research tool. Nevertheless, identifiability (Hengl et al, 2007;Godfrey and DiStefano, 1985) of the inferred network parameters within a specific perturbation setup has not yet been rigorously analysed, even though a limited number of practically feasible perturbations renders many systems underdetermined (De Smet and Marchal, 2010;Meinshausen et al, 2016;Bonneau et al, 2006). Some inference methods do apply different heuristics, such as network sparsity, to justify parameter regularisation (Gardner et al, 2003;Bonneau et al, 2006;Tegner et al, 2003), or numerically analyse identifiability through an exploration of the parameter space using a profile likelihood approach (Raue et al, 2009).…”

Inferability of transcriptional networks from large scale gene deletion studies

“…knockout libraries, ranging from microbes 3,4 to higher eukaryotes 5 and open up a much more informative data source than inferring gene regulatory networks from unspecific perturbations, such as stress or changes in growth conditions 6 . However, the detection of direct interactions between two genes from association measures -for example the covariance between transcript levels -remains a highly non-trivial task, given the significant noise among biological replicates, the frequent case where the number of parameters exceeds the number of independent data points, and the high dimensionality of the inference problem.…”

“…Inference of transcriptional networks on a genome scale is best realised by methods that are (i) asymptotically unbiased, (ii) scalable to large network sizes, (iii) sensitive to feed-forward loops 10 , and (iv) can handle data sets with and without knowledge about which nodes are targeted by experimentally induced perturbations 7,[11][12][13][14][15] (Supplementary Note 2). Inference methods for directed networks typically require individual perturbation of all nodes 7 or many perturbations of different strengths to compute conditional association measures 6,16 or conditional probabilities 17 .…”

“…Comparison of the analytical formula, Eq. (1) and the inference algorithm by calculating the number of inferable links with respect to the number of perturbed nodes, N p .Supplementary NotesAlgorithms based on partial correlations [1, 2] -a method designed to discriminate 5 between direct and indirect interactions -show comparatively low performance for6 predicting direct correlations between transcript levels using transcriptome data but excellent performance for predicting contact points of protein structures . To understand the difference in performance of partial correlations, we9 investigate Eq.…”