Joint estimation of causal effects from observational and intervention gene expression data

Andrea Rau,Florence Jaffrézic,Grégory Nuel

doi:10.1186/1752-0509-7-111

Abstract

BackgroundIn recent years, there has been great interest in using transcriptomic data to infer gene regulatory networks. For the time being, methodological development in this area has primarily made use of graphical Gaussian models for observational wild-type data, resulting in undirected graphs that are not able to accurately highlight causal relationships among genes. In the present work, we seek to improve the estimation of causal effects among genes by jointly modeling observational transcriptomic data with arbitrarily complex intervention data obtained by performing partial, single, or multiple gene knock-outs or knock-downs.ResultsUsing the framework of causal Gaussian Bayesian networks, we propose a Markov chain Monte Carlo algorithm with a Mallows proposal model and analytical likelihood maximization to sample from the posterior distribution of causal node orderings, and in turn, to estimate causal effects. The main advantage of the proposed algorithm over previously proposed methods is its flexibility to accommodate any kind of intervention design, including partial or multiple knock-out experiments. Using simulated data as well as data from the Dialogue for Reverse Engineering Assessments and Methods (DREAM) 2007 challenge, the proposed method was compared to two alternative approaches: one requiring a complete, single knock-out design, and one able to model only observational data.ConclusionsThe proposed algorithm was found to perform as well as, and in most cases better, than the alternative methods in terms of accuracy for the estimation of causal effects. In addition, multiple knock-outs proved to contribute valuable additional information compared to single knock-outs. Finally, the simulation study confirmed that it is not possible to estimate the causal ordering of genes from observational data alone. In all cases, we found that the inclusion of intervention experiments enabled more accurate estimation of causal regulatory relationships than the use of wild-type data alone.

Highlights

In recent years, there has been great interest in using transcriptomic data to infer gene regulatory networks
In the simulation study presented above, the proposed Markov chain MonteCarlo (MCMC)-Mallows algorithm was found to perform better than Pinna [11] and IDA [7] in terms of accuracy of estimation of the causal effects, as evidenced by the tendancy to have larger Area under the ROC curve (AUROC), larger Spearman correlation coefficients and smaller mean squared error (MSE) than the other approaches
Our simulations demonstrated that multiple knock-out designs contributed valuable additional information for causal network inference beyond single knockouts; we anticipate that the need for methods able to accommodate complex intervention designs will only increase as such data become more common

Summary

Introduction

There has been great interest in using transcriptomic data to infer gene regulatory networks. In the IDA, the PC-algorithm [2,8,9] is first applied to find the associated completed partially directed acyclic graph (CPDAG), corresponding to the graphs belonging to the appropriate equivalence class Following this step, bounds for total causal effects of each gene on the others are estimated using intervention calculus [10] for each directed acyclic graph (DAG) in the equivalence class. If intervention experiments such as gene knock-outs or knock-downs are available, it is valuable to jointly perform causal network inference from a combination of wild-type and intervention data One such approach has been proposed by Pinna et al [11], based on the simple idea of calculating the deviation between observed gene expression values and the expression under each systematic intervention. As with the originally proposed method, this approach requires systematic single knock-outs for all genes in the network

Objectives

Methods

Results

Conclusion