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Abstract
The mainstream of research in genetics, epigenetics, and imaging data analysis focuses on statistical association or exploring statistical dependence between variables. Despite their significant progresses in genetic research, understanding the etiology and mechanism of complex phenotypes remains elusive. Using association analysis as a major analytical platform for the complex data analysis is a key issue that hampers the theoretic development of genomic science and its application in practice. Causal inference is an essential component for the discovery of mechanical relationships among complex phenotypes. Many researchers suggest making the transition from association to causation. Despite its fundamental role in science, engineering, and biomedicine, the traditional methods for causal inference require at least three variables. However, quantitative genetic analysis such as QTL, eQTL, mQTL, and genomic-imaging data analysis requires exploring the causal relationships between two variables. This paper will focus on bivariate causal discovery with continuous variables. We will introduce independence of cause and mechanism (ICM) as a basic principle for causal inference, algorithmic information theory and additive noise model (ANM) as major tools for bivariate causal discovery. Large-scale simulations will be performed to evaluate the feasibility of the ANM for bivariate causal discovery. To further evaluate their performance for causal inference, the ANM will be applied to the construction of gene regulatory networks. Also, the ANM will be applied to trait-imaging data analysis to illustrate three scenarios: presence of both causation and association, presence of association while absence of causation, and presence of causation, while lack of association between two variables. Telling cause from effect between two continuous variables from observational data is one of the fundamental and challenging problems in omics and imaging data analysis. Our preliminary simulations and real data analysis will show that the ANMs will be one of choice for bivariate causal discovery in genomic and imaging data analysis.
Highlights
Despite significant progress in dissecting the genetic architecture of complex diseases by association analysis, understanding the etiology, and mechanism of complex diseases remains elusive
To illustrate application of the algorithmic mutual information, we show that independence of cause and mechanism will imply that the cause X and error EY in the non-linear function model (1) are independent (For details, please see Supplementary Note C)
additive noise model (ANM) With Different Non-linear Functions. To investigate their feasibility for causal inference, the ANMs were applied to simulation data
Summary
Despite significant progress in dissecting the genetic architecture of complex diseases by association analysis, understanding the etiology, and mechanism of complex diseases remains elusive. Using association analysis and machine learning systems that operate, almost exclusively, in a statistical, or model-free modes as a major analytic platform for genetic studies of complex diseases is a key issue that hampers the discovery of mechanisms underlying complex traits (Pearl, 2018). In terms of daily life language, causation is the effects of actions or interventions that perturb the system or indicates that one event is the result of the occurrence of the other event. The causal effect can be defined using intervention calculus (Mooij et al, 2016). If an external intervention that is from outside the system under consideration forces the variable X to have the value x and keeps the rest of the system unchanged, after Y is measured, the resulting distribution of Y, P(Y|do (x)) is defined as the causal effect of X on Y. Power of causal inference is its ability to predict effects of actions on the system (Mooij et al, 2016)
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