Inferring Regulatory Networks From Mixed Observational Data Using Directed Acyclic Graphs

Construction of regulatory networks using cross-sectional expression profiling of genes is desired, but challenging. The Directed Acyclic Graph (DAG) provides a general framework to infer causal effects from observational data. However, most existing DAG methods assume that all nodes follow the same type of distribution, which prohibit a joint modeling of continuous gene expression and categorical variables. We present a new mixed DAG (mDAG) algorithm to infer the regulatory pathway from mixed observational data containing both continuous variables (e.g. expression of genes) and categorical variables (e.g. categorical phenotypes or single nucleotide polymorphisms). Our method can identify upstream causal factors and downstream effectors closely linked to a variable and generate hypotheses for causal direction of regulatory pathways. We propose a new permutation method to test the conditional independence of variables of mixed types, which is the key for mDAG. We also utilize an L ₁ regularization in mDAG to ensure it can recover a large sparse DAG with limited sample size. We demonstrate through extensive simulations that mDAG outperforms two well-known methods in recovering the true underlying DAG. We apply mDAG to a cross-sectional immunological study of Chlamydia trachomatis infection and successfully infer the regularity network of cytokines. We also apply mDAG to a large cohort study, generating sensible mechanistic hypotheses underlying plasma adiponectin level. The R package mDAG is publicly available from CRAN at https://CRAN.R-project.org/package=mDAG.