Directed Acyclic Graphs (DAGs), which offer systematic representations of causal relationships, have become an established framework for the analysis of causal inference in epidemiology; often being used to determine covariate adjustment sets for minimizing confounding bias. DAGitty is a popular web application for drawing and analysing DAGs. Here we introduce the R package ÔdagittyÕ, which provides access to all of the capabilities of the DAGitty web application within the R platform for statistical computing, and also offers several new functions. We describe how the R package ÔdagittyÕ can be used to: evaluate whether a DAG is consistent with the dataset it is intended to represent; enumerate Ôstatistically equivalentÕ but causally different DAGs; and identify exposure-outcome adjustment sets that are valid for causally different but statistically equivalent DAGs. This functionality enables epidemiologists to detect causal misspecifications in DAGs and make robust inferences that remain valid for a range of different DAGs. AvailabilityThe R package ÔdagittyÕ is available through the comprehensive R archive network (CRAN) at https://cran.r-project.org/web/packages/dagitty/. The source code is available on github at https://github.com/jtextor/dagitty. The web application ÔDAGittyÕ is free software, licensed under the GNU general public license (GPL) version 2 and is available at http://dagitty.net/.

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Principled reasoning about the identifiability of causal effects from non-experimental data is an important application of graphical causal models. This paper focuses on effects that are identifiable by covariate adjustment, a commonly used estimation approach. We present an algorithmic framework for efficiently testing, constructing, and enumerating m-separators in ancestral graphs (AGs), a class of graphical causal models that can represent uncertainty about the presence of latent confounders. Furthermore, we prove a reduction from causal effect identification by covariate adjustment to m-separation in a subgraph for directed acyclic graphs (DAGs) and maximal ancestral graphs (MAGs). Jointly, these results yield constructive criteria that characterize all adjustment sets as well as all minimal and minimum adjustment sets for identification of a desired causal effect with multiple exposures and outcomes in the presence of latent confounding. Our results extend several existing solutions for special cases of these problems. Our efficient algorithms allowed us to empirically quantify the identifiability gap between covariate adjustment and the do-calculus in random DAGs and MAGs, covering a wide range of scenarios. Implementations of our algorithms are provided in the R package DAGITTY.

In practice the vast majority of causal effect estimations from observational data are computed using adjustment sets which avoid confounding by adjusting for appropriate covariates. Recently several graphical criteria for selecting adjustment sets have been proposed. They handle causal directed acyclic graphs (DAGs) as well as more general types of graphs that represent Markov equivalence classes of DAGs, including completed partially directed acyclic graphs (CPDAGs). Though expressed in graphical language, it is not obvious how the criteria can be used to obtain effective algorithms for finding adjustment sets. In this paper we provide a new criterion which leads to an efficient algorithmic framework to find, test and enumerate covariate adjustments for chain graphs - mixed graphs representing in a compact way a broad range of Markov equivalence classes of DAGs.

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