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\documentclass[12pt,letterpaper]{article} | ||
\usepackage{ucs} | ||
\usepackage[utf8x]{inputenc} | ||
%\renewcommand{\baselinestretch}{2} | ||
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\usepackage{hyperref} | ||
\usepackage{mathptmx} | ||
\usepackage{fullpage} | ||
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\raggedright | ||
\urlstyle{rm} | ||
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\title{DAGitty: A Graphical Tool for Analyzing Causal Diagrams} | ||
\author{Johannes Textor \and Juliane Hardt \and Sven Kn\"uppel} | ||
\date{\today\footnote{This is an updated pre-print | ||
version of a ``research letter'' published in the journal Epidemiology | ||
(\url{http://dx.doi.org/10.1097/EDE.0b013e318225c2be}).}} | ||
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\setlength{\parindent}{0em} | ||
\setlength{\parskip}{1em} | ||
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\begin{document} | ||
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\maketitle | ||
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Causal diagrams, also known in epidemiology as directed | ||
acyclic graphs \cite{Pearl2000,GreenlandPR1999}, | ||
provide an entirely graphical, yet mathematically | ||
rigorous methodology for minimizing bias in epidemiological studies | ||
\cite{ShrierP2008,RothmanGL2008}. | ||
The analysis of causal diagrams can be cumbersome in practice, | ||
and lends itself well | ||
to automization by a computer program. Important first steps in this | ||
regard include the development of the \emph{DAG program} by | ||
Knüppel \cite{KnueppelS2010} and \emph{dagR} by Breitling | ||
\cite{Breitling2010}. We are writing to announce the release of | ||
\emph{DAGitty}, which to our knowledge is the first program | ||
in the field of epidemiology that provides a graphical user interface | ||
tailored to draw and analyze causal diagrams. Furthermore, DAGitty overcomes | ||
some performance obstacles (pointed out by Breitling \cite{Breitling2010}) | ||
that affect earlier software when analyzing large diagrams. | ||
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The addressed performance issues are two-fold. | ||
First, previous software employed back-tracking algorithms \cite{KnueppelS2010} | ||
to enumerate and categorize | ||
all paths from exposure to outcome. This is a reasonable approach for small diagrams, | ||
but diagrams with tens of variables can already contain millions of paths. | ||
A full listing of these is of little interest to the human user, | ||
but can take hours or days to generate. | ||
Instead of a path list, | ||
DAGitty identifies the subdiagrams involved | ||
in causal and biasing paths and highlights them in different colours. | ||
This highlighting algorithm scales to very large diagrams (M Liśkiewicz and J Textor, | ||
submitted manuscript, 2011). It provides to the user | ||
a vivid impression about how causal and biasing effects ``flow'' in the | ||
diagram, i.e., via which variables and causal arrows these effects are mediated. | ||
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The second problem with previous software | ||
arose when identifying \emph{minimal sufficient adjustment sets} | ||
(MSA sets). According to causal diagram theory, | ||
adjustment for the covariates in an MSA set minimizes bias | ||
when estimating the total effect from exposure to outcome. | ||
A straightforward approach | ||
to find MSA sets is checking for each covariate set | ||
whether it is an MSA set. In a diagram with | ||
50 covariates, this means that $2^{50}$ sets may have to be tested -- | ||
a 16-digit number which is too large even for computers. | ||
To identify MSA sets more efficiently, | ||
we adapted an algorithm proposed recently for a related | ||
graph-theoretical problem \cite{Takata2010}. This algorithm | ||
is guaranteed to output the list of MSA sets reasonably quickly | ||
(i.e., in polynomial time per MSA set output). Note however | ||
that very large or very regularly structured diagrams could in | ||
theory have millions of different MSA sets. If such diagrams become | ||
practically relevant, further research will be necessary to develop appropriate | ||
computational methods for helping the user to choose appropriate MSA | ||
sets. | ||
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The described algorithms enable DAGitty's graphical interface to instantly reflect | ||
changes made to the diagram, such as adding a new arrow or inverting an arrow | ||
with unclear causal direction. Thus, users can interactively assess the effects | ||
of their modifications to MSA sets and the flow of causal and biasing effects. We anticipate | ||
that these interactive possibilies will be of great help to novice users | ||
in developing an intuition about causal diagram theory, and hope that more | ||
experienced users will find these features useful when comparing | ||
and deciding between different causal diagrams. | ||
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DAGitty is available under an open-source license allowing free | ||
access, redistribution, and modification. It runs directly in | ||
most modern web browsers and is available online and for | ||
download at \url{www.dagitty.net}. The current version of the | ||
manual is available on arXiv \cite{Textor2015}. | ||
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%\bibliographystyle{unsrt} | ||
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\begin{thebibliography}{1} | ||
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\bibitem{Pearl2000} | ||
Pearl J. | ||
\newblock {\em Causality: Models, Reasoning, and Inference}. | ||
\newblock Cambridge: Cambridge University Press; 2000. | ||
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\bibitem{GreenlandPR1999} | ||
Greenland S, Pearl J, and Robins JM. | ||
\newblock Causal diagrams for epidemiologic research. | ||
\newblock {\em Epidemiology.} 1999;10:37--48. | ||
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\bibitem{ShrierP2008} | ||
Shrier I, Platt RW. | ||
\newblock Reducing bias through directed acyclic graphs. | ||
\newblock {\em BMC Medical Research Methodology.} 2008;8:70. | ||
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\bibitem{RothmanGL2008} | ||
Glymour MM, Greenland S. | ||
\newblock Causal diagrams. | ||
\newblock In: Rothman KJ, Greenland S, Lash TL, eds. {\em Modern Epidemiology}. | ||
3rd ed. | ||
\newblock Philadelphia: Lippincott Williams \& Wilkins; 2008:183--209. | ||
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\bibitem{KnueppelS2010} | ||
Kn\"uppel S, Stang A. | ||
\newblock {DAG} program: identifying minimal sufficient adjustment sets [Letter]. | ||
\newblock {\em Epidemiology.} 2010;21:159. | ||
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\bibitem{Breitling2010} | ||
Breitling L. | ||
\newblock {dagR}: A suite of {R} functions for directed acyclic graphs [Letter]. | ||
\newblock {\em Epidemiology.} 2010;21:586--587. | ||
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\bibitem{Takata2010} | ||
Takata K. | ||
\newblock Space-optimal, backtracking algorithms to list the minimal vertex | ||
separators of a graph. | ||
\newblock {\em Discrete Applied Mathematics.} 2010;158:1660--1667. | ||
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\bibitem{Textor2015} | ||
Textor J. | ||
\newblock | ||
Drawing and Analyzing Causal DAGs with DAGitty. | ||
\newblock CoRR abs/1508.04633 (2015). Available at | ||
\url{http://arxiv.org/abs/1508.04633}. | ||
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\end{thebibliography} | ||
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\end{document} |