Drawing and Analyzing Causal DAGs with DAGitty User Manual for
Contents
1. DAGitty s textual syntax for causal diagrams DAGitty s textual syntax for causal diagrams is based on the one used by the DAG program by Sven Kniippel 4 A diagram description model text data consists of two parts 1 A list of the variables in the diagram 2 A list of connections between the variables The list of variables consists of one variable per line blank lines are ignored by DAGitty After each variable name follows a character that indicates the status of the variable which can be one of 1 normal variable A adjusted for U latent unobserved E exposure or O outcome If you prepare your diagram description in a word processor rather than construct ing the diagram in DAGitty itself you may encounter problems when you use spaces or other special symbols in variable names e g instead of patient sex you should write patient_sex This restriction does not apply when you construct the diagram using DAGitty s graphical user interface The list of connections consists of several lines each starting with a start variable name followed by one or more other target variables that the start variable is connected to Figure 1 contains a worked example of a textual model description When you modify a diagram within DAGitty the vertex labels will be augmented by additional information to help DAGitty remember the layout of the vertices and for other purposes see rightmost colum2. path E A Z B e D Because both E and D depend on Z adjusting for Z will induce additional correlation between E and D 4 2 3 Finding minimal sufficient adjustment sets Whenever you create a new causal model or make changes to it DAGitty will calculate all minimal sufficient adjustment sets and display them in the Adjustment for total effect and Adjustment for direct effect fields respectively 4 2 4 Forcing adjustment for specific covariates You can also tell DAGitty that you wish a specific covariate to be included into every adjustment set To do this move the mouse over the vertex of that covariate and press the a key DAGitty will then update the list of minimal sufficient adjustment sets accordingly every set displayed is now minimal in the sense that removing any variable except those you specified will render that set insufficient However when you adjust for an intermediate or another descendant of the exposure DAGitty might tell you that it is no longer possible to find a valid adjustment set 4 2 5 Avoiding adjustment for unobserved covariates You can tell DAGitty that a certain variable is unobserved e g not measured at present or not measurable because it is a latent variable by moving the mouse over that covariate and pressing the u key DAGitty will only calculate adjustment sets that do not contain unobserved variables However if too many or some important variables are unobserved then it may b
3. Drawing and Analyzing Causal DAGs with DAGitty User Manual for Version 2 0 Johannes Textor January 24th 2013 Abstract DAGitty is a software for drawing and analyzing acyclic causal diagrams also known in epidemiology as directed acyclic graphs DAGs DAGitty s functions include the identifica tion of minimal sufficient adjustment sets for estimating causal effects diagnosis of insufficient or invalid adjustment via the identification of biasing paths and the derivation of testable implications DAGitty is written with typical epidemiological use cases of DAGs in mind but researchers and students of other disciplines such as econometrics sociology or psychology could find it useful as well DAGitty should run directly and without installation in any web browser that supports modern HTML and JavaScript Contents 1 Introduction Peau ODE eee Re Peewee eee Reo es t2 Citing DAGI 63 4 aee 6 a 8 a oe eG ee ee 1 5 Migrating from earlier versions of DAGitty 2 Loading and saving diagrams 2 1 DAGitty s textual syntax for causal diagrams 000 2 2 Loading a textually defined diagram into DAGitty tg tay as oe Gute a in eae gaa ae ae weg a eS Me ans eee oe Jo Reba Paw eae ieee avaweea eee behaaaa ha hide aaa eos the ens ees Coe bobs d 6 ek ee oe eh SRA 3 7 Deleting connections 2 2 a 3 8 Displaying the moral graph 2 2 0 0 0 0000000000000 PP wWwWDny
4. Pearl Sabine Schipf and Felix Thoemmes in alphabetical order for enlightening discussions either in person per e mail or on the SEMnet discussion list about DAGs that made this program possible Furthermore I thank Marlene Egger Angelo Franchini Ulrike Forster Dirk van Kampen Jeff Martin Jillian Martin Karl Micha lsson David Tritchler Eric Vittinghof and other users for sending feedback and bug reports that greatly helped to improve DAGitty 6 Legal notice Use of DAGitty is and will always remain freely permitted and free of charge You may download a copy of DAGitty s source code from its website at The source code is available under the GNU General Public License GPL either version 2 0 or any later version at the licensee s choice see the file LICENSE txt in the download archive for details In particular the GPL permits you to modify and redistribute the source as you please as long as the result remains itself under the GPL 7 Bundled libraries DAGitty ships along with the following JavaScript libraries e Prototype js a framework that makes life with JavaScript much easier Only some parts of Prototype mainly those focusing on data structures are included to keep the code small Developed by the Prototype Core Team and licensed under the MIT license f Furthermore DAGitty uses some modified code from the Dracula Graph Library by Philipp Strathausen which is also licensed under the MIT license 12 Versi
5. anipulating the graphical layout of the diagram and 3 saving the diagram First of all any causal diagram consists of vertices variables and edges direct causal effects You can either create the diagram directly using DAGitty s graphical user interface explained in the next section or prepare a textual diagram description in a word processor such as Microsoft Word and then import this description into DAGitty In addition DAGitty contains some pre defined examples that you can use to become familiar with the program To do so just select one of the pre define examples from the Examples menu While this would be redeemable I d much rather invest my time in improving DAGitty for modern browsers than fixing it for old IE versions If you absolutely need to run DAGitty on older IEs and encounter severe problems please contact me a verter labels b adjacency list c resulting graph d augmented vertex la EE ED A B bels DO AEZ E E 2 2 16 Al BDZ NO D O 1 4 1 6 B1 ZED A 1 2 2 1 5 Z1 Z N B 1 1 4 1 5 E D Z 1 0 3 0 1 Figure 1 Example for a textual model definition with DAGitty a b model text data c resulting diagram When the diagram is edited within DAGitty d the vertex labels and adjustment status are augmented with additional information that DAGitty uses to layout the vertices on the canvas rightmost column the layout coordinates of each variable are indicated behind the sign 2 1
6. c Connections are by default drawing using a straight line but you can change that moving the mouse pointer to the line pressing and holding down the left mouse button and bending the line by dragging as appropriate 3 6 Deleting variables To delete a variable move the mouse pointer over that variable and hit the del key on your keyboard All connections to that variable will be deleted along with the variable In contrast to DAGitty versions prior to 2 0 all variables can now be deleted including exposure and outcome 3 7 Deleting connections A connection is deleted just like it has been inserted i e by double clicking first on the start variable and then on the target variable A connection is also deleted automatically if a new one is inserted in the opposite direction see above 3 8 Displaying the moral graph To identify minimal sufficient adjustment sets DAGitty uses the so called moral graph which results from a transformation of the model to an undirected typically smaller graph This pro cedure is also highly recommended if you wish to verify the calculation by hand See the nice explanation by Shrier and Platt II for details on this procedure In DAGitty you can switch between display of the model and its moral graph by pressing the m key 4 Analyzing diagrams 4 1 Paths Causal diagrams contain two different kinds of paths e Causal paths start at the exposure contain only arrows pointing away
7. carrying matches in one s pocket and developing lung cancer we would probably find a correlation between these two variables However as the above diagram indicates this correlation would not imply that carrying matches in your pocket causes lung cancer Smokers are more likely to carry matches in their pockets and also more likely to develop lung cancer This is an example of a confounded association between two variables which is mediated via the biasing path bold In this example let us assume with a leap of faith that the simplistic diagram above is accurate Under this assumption would we adjust for smoking e g by averaging separate effect estimates for smokers and non smokers we would no longer find a correlation between carrying matches and lung cancer as such adjustment would close the biasing path Adjustment sets will be explained in more detail in Section The purpose of DAGitty is to aid study design through the identification of suitable small suf ficient adjustment sets in complex causal diagrams and more generally through the identification of causal and biasing paths as well as testable implications in a given diagram 1 2 Citing DAGitty If you publish research results obtained with the help of DAGitty please cite either the letter in Epidemiology where DAGitty is announced or the research paper that describes the algorith mic methods that had to be developed to make DAGitty possible or both 1 3 Running DAGitty onli
8. dN OOO A NAINNNDDDDOH 7 Al Paths 244 hee ee ede PEER POA di dir ee See G A e a 7 ah ee ae Sent Ao nee aie ga oe A es ee ana an 8 4 2 1 Total versus direct effect 2 2 ee ee 8 D N se a a aay Ne Gees Gee Galas os oe a 9 eee re tere eees 9 og aKa Ree hag 0934 9 4 2 5 Avoiding adjustment for unobserved covariates 0 0 9 re en ee re re ee ee ee ee 9 10 E Legal notice 10 7 Bundled libraries 10 Bundled examples 10 9 Author contact 11 1 Introduction 1 1 Causal diagrams To convey an idea of the purpose of DAGitty we give a very brief introduction on the subject of causal diagrams for a more detailed account we recommend the book Causality by Judea Pearl 7 or the corresponding chapter Causal Diagrams in the epidemiology textbook of Rothman Greenland and Lash 8 Note that in epidemiology causal diagrams are also frequently called DA Gsp Simply put a DAG is a graphic model that depicts causal relationships between certain variables of interest An arrow X Y is drawn if there is a direct causal effect of X on Y Intuitively this means that the natural process determining Y is directly influenced by the status of X and that altering X via external intervention would also alter Y However an arrow X Y only represent that part of the causal effect which is not mediated by any of the other variables in the diagram If one is certain that X does not have a direct cau
9. e pages 3 10 1996 2 Dmitry Baranovskiy Raphael javascript library http raphaeljs com 2010 3 Ines Polzer et al 2010 personal communication 4 Sven Kniippel and Andreas Stang DAG program identifying minimal sufficient adjustment sets Epidemiology Cambridge Mass 21 1 159 2010 5 S L Laurizen A P Dawid B N Larsen and H G Leimer Independence properties of directed markov fields Networks 20 5 491 505 1990 6 Judea Pearl Causality models reasoning and inference Cambridge University Press 2000 7 Judea Pearl Causality Models Reasoning and Inference Cambridge University Press New York NY USA 2nd edition 2009 8 Kenneth J Rothman Sander Greenland and Timothy L Lash Modern Epidemiology Wolters Kluwer 2008 9 Sabine Schipf Robin Haring Nele Friedrich Matthias Nauck Katharina Lau Dietrich Alte Andreas Stang Henry V lzke and Henri Wallaschofski Low total testosterone is associated with increased risk of incident type 2 diabetes mellitus in men Results from the study of health in pomerania SHIP The Aging Male 2010 in press 10 P Sebastiani M F Ramoni V Nolan C T Baldwin and M H Steinberg Genetic dissec tion and prognostic modeling of overt stroke in sickle cell anemia Nat Genet 37 435 440 Apr 2005 4The example actually shows only a small part of their DAG 11 11 Ian Shrier and Robert W Platt Reducing bias through directed acyclic
10. e impossible to close all biasing paths 4 3 Testable implications The adjustment sets obtained from a causal diagram will only be appropriate for estimating the desired total or direct effect if the causal assumptions encoded in the diagram are accurate To some extent these assumptions can be tested via the conditional independences implied by the diagram If two variables x and y are d separated by a set Z then x and y should be conditionally independent given Z The converse is not true Two variables x and y can be independent given a set Z even though they are not d separated in the diagram Furthermore two variables can also be d separated by the empty set Z In that case the diagram implies that x and y are unconditionally independent DAGitty displays all minimal testable implications in the Testable implications text field Only such implications will be displayed that are in fact testable i e that do not involve any unobserved variables Note that the set of testable implications displayed by DAGitty does not constitute a basis set 7 Future versions will allow choosing between different basis sets In general the less arrows a diagram contains the more testable predictions it implies For this reason simpler models with fewer arrows are in general easier to falsify Occam s razor 5 Acknowledgements The author wishes to thank Michael Elberfeld Juliane Hardt Sven Kniippel Keith Marcus Judea
11. from the exposure and end at the outcome That is they have the form e gt z sea BE o e Biasing paths are all other paths in the model With respect to a set Z of adjusted variables that can also be empty if we are not adjusting for anything paths can be either open or closed also called d separated 6 A path is closed with respect to Z if one or both of the following holds Figure 2 A causal diagram where the total and direct effects are not equal The total effect is the effect mediated only via the thick both dashed and solid arrows while the direct effect is the effect mediated only via the thick arrow e The path p contains a chain z gt m gt y or a fork x m gt y such that m is in Z e The path p contains a collider zx c y such that c is not in Z and furthermore Z does not contain any successor of c in the graph Otherwise the path is open Note that in particular a path consisting of only one arrow is always open no matter the content of Z Also it is possible that a path is closed with respect to the empty set Z It is not easy to verify by hand which paths are open and which paths are closed especially in larger diagrams DAGitty highlights all arrows lying on open biasing paths in red and all arrows lying on open causal paths in green This highlighting is optional and is controlled via the highlight causal paths and highlight biasing paths checkboxes 4 2 Adjust
12. graphs BMC Medical Research Methodology 8 70 2008 12 Philipp Strathausen Dracula graph layout and drawing framework 2010 13 Prototype Core Team Prototype http www prototypejs org 2010 14 J Textor J Hardt and S Kniippel Dagitty A graphical tool for analyzing causal diagrams Epidemiology 22 5 745 2011 15 J Textor and M Liskiewicz Adjustment criteria in casual diagrams an algorithmic perspec tive In Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence pages 681 688 Corvallis OR AUAI Press 2011 16 Jin Tian Azaria Paz and Judea Pearl Finding minimal d separators Technical Report R 254 UCLA 1998 12
13. h between exposure and outcome is the path e o the total effect and the direct effect are equal This is true e g for the diagram in Figure 1 An example diagram where the direct and total effects are not equal is shown in Figure As proved by Lauritzen et al 5 see also Tian et al 16 it suffices to restrict our attention to the part of the model that consists of exposure outcome and their ancestors for identifying sufficient adjustment sets This is indicated by DAGitty by coloring irrelevant nodes in gray The relevant variables are colored according to which node they are ancestors of exposure outcome or both see the legend on the left hand side of the screen The highlighting may be turned on and off by toggling the highlight ancestors checkbox 4 2 2 Minimal sufficient adjustment sets A minimal sufficient adjustment set MSAS is a sufficient adjustment set of which no proper subset is itself sufficient For example consider again the causal diagram in Figure In this example the following three sets are sufficient adjustment sets for the total and direct effects which are equal in this diagram A B Z A Z B Z All these sets block all biasing paths while leaving the causal path open and are thus sufficient The sets A Z and B Z are minimal sufficient adjustment sets while the set A B Z is sufficient but not minimal In contrast the set Z is not sufficient since this would un block the
14. ment sets Finding sufficient adjustment sets is one main purpose of DAGitty In a nutshell a sufficient adjustment set is a set S of covariates such that adjustment stratification or selection e g by restriction or matching will minimize bias when estimating the causal effect of the exposure on the outcome assuming that the causal assumptions encoded in the diagram hold You can read more about controlling bias and confounding in Pearl s textbook chapter 3 3 and epilogue 6 Moreover Shrier and Platt give a nice step by step tutorial on how to test if a set of covariates is a sufficient adjustment set To identify adjustment sets the diagram must contain at least one exposure and at least one outcome 4 2 1 Total versus direct effect One can understand adjustment sets graphically by viewing an adjustment set as a set Z that blocks all all biasing paths while keeping desired causal paths open see previous section DAGitty considers two kinds of adjustment sets e Adjustment sets for the total effect are sets that block all biasing paths and leave all causal paths unblocked In the literature if the effect is not mentioned e g I 4 then usually this kind of adjustment set is meant e Adjustment sets for the direct effect are sets that block all biasing paths and all causal paths and leave only the direct arrow from exposure to outcome i e the path e o if it exists unblocked In a diagram where the only causal pat
15. n in Figure i 2 2 Loading a textually defined diagram into DAGitty To load a textually defined diagram into DAGitty simply copy amp paste the variable list followed by a blank line followed by the list of connections into the Model text data text box Then click on Update DAG DAGitty will now generate a preliminary graphical layout for your diagram on the canvas which may not yet look the way you intended it to look but can be freely modified 2 3 Modifying the graphical layout of a diagram To layout the vertices and edges of your diagram more clearly than DAGitty did simply drag the vertices with your mouse on the canvas You may notice that DAGitty modifies the information in the Model text data field on the fly and augments it with additional position information for each vertex In general all changes you make to your diagram within DAGitty are immediately reflected in the model text data 2 4 Saving the diagram To save your diagram locally just copy amp paste the contents of the Model text data field to a text file e g a Microsoft Word Q document and save that file locally to your computer When you wish to continue working on the diagram copy the model text data back into DAGitty as explained above 2 5 Exporting the diagram DAGitty can export the diagram as a PDF or SVG vector graphic publication quality or a JPEG or PNG bitmap graphic e g for inclusion in Powerpoint Select the correspo
16. nding function from the Model menu If you want to edit the graphical layout of the diagram or annotate it it is recommended to export the diagram as an SVG file and open that in a vector graphics program such as Inkscape 3 Editing diagrams using the graphical user interface You are free to make changes directly to the textual description of your diagram which will be reflected on the canvas next time you click on Update DAG However you can also create modify and delete vertices and connections graphically using the mouse 3 1 Creating a new diagram To create a new diagram select New Model from the Model menu You will be asked for the names of the exposure and the outcome variable and an initial model containing just those variables and an arrow between them will be drawn Then you can add variables and connections to the model as explained below 3 2 Adding new variables To add a new variable to the model double click on a free space in the canvas i e not on an existing variable or press the n key A dialog will pop up asking you for the name of the new variable Enter the name into the dialog and press the enter key or click OK If you click Cancel no new variable will be created 3 3 Renaming variables To rename an existing variable move the mouse pointer over that variable and hit the r key A dialog will pop up allowing you to change the variable name 3 4 Setting the status of a va
17. ne There are two ways to run DAGitty either from the internet or from your own computer To run DAGitty online simply open its URL in your favourite browser http www dagitty net DAGitty should run in every modern browser Specifically I expect it to work well on recent versions of Firefox Chrome Opera and Safari as well as on Internet Explorer IE version 9 0 or later i e IE versions that support SVG graphics IE versions prior to 9 0 that don t support SVG graphics should allow performing all diagnosis functions but cannot display the graphics as well as modern browser If you encounter any problems please send me an E Mail so I can fix the problem see contact information at the end of this manual Keep in mind that DAGitty is used daily by dozens to hundreds of people throughout the world and they all benefit from bug fixes so please do consider investing the time to notify me if you encounter any bugs 1 4 Installing DAGitty on your own computer DAGitty can be installed on your computer for use without an internet connection To do this download the file which is a ZIP archive containing DAGitty s source Unpack this ZIP file anywhere in your file system To run DAGitty just open the file dags html in the unpacked folder However exporting models as PDF JPEG or PNG graphics currently only works with an internet connection because the conversion is performed by the DAGitty server 1 5 Migrating from earlie
18. ons of DAGitty prior to 2 0 used the Rapha l library for smooth cross browser vector graphics in SVG and VML developed by Dmitry Baranovskiy 2 However the dependency on Rapha l was removed starting from version 2 0 as I anticipate only supporting SVG capable browsers in the future I am grateful to all authors of these libraries for their valuable work 8 Bundled examples DAGitty contains some builtin examples for didactic and illustrative purposes Some of these examples are taken from published papers or talks given at scientific meetings These are in inverse chronological order e Polzer et al 2010 3 10 e Schipf et al 2010 9 e Shrier amp Pratt 2008 e Sebastiani et alf 2005 e Aicd amp Campos 1996 Another example was provided by Felix Thoemmes via personal communication 2013 9 Author contact The author of DAGitty i e me would be glad to receive feedback from those who use DAGitty in their research or for educational purpose Also you are welcome to send me your with suggestions or requests for features that you miss in DAGitty Johannes Textor Theoretical Biology amp Bioinformatics Universiteit Utrecht The Netherlands johannes textor gmx de bioinformatics bio uu nl textor References 1 Silvia Acid and Luis M De Campos An algorithm for finding minimum d separating sets in belief networks In Proceedings of the twelfth Conference of Uncertainty in Artificial Intelli genc
19. r versions of DAGitty The following two issues are important for users of older DAGitty versions New users can skip this section e It is now possible to have more than one exposure and or outcome This means that the old model text data convention where the variable in the first line is the exposure and the variable in the second line is the outcome is no longer used Hence if you open a model created with an earlier version in DAGitty 2 0 it will seem that exposure and outcome have become normal variables To fix this simply use the e and o keys to set exposure and outcome again and save the new model text data e Spaces in variables are now finally reliably supported The way this works is that any variable name containing spaces or other special symbols is converted using URL encoding e g patient sex will turn into patient 20sex of course DAGitty will do this automatically for you This may look strange but ensures that DAGitty models can be safely e mailed posted on websites stored in word documents etc without having to worry about line breaking If you have an older DAGitty model containing spaces in variable names DAGitty 2 0 should open this model correctly and perform the conversion itself If it does not consider sending me your model by e mail so I can investigate 2 Loading and saving diagrams This section covers the three basic steps of working with DAGitty 1 loading a diagram 2 m
20. riable In DAGitty variables can have one of the following statuses e Exposure e Outcome e Unobserved latent Adjusted e Other 3This is most easily done by clicking in the text field pressing CTRL A to select the entire content of the text field then pressing CTRL C to copy the selected content You can then paste the content into Microsoft Word using CTRL V To turn a variable into an exposure move the mouse pointer over that variable and hit the e key for an outcome hit the o key instead To toggle whether a variable is observed or unobserved hit the u key to toggle whether it is adjusted hit the a key Changing the status of variables may change the colors of the diagram vertices to reflect the new structure and information flow in the diagram see below At present each variable can only have one status at a time e g variables can not be both unobserved and adjusted or both exposure and unobserved This may also change in future versions of DAGitty 3 5 Adding new connections To add a new connection double click first on the source vertex which will become highlighted and then on the target vertex The connection will be inserted If a connection existed before in the opposite direction that connection will be deleted because otherwise there would now be a cycle in the model Instead of double clicking on a vertex you can also move the mouse pointer over the vertex and press the key
21. sal influence on Y then the arrow is omitted This has two important implications 1 arrow directions should be congruent to temporal order or else the diagram violates the principle of causality causes must precede their effects 2 the omission of an arrow is a stronger claim than the inclusion of an arrow the presence of an arrow depicts merely the causal null hypothesis that X might have an effect on fe Mathematically the semantics of an arrow X Y can be defined as follows Given a DAG G and a variable Y in G let X Xn be all variables in G that have direct arrows X Y Then G claims that the causal process determining the value of Y can be modelled as a mathematical function Y f X1 Xn ey where ey the causal residual is a random variable which is independent of all the X For example the sentence smoking causes cancer could be translated into the following simple causal diagram smoking lung cancer 1The term DAG is somewhat confusing to computer scientists and mathematicians for whom a DAG is simply an abstract mathematical structure without specific semantics attached to it We would interpret this diagram as follows 1 The variable smoking refers to the smoking behaviour prior to a later assessment of cancer in that person 2 the natural process by which a person develops cancer might be influenced by the smoking behaviour of that person 3 there exi
22. st no other variables that have a direct influence on both smoking behaviour and cancer A slightly more complex version of this diagram might look as follows smoking tar deposit in lungs lung cancer This diagram is about a person s smoking behaviour at a time t the tar deposit in her lungs at a later time fo and finally the development of cancer at an even later time t3 We claim that 1 the natural process which determines the amount of tar in the lungs is affected by smoking 2 the natural process by which lung cancer develops is affected by the amount of tar in the lung 3 the natural process by which lung cancer develops is not affected by the person s smoking other than indirectly via the tar deposit and finally 4 no variables having relevant direct influence on more than one variable of the diagram were omitted A causal diagram is thus an encoding of assumptions about the causal relationships between the variables of interest In an epidemiologic context one of these variables is usually called the ez posure and another special variable is called the outcome Importantly if all assumptions encoded in the diagram hold then we can infer sets of variables for which to adjust in an observational study to minimize bias For example consider the following causal diagram smoking lt carry matches _ gt cancer If we were to perform an association study on the relationship between
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