Manual - DAGitty
Contents
1. B Z Each of these sets is sufficient because it closes all biasing paths and leaves the causal path open 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 open the path E A gt Z e B e D Because both E and D depend on Z adjusting for Z will induce additional correlation between E and D Finding minimal sufficient adjustment sets To find minimal sufficient adjustment sets select the option Adjustment total effect or Adjustment direct effect in the Causal effect identification field DAGitty will then calculate all minimal sufficient adjustment sets and display them in that field Any changes made to the diagram will be instantly reflected in the list of adjustment sets 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 will tell you that it is no longer possible to find a valid adjustment set 112. 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 ad justment sets that do not contain unobserved variables However if too many or some important variables are unobserved then it may be impossible to close all biasing paths 5 5 2 Instrumental variables Sometimes it is not possible to estimate a causal effect by simple covariate adjustment For example this is the case whenever there is an unobserved confounder that directly effects the exposure and outcome variables However this does not necessarily mean that it is impossible to estimate the causal effect at all Instrumental variable regression is a technique that is often used in situations with unobserved confounders Note that this technique depends on linearity assumptions For further information on instrumental variables please refer to the literature BIB DAGitty can find instrumental variables in DAGs as explained below The validity of an instrumental variable I depends on two causal conditions exogeneity and exclusion restriction These two conditions can be expressed in the language of DAGs and paths as follows 1 there must be an open path between I and the exposure X and 2 all paths between I and the outcome Y must be closed in a modified graph
3. all cause and circulatory mortality Is there a benefit of replaced teeth A systematic review and meta analysis Clinical Oral Investigations 16 2 333 351 2012 4The example actually shows only a small part of their DAG 14 10 Kenneth J Rothman Sander Greenland and Timothy L Lash Modern Epidemiology Wolters Kluwer 2008 11 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 14 3 168 75 2011 12 Paola Sebastiani Marco F Ramoni Vikki Nolan Clinton T Baldwin and Martin H Steinberg Genetic dissection and prognostic modeling of overt stroke in sickle cell anemia Nature Genetics 37 435 40 2005 13 Ian Shrier and Robert W Platt Reducing bias through directed acyclic graphs BMC Medical Research Methodology 8 70 2008 14 Philipp Strathausen Dracula graph layout and drawing framework 2010 15 Prototype Core Team Prototype javascript library 2010 16 Johannes Textor Juliane Hardt and Sven Kniippel Dagitty A graphical tool for analyzing causal diagrams Epidemiology 22 5 745 2011 17 Johannes Textor Alexander Idelberger and Maciej Liskiewicz Learning from pairwise marginal independencies In Proceedings of the 31st Con
4. it exists open In a diagram where the only causal path between exposure and outcome is the path X Y the total effect and the direct effect are equal This is true e g for the diagram in Figure I An example diagram where the direct and total effects are not equal is shown in Figure 2 10 Figure 2 A causal diagram where the total and direct effects of exposure X on outcome Y 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 As proved by Lauritzen et al see also Tian et al 19 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 Minimal sufficient adjustment sets A minimal sufficient adjustment set is a sufficient adjust ment set of which no proper subset is itself sufficient For example consider again the causal diagram in Figure The following three sets are sufficient adjustment sets for the total and direct effects which are equal in this case A B Z 1A Z
5. of arrows 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 column in Figuref1 3 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 arrows into the Model code 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 but can be freely modified a vertex labels b adjacency list c resulting graph d augmented vertex labels EE ED A B E E 2 2 1 6 DO AEZ D O 1 4 1 6 Al BDZ z A 1 2 2 1 5 B1 ZED B 1 1 4 1 5 Z1 f g Z 1 0 3 0 1 E D Figure 1 Example for a textual model definition with DAGitty a b model code c resulting diagram When the diagram is edited within DAGitty the vertex labels and adjustment status are augmented with additional information that DAGitty uses to layout the vertices on the canvas d the layout coordinates of each variable are indicated behind the sign 3 3 Modifyin
6. where all edges out of X are removed A variable that fulfills these two conditions is called an instrumental variable or simply an instrument Instrumental variables can also be generalized such that the two conditions are required to hold conditional on a set of covariates Z 4 The two conditions then read as follows 1 there must be a path between I and X that is opened by Z and 2 all paths between I and Y must be closed by Zin a modified graph where all edges out of X are removed A variable that fulfills these two conditions is called a conditional instrument DAGitty will find both classic and conditional instruments when the option Instrumental Variable is selected under the Causal effect identification field Note that DAGitty will not always list all possible instruments instead it will restrict itself to a certain well defined subset that we call ancestral instruments However whenever any instrument or conditional instrument exists at all then DAGitty is guaranteed to find one Note also that if there are several instruments available then it is best to choose the one that is most strongly correlated with X conditional on Z in the case of a conditional instrument For details regarding ancestral instruments and how DAGitty computes them please refer to the research paper where we describe these methods 21 5 6 Testable implications Any implications that are obtained from a causal diagram such as pos
7. Drawing and Analyzing Causal DAGs with DAGitty Johannes Textor August 19th 2015 Abstract DAGitty is a software for drawing and analyzing causal diagrams also known as directed acyclic graphs DAGs Functions include identification of minimal sufficient adjustment sets for estimating causal effects diagnosis of insufficient or invalid adjustment via the identification of biasing paths identification of instrumental variables and derivation of testable implications DAGitty is provided in the hope that it is useful for researchers and students in Epidemiology Sociology Psychology and other empirical disciplines The software should run in any modern web browser that supports JavaScript HTML and SVG This is the user manual for DAGitty version 2 3 The manual is updated with every release of a new stable version DAGitty is available at Contents 11 Citing DAGitty 1 4 Migrating from earlier versions of DAGitty 2 A brief introduction to causal diagrams 2 Loading a textually defined diagram into DAGitty a ewe gh Akad eae a eee ee Ge eee Q Q Z Deleting arrows eses ai pte eo i G Rd hes es ae ee a 8 Choosing the style of display SESE Q WWNNN AAAA UI O N NNNYN 5 Analyzing diagrams 8 SL Patil dx St ah eo ae e ae de Recency tn ae Gt de Be HA e gece ede ete ed ee te amp Bw 8 9 9 9 5 4 1 The correlation graph aoaaa aaae 10 54 2
8. Themoralgrtaph sso e sers passede nta basana t BEI eamaid 10 5 5 Causal effect identification o oo ea e a a 10 59 1 Adjustment setsjes aa ii as a a ee 10 5 5 2 Instrumental variables oaaae aa a a eee ee 12 5 6 Testableimplications gt lt cse 0 reto eepe dataa PERS EnA 12 6 Acknowledgements 13 13 8 Bundled libraries 13 9 Bundled examples 13 10 Author contact 14 11 References 14 1 Introduction DAGitty is a web based software for analyzing causal diagrams It contains some of the fastest algorithms available for this purpose This manual describes how causal diagrams can be created Section 3 and manipulated Section 4 using DAGitty In Section J DAGitty s capabilities to analyze causal diagrams are described A brief introduction to causal diagrams is given in Section 2 1 1 Citing DAGitty Developing and maintaining DAGitty requires a substantial amount of work thus if you publish research results obtained with the help of DAGitty please consider giving us credit by citing our work Depending on the context you could cite the letter in Epidemiology where DAGitty has first been announced 16 or the research papers describing the specific algorithms used to identify biasing paths 18 adjustment sets 20 and instrumental variables 21 1 2 Running DAGitty online There are two ways to run DAGitty either from the internet or from your own computer To run DAGitty online visit the URL dagitty
9. ct pathway exists After drawing an initial DAG one might reconsider these arrows and judge whether they are really necessary given the indirect pathways already present in the diagram For example suppose after thinking about the pairwise causal relationships between our variables X M Y we came up with this DAG 2 X gt M gt Y For the arrows drawn in bold there is no corresponding indirect path removing one of these arrows from the diagram means that there will no longer be any causal effect between the corresponding variables These arrows are called atomic direct effects in DAGitty and they can be highlighted like in the above DAG by ticking the checkbox with that name On the other hand for the thin arrow X gt Y there is also the indirect pathway X M Y One may therefore reconsider whether the arrow X gt Y is truly necessary perhaps the causal effect from X to Y is entirely mediated through M 5 4 View mode There are several ways to transform a given DAG such thatit becomes better suited for a particular purpose We call such a transformed DAG a derived graph Currently DAGitty can display two kinds of derived graphs correlation graphs and moral graphs These derived graphs can be shown by clicking on the respective radio button in the View mode field on the left hand side of the screen 5 4 1 The correlation graph The correlation graph is not a DAG but a simple graph with lines instead of ar
10. ctually implemented on the web server Currently these features are e Exporting model drawings as PDF JPEG or PNG files e Publishing models on line 1 4 Migrating from earlier 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 variable This means that the old model code convention where the variable in the first line is the exposure and the variable in the second line is the outcome no longer works Hence if you open a model created with an earlier version in DAGitty 2 0 exposure and outcome will appear like normal variables To fix this simply set exposure and outcome again using the e and o keys and save the new model code 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 stored using URL encoding e g patient sex will turn into patient 20sex of course DAGitty will do this auto matically for you This may look strange but ensures that DAGitty models can be safely e mailed posted on websites stored in word documents and so forth without having to worry about line breaks messing up variable names If you have an older DAGitty model containing spaces in variable names DAGitty 2 0 or higher should open this model correctly and perform the conversion itself If
11. ether with the data and interpretation I have however seen many articles where people report having used DAGs but do not actually show them If researchers reviewers or editors deem it inappropriate to include the DAG or its model code in the manuscript itself here s another option Store the DAG on the DAGitty website and get a short URL under which this DAG will be accessible Then include this URL in the manuscript or its supporting information For example one of the DAGitty examples is stored at the URL dagitty net mvcFQ Here s how it works Draw your DAG to full satisfaction then choose Publish on dagitty net from the Model menu You have two options how to publish your DAG anonymously or linking it to an e mail address If you store the DAG anonymously you will later on not be able to edit it or delete it from the server After choosing Publish on dagitty net from the Model menu a small form will appear where you can enter some metadata on the DAG and provide your e mail address if you so wish Upon 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 content You can then paste the content in another program using CTRL V clicking Publish the DAG will be sent to the dagitty net server and you will receive a URL under which the DAG is now available If you provided your e
12. ference on Uncertainty in Artificial Intelligence pages 882 91 AUAI Press 2015 18 Johannes Textor and Maciej Liskiewicz Adjustment criteria in casual diagrams an algorith mic perspective In Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence pages 681 88 AUAI Press 2011 19 Jin Tian Azaria Paz and Judea Pearl Finding minimal d separators Technical Report R 254 UCLA 1998 20 Benito van der Zander Maciej Liskiewicz and Johannes Textor Constructing separators and adjustment sets in ancestral graphs In Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence pages 907 16 AUAI Press 2014 21 Benito van der Zander Johannes Textor and Maciej Liskiewicz Efficiently finding condi tional instruments for causal inference In Proceedings of the 24th International Joint Conference on Artificial Intelligence IJCAI 2015 pages 3243 49 AAAI Press 2015 22 Dirk van Kampen The ssq model of schizophrenic prodromal unfolding revised An analysis of its causal chains based on the language of directed graphs European Psychiatry 29 7 437 48 2014 15
13. g the graphical layout of a diagram To layout the vertices and arrows 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 code 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 code 3 4 Saving the diagram To save your diagram locally just copy amp paste the contents of the Model code field to a text file and save that file locally to your compute a When you wish to continue working on the diagram copy the model code back into DAGitty as explained above 3 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 corresponding 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 6 Publishing diagrams online Part of the appeal of using DAGs is that the assumptions underlying one s research are made explicit and the conclusions drawn from the data can be later re checked if some of the assump tions are found to not hold Of course this requires to make the DAG available tog
14. informatics Universiteit Utrecht The Netherlands johannes textor gmx de theory bio uu nl textor Twitter dagitty 11 References 1 Silvia Acid and Luis M De Campos An algorithm for finding minimum d separating sets in belief networks In Proceedings of the 12th Conference of Uncertainty in Artificial Intelligence pages 3 10 1996 2 Joshua D Angrist Guido W Imbens and Donald B Rubin Identification of causal effects using instrumental variables Journal of the American Statistical Association 91 434 444 55 1996 3 Dmitry Baranovskiy Raphael javascript library http raphaeljs com 2010 4 Carlos Brito and Judea Pearl Generalized instrumental variables In Proceedings of the 18th Conference on Uncertainty in Artificial Intelligence pages 85 93 2002 5 Guido Imbens Instrumental variables An econometrician s perspective Statistical Science 29 3 323 58 2014 6 Sven Kniippel and Andreas Stang DAG program identifying minimal sufficient adjustment sets Epidemiology 21 1 159 2010 7 Steffen L Laurizen A Philip Dawid Birgitte N Larsen and Hanns Georg Leimer Indepen dence properties of directed markov fields Networks 20 5 491 505 1990 8 Judea Pearl Causality Models Reasoning and Inference Cambridge University Press New York NY USA 2nd edition 2009 9 Ines Polzer Christian Schwahn Henry V lzke Torsten Mundt and Reiner Biffar The association of tooth loss with
15. ipt 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 15 Furthermore DAGitty uses some modified code from the Dracula Graph Library by Philipp Strathausen which is also licensed under the MIT license 14 Versions 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 3 However the dependency on Rapha l was removed starting from version 2 0 and only SVG capable browsers will be supported in the future Iam grateful to the authors of these libraries for their valuable work 9 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 van Kampen 2014 e Polzer et al 2012 9 e Schipf et al 2010 13 e Shrier amp Pratt 2008 e Sebastiani et alfj 2005 e Acid amp de Campos 1996 Another example was provided by Felix Thoemmes via personal communication 2013 10 Author contact I would be glad to receive feedback from those who use DAGitty for research or educational purposes Also you are welcome to send me your suggestions or requests for features that you miss in DAGitty Johannes Textor Theoretical Biology amp Bio
16. it does not consider sending me your model so I can investigate 2 A brief introduction to causal diagrams In this section we will briefly review what causal diagrams are and how they can be applied in empirical sciences For a more detailed account we recommend the book Causality by Judea Pearl 8 or the chapter Causal Diagrams in the Epidemiology textbook of Rothman Greenland and Lash 10 Also take a look at the web page dagitty net learn where I am collecting several tutorials some of them interactive on specific DAG related topics In Epidemiology causal diagrams are also frequently called DAGsP In a nutshell a DAG is a graphic model that depicts a set of hypotheses about the causal process that generates a set of 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 represents 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 causal influence on Y then the arrow The 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 is omitted This has two important implicatio
17. mail address you will also receive a message requesting you to confirm your ownership of the DAG This is simply done by clicking on a confirmation link Only then will the DAG be linked to your e mail address and you will receive a password to use when deleting or modifying the published DAG If you did link your DAG to your e mail address you can delete it by choosing Delete on dagitty net from the Model menu which will prompt you to enter the DAG s URL and the password If the URL and password match the DAG will be deleted Similarly you can update a stored DAG using the Load from dagitty net function from the Model menu modifying it and saving it again You can view published DAGs if you know their URL by just putting the URL into your address bar of course but you can also do so using the Load from dagitty net function Please note that all DAGs stored on dagitty net are meant to be public information Do not store any data that you consider private or in any way secret Once stored on dagitty net every person in the world who knows your DAG s URL can view it but not your e mail address if you provided one Also note that there is no guarantee that dagitty net will keep running forever Storing your DAGs is done at your own risk Still you may find this feature useful for instance to e mail your DAGs to colleagues or to include links to DAGs in papers under review For archival purposes it may be more a
18. n are supported adjustment sets and instrumental variables 5 5 1 Adjustment sets Finding sufficient adjustment sets is one main purpose of DAGitty In a nutshell a sufficient adjustment set Z is a set 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 8 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 Total and direct effects One can understand adjustment sets graphically by viewing an adjust ment set as a set Z that closes 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 close all biasing paths and leave all causal paths open In the literature if the effect is not mentioned e g 6 then usually this kind of adjustment set is meant e Adjustment sets for the direct effect are sets that close all biasing paths and all causal paths and leave only the direct arrow from exposure X to outcome Y i e the path X Y if
19. 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 which all support scalable vector graphics SVG IE versions prior to 9 0 do not support SVG These should be able to perform all diagnosis functions but cannot display the graphics as well as modern browsers car If you encounter any problems please send me an e mail so I can fix them my contact information is at the end of this manual Keep in mind that DAGitty is often used by hundreds of people per day from all lWhile 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 over the world these people all benefit if the problem you found is fixed so please do consider investing the time to notify me if you encounter any bugs 1 3 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 dagitty net dagitty zip 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 Some features of DAGitty will not work in the offline version because they are a
20. ng habits at a time t4 the tar deposit in her lungs at a later time tz and finally the development of lung 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 In an epidemiological context we are often interested in the putative effect of a set of variables called exposures on another set of variables called outcomes A key question in Epidemiology and many other empirical sciences is how can we infer the causal effect of an exposure on an outcome of interest from an observational study Typically a simple regression will not suffice due to the presence of confounding factors If the assumptions encoded in a given the diagram hold then we can infer from this diagram sets of variables for which to adjust in an observational study to minimize such confounding bias For example consider the following diagram smoking 27 N carry matches _ _ gt cancer If we were to perform an association study on the relationship between carrying matches in one s pocket and developing lung cancer we
21. ns 1 arrows should follow time order or else the diagram contradicts the basic principle that 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 Y 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 also called the parents of Y Then G claims that the causal process determining the value of Y can be modelled as a mathematical function Y f X1 Xn y where ey the causal residual is a random variable that is jointly independent of all X For example the sentence smoking causes lung cancer could be translated into the following simple causal diagram smoking lung cancer We would interpret this diagram as follows 1 The variable smoking refers to a person s smoking habit prior to a later assessment of cancer in that same person 2 the natural process by which a person develops cancer might be influenced by the smoking habits of that person 3 there exist no other variables that have a direct influence on both smoking habits 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 smoki
22. oth of the following holds e The path p contains a chain x gt m gt y ora fork x m gt y such that m is in Z e The path p contains a collider x 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 The above criteria imply that paths consisting of only one arrow are always open no matter the content of Z Also it is possible that a path is closed with respect to the empty set Z 5 2 Coloring 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 5 3 Effect analysis As mentioned above arrows in DAGs represent direct effects That is in a DAG with three variables X M and Y an arrow X Y means that there is a causal effect of X on Y that is not mediated through the variable M Often when building DAGs people tend to forget this aspect and think only about whether any kind of causal effect exists without paying attention to how it is mediated This may result in DAGs with too many arrows To aid users with this George Ellison Leeds University suggested to implement a function that identifies arrows for which also a corresponding indire
23. ppropriate to include the DAG or the model code in the paper itself or its supporting information 4 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 arrows graphically using the mouse 4 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 arrows to the model as explained below 4 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 4 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 4 4 Setting the status of a variable Variables can have one of the following statuses e Exposure e Outcome e Unobserved latent e Adjusted e Other To
24. ram directly using DAGitty s graphical user interface explained in the next section or prepare a textual diagram description in a word processor 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 and with DAGs in general To do so just select one of the pre defined examples from the Examples menu 3 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 Knitippel 6 A diagram description model code somewhat clumsily called model text data in older DAGitty versions consists of two parts 1 A list of the variables in the diagram 2 A list of arrows between the variables The list of variables consists of one variable per line 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 constructing 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
25. rows It connects each pair of variables that according to the diagram could be statistically dependent In other words variables not connected by a line in the correlation graph must be statistically independent These pairwise independencies are also listed in the Testable implications field on the right hand side of the screen and so the correlation graph could be seen as encoding a subset of those implications Although this is not implemented in DAGitty yet it is also possible to take a given correlation graph which can be obtained e g by thresholding a covariance matrix and list all the DAGs that are compatible with it in the sense that they entail exactly the given correlation graph 17 5 4 2 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 graph This procedure is also highly recommended if you wish to verify the calculation by hand See the nice explanation by Shrier and Platt for details on this procedure In DAGitty you can switch between display of the model and its moral graph choosing moral graph in the view mode section on the left hand side of the page 5 5 Causal effect identification Some of the most important features of DAGitty are concerned with the question how can causal effects be estimated from observational data Currently two types of causal effect identificatio
26. sible adjustment sets or instrumental variables are of course dependent on the assumptions encoded in the diagram 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 8 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 12 6 Acknowledgements I would like to thank my collaborators Maciej Li kiewicz and Benito van der Zander both at the Institute for Theoretical Computer Science University of Liibeck Germany for our collaborations on developing efficient algorithms to analy
27. 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 these statuses are mutually exclusive e g a variable cannot be both unobserved and adjusted or both exposure and unobserved This could change in future versions of DAGitty 4 5 Adding new arrows To add a new arrow double click first on the source vertex which will become highlighted and then on the target vertex The arrow will be inserted If an arrow existed before in the opposite direction that arrow 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 c Arrows are by default drawn 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 4 6 Deleting variables To delete a variable move the mouse pointer over that variable and hit the del key on your keyboard or alternatively the d key the latter comes in handy if
28. 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 In other words adjustment for smoking would close the biasing path Adjustment sets will be explained in more detail in Section 5 5 1 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 3 Loading saving and sharing diagrams This section covers the three basic steps of working with DAGitty 1 loading a diagram 2 manipulating the graphical layout of the diagram and 3 saving the diagram First of all any causal diagram consists of vertices variables and arrows direct causal effects You can either create the diag
29. you re on a Mac which has no real delete key All arrows 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 4 7 Deleting arrows An arrow is deleted just like it has been inserted i e by double clicking first on the start variable and then on the target variable An arrow is also deleted automatically if a new one is inserted in the opposite direction see above 4 8 Choosing the style of display At present you can choose between two DAG diagram styles classic where nodes and their labels are separate from each other and SEM like where labels are inside nodes Both have their advantages and disadvantages By the way SEM refers to structural equation modeling 5 Analyzing diagrams 5 1 Paths Causal diagrams contain two different kinds of paths between exposure and outcome variables e Causal paths start at the exposure contain only arrows pointing away from the exposure and end at the outcome That is they have the forme gt x gt gt Xk gt 0 e Biasing paths are all other paths from exposure to outcome For example such paths can have the forme e x gt gt Xk gt 0 With respect to a set Z of conditioning variables that can also be empty if we are not condi tioning on anything paths can be either open or closed also called d separated 8 A path is closed by Z if one or b
30. ze causal diagrams I also thank Michael Elberfeld Juliane Hardt Sven Kniippel Keith Marcus Judea 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 Robert Balshaw George Ellison Marlene Egger Angelo Franchini Ulrike Forster Mark Gilthorpe 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 The development of DAGitty was sponsored by funding from the Institute of Genetics Health and Therapeutics at Leeds University UK I thank George Ellison for arranging this generous support 7 Legal notice Use of DAGitty is and will always be freely permitted and free of charge You may download a copy of DAGitty s source code from its website at www dagitty net 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 8 Bundled libraries DAGitty ships along with the following JavaScript libraries e Prototype js a framework that makes life with JavaScr
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