Deutsches Institut für Ernährungsforschung Potsdam-Rehbrücke. DAG program (v0.21)

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1 Deutsches Institut für Ernährungsforschung Potsdam-Rehbrücke DAG program (v0.21) Causal diagrams: A computer program to identify minimally sufficient adjustment sets SHORT TUTORIAL Sven Knüppel May 12,

2 General notes Confounding is an important source of bias in epidemiologic studies. With the introduction of causal diagrams (directed acyclic graphs, DAG) a new approach to conceptualize confounding and new rules to identify the minimal sufficient adjustment set have been established (Greenland, Pearl & Robins, Epidemiology, 1999, 10(1):37-48). The DAG program is a analysis tool, designed to select minimal sufficient adjustment sets within directed acyclic graphs. The first version (v0.12) of the DAG program can be used as MS DOS command line program. Using the framework Qt ( we have developed a Windows GUI that allows analyzing and changing causal diagrams more easier. 2

3 General notes If you use DAG program (v0.21), you need the same input files as they used in the previous version. To visualize causal diagrams we refer to the webtool DAGitty ( developed by Johannes Textor (University of Luebeck). Please note that we continuously improve the DAG program. If you have any problems, would like to report a bug or comment on the DAG program, please send an to sven.knueppel@dife.de. 3

4 Background: How to identify a minimally sufficient set? Definition: Back-door criterion A set of variables S satisfies the back-door criterion of exposure and outcome in a DAG if: (i) no node in S is a descendant of exposure; and (ii) S blocks every path between exposure and outcome that contains an arrow into exposure. Theorem If a set of variables S satisfies the back-door criterion, then the causal effect of exposure on outcome is identifiable. Pearl, Causality, 2009, p.79 4

5 Background: How to identify a minimally sufficient set? Theorem The problem of finding a minimum d-separating set S for exposure and outcome in a dag G is equivalent to the problem of finding a minimum separating set for exposure and outcome in the undirected moral graph. Acid and Campos (1996), p10 As introduction of the usage of moral graph see Pearl, Causality (2009, pp ) or Shrier and Platt (2008). 5

6 Citing DAG program If you use DAG program in any published work, please cite both the software (as an electronic resource/url) and the research letter describing the methods. Package: Author: URL: DAG program (including version number) Sven Knüppel Knüppel S, Stang A (2010) DAG program: identifying minimal sufficient adjustment sets. Epidemiology,21(1):159. 6

7 Run DAG program The DAG program runs as Windows program and can be started by clicking on the program icon. While running the program you need to set variable information and a graph description (adjacency list or adjacency matrix). If you wish to determine if a given set of covariates is a sufficient, minimally sufficient, or insufficient then specify these sets. 7

8 Main window 8

9 Input data: variable information The variable information is a white-space (space or tab) delimited text consisting of two columns: Column 1: Name of variable Alphanumeric value (without blanks or other white-spaces) Column 2: Measurement status Measurement status is set to 1 if the variable is measured otherwise it is set to 0. The first line must contain the exposure of interest. The second line needs to contain the event of interest. Thereafter, you can add covariates in any order. Add the variable information in the variable information text field. 9

10 Input data: graph description Adjacency list ( edge statements ) The first possibility to define a DAG is a list of white-space delimited edge statements. All statements are edge statements that name a tail node (parent) and a list of head nodes (childs). Edge starts from the parent and means edge from parent to child_1, to child_2 etc. Only one edge statement is allowed per line. Every parent needs to be described in this file. For further information see section examples. Add the graph description in the Adjacency matrix / Adjacency list text field. 10

11 Input data: graph description Adjacency matrix The second possibility to define a DAG is a adjacency matrix that describes the graph by a matrix containing all arrow directions. Create a matrix consisting of all variables in the same order as in the information text field and code their connection by 1 (arrow) and 0 (no arrow). For better understanding see the examples. Add the graph description in the Adjacency matrix / Adjacency list text field. 11

12 Example 1: Classical confounder triangle Suppose the following DAG is given. E is the exposure of interest, D is the outcome, and C is a possible confounder. All three variables are measured. Create information and graph description. 1. Variable information 2. Definition of causal graph E C? D Variable name E 1 D 1 C 1 Status 1 = measured 0 = unmeasured 1th line: exposure 2nd line: outcome Other variable(s) a. Adjacency list ( edge statements ) edge from parent to child_1, to child_2 etc. E D C E D The edge statement E D makes an edge from E to D. The next edge statement C E D makes an edge from C to E and another from C to D. 12

13 Example 1: Find minimally sufficient set 13

14 Example 1: Variable description 14

15 Example 1: Graph description and minimally sufficient set Suppose the following DAG is given. E is the exposure of interest, D is the outcome, and C is a possible confounder. All three variables are measured. Create information and graph description. 1. Variable information 2. Definition of causal graph E C? D Variable name E 1 D 1 C 1 Status 1 = measured 0 = unmeasured 1th line: exposure 2nd line: outcome Other variable(s) a. Adjacency list ( edge statements ) edge from parent to child_1, to child_2 etc. E D C E D The edge statement E D makes an edge from E to D. The next edge statement C E D makes an edge from C to E and another from C to D. 15

16 Example 1: Classical confounder triangle (cont.) Suppose the following DAG is given. E is the exposure of interest, D is the outcome, and C is a possible confounder. All three variables are measured. C Alternatively, you can specify the DAG with an adjacency matrix. E? D 2. Definition of causal graph b. Adjacency matrix Make a matrix of all arrow directions. Set 1 if there is an arrow otherwise set 0. to E D C E From D C

17 Example 1: Classical confounder triangle (cont.) 17

18 Example 2: DAG including collider adjustment A B C E Z? D Variable information E 1 D 1 A 1 B 1 C 1 Z 1 Adjacency list E D A E Z B Z D C Z D Z E D 18

19 Example 2: Variable description Variable information Adjacency list 19

20 Example 3: Specification of a set of covariates Suppose the DAG from example 2 is given. A B C Z E? D We would like to test three different sets of covariates if they are sufficient. Set 1 = {A} Set 2 = {A, Z} Set 3 = {A, B, C, Z} Additional to the variable information and graph definition we need a definition which specified the test sets. 20

21 Example 3: Specification of a set of covariates The numbers are the path numbers from the graph description. 21

22 Example 3: Specification of a set of covariates 22

23 Remark DAG program distincts between three types of paths: Front-door paths: starting with in arrow pointing away from the exposure Back-door paths: starting with an arrow pointing into the exposure Other paths: starting with an arrow pointing away from the outcome Other paths are unconditional no biasing paths. Other paths could be opened by conditioning on a specified set. 23

24 Remark If a specified set contains a descendant of exposure or outcome, the total effect might not estimated. In this case the found minimally sufficient set conditional on specified set (MSA) means that all backdoor and other paths are closed conditional on this MSA. Those MSAs must not fullfill the Backdoor criterion and therefore should be used carefully. Direct paths from outcome to exposure are not allowed because this would violate the temporality assumption that the exposure should not be a consequence of the outcome. Such a path would create a loop between exposure and outcome. 24

25 Loading existing files To load a graph you need the two input files: Variable information (often saved as *.info) Graph description file (often saved as *.txt) By clicking on File>New you can load the graph. 25

26 Loading existing files 26

27 Save You can save your result by clicking on File>Save. 27

28 Save 28

29 Options It is possible to specify the maximum number to show paths and it is also possible to set a upper limit for counting paths. 29

30 Integrated examples Sehrndt A, Stang A, Lehmkuhl E, Regitz-Zagrosek V, Babitsch B (2010). Influence of the socioeconomic status on the health related quality of life in patients before and after coronary artery bypass grafting an example of using DAG. Presentation at DAG workshop of DGEpi at BAuA (Berlin), 26.Nov.2010 Polzer et al. personal communication, Schipf S, Haring R, Friedrich N, Nauck M, Lau K, Alte D, Stang A, Völzke H, Wallaschofski H. 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, in press. Shrier I, Platt WP Reducing bias through directed acyclic graphs. BMC Medical Research Methodology 2008, 8:70. Acid S, De Campos LM. An algorithm for finding minimum d-separating sets in belief networks. In Proceedings of the twelfth Conference of Uncertainty in Artificial Intelligence, pages 3-10,

31 References Acid S, De Campos L.M. (1996).. An algorithm for finding minimum d-separating sets in belief networks. In Proceedings of the twelfth Conference of Uncertainty in Artificial Intelligence, pages 3-10 Clark, J. and Holton, D.A. (1994). Graphentheorie. Grundlagen und Anwendungen. Heidelberg: Spektrum Akad. Vlg. Glymour, M.M. and Greenland, S. (2008). Causal diagrams. Ch. 12 in: Rothman, K.J., Greenland, S., Lash,T.L. Modern Epidemiology, 3rd ed. Philadelphia: Lippincott. Greenland, S., Pearl, J. and Robins, J.M. (1999). Causal diagrams for epidemiologic research. Epidemiology, 10, Greenland, S. and Brumback, B.A. (2002). An overview of relations among causal modelling methods. International Journal of Epidemiology, 31, Hernán, M.A., Hernandez-Diaz, S., Werler, M.M., Mitchell, A.A. (2002). Causal knowledge as a prerequisite for confounding evaluation. American Journal of Epidemiology, 155,

32 References Pearl, J. (1995). Causal diagrams for empirical research (with discussion). Biometrika,82, Pearl, J. (2009). Causality. New York: Cambridge University Press. 2nd Edition. Pearl, J., (2009). Causal inference in statistics: An overview. Statistics Surveys, 3, Robins, J.M. (2001). Data, design, and background knowledge in etiologic inference. Epidemiology;12: Schipf S, Haring R, Friedrich N, Nauck M, Lau K, Alte D, Stang A, Völzke H, Wallaschofski H. (2010). 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. in press. 32

33 References Sehrndt A, Stang A, Lehmkuhl E, Regitz-Zagrosek V, Babitsch B (2010). Influence of the socioeconomic status on the health related quality of life in patients before and after coronary artery bypass grafting an example of using DAG. Presentation at DAG workshop of DGEpi at BAuA (Berlin), 26.Nov.2010 Shrier I, Platt W.P. (2008). Reducing bias through directed acyclic graphs. BMC Medical Research Methodology, 8:70. Skienna S.S. (2008). The Algorithm Design Manual, 2n ed., Berlin, Springer. Spirtes, P., Glymour, C., Scheines, R. (2001). Causation, Prediction, and Search, 2nd ed. Cambridge, MA: MIT Press. 33

34 Sven Knüppel Department Epidemiology Deutsches Institut für Ernährungsforschung German Institute of Human Nutrition Potsdam-Rehbrücke DAG program: Thanks to Johannes Textor, Juliane Hardt, Dagmar Drogan, and Karina Meidtner for helpful comments. Special thanks to Andreas Stang and Charles Poole for their helpful comments on the first version of DAG program. 34