Deutsches Institut für Ernährungsforschung. DAG-Programm I: Minimierung von Confounding bei komplexen kausalen Graphen (directed acyclic graphs)
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1 Deutsches Institut für Ernährungsforschung DAG-Programm I: Minimierung von Confounding bei komplexen kausalen Graphen (directed acyclic graphs) Sven Knüppel 1, Johannes Textor 2 Workshop 26. November 2010 (Berlin) 1 Abteilung Epidemiologie, Deutsches Institut für Ernährungsforschung Potsdam-Rehbrücke 2 Institut für Theoretische Informatik, Universität zu Lübeck 1
2 Objectives Directed Acyclic Graphs (DAGs) are used to understand, identify, and control for confounding. To identify minimally sufficient adjustment sets (MSAS), a procedure of strict rules should be followed. As the DAG rules are logical rules, a software program can be developed to identify the MSAS: DAG program (developed by Sven Knüppel) DAGitty (developed by Johannes Textor) dagr (developed by Lutz Breitling) 2
3 Back-door criterion Definition 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 (back-door path). 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 3
4 Sufficiency Sufficient adjustment set A set of adjusting variables S that leaves only causal paths open and blocks all back-door paths (S satisfies the backdoor-criterion) is called sufficient set. The effect of exposure on the outcome is unbiased given S. Minimally sufficient adjustment set (MSAS) A sufficient set of which no proper subset is sufficient. 4
5 Two upcoming questions 1. How to find all paths in a graph? Example: Backtracking 2. How to identify the minimally sufficient adjustment sets? Check if all back-door paths are blocked after conditioning on specified set. Using the properties of a DAG it is possible to find sufficient sets without enumeration of all back-door paths (Johannes Textor will talk about that detailed). 5
6 Type of paths How to find all paths in a graph? Path Type Status Remark Front-door causal unblocked (open) Direct and indirect effects Front-door non-causal blocked (closed) Back-door non-causal unblocked (open) Contain ancestors of exposure and outcome: biasing paths Back-door non-causal blocked (closed) No biasing path Other non-causal blocked (closed) Contain descendants of outcome 6
7 How to find all paths in a graph? Solution: Backtracking algorithm The backtracking algorithm is used to identify front-door, back-door paths, and other paths. Backtracking: based on trial and error principle. The algorithm incrementally adds a new candidate to the interim solutions until a final solution is found. All paths will be systematically determined. 7
8 Backtracking algorithm Popular german children's game Haus des Nikolaus (The house of the St Nicolas) Task Draw the house of Nicolas without lifting your pencil off the paper or going along the same way twice. How many possibilities do you have to draw the house? 8
9 Backtracking - Example How do we find a path from the start to the end? Procedure: Trial and error Problem: The path comes to a dead end! Solution: Go back and try another edge. Path from start to end found. Start End 9
10 How to identify the minimally sufficient adjustment sets (MSAS)? Algorithm used by DAG program 1) Check the empty set. The existence of one or more confounding paths makes that set insufficient. 2) Check the one-covariate sets that do not contain colliders. 3) Check the two-covariate sets and remove sufficient sets which contain proper subsets. 4) Repeat this process for candidate covariate sets containing 3, 4, 5 etc. covariates. All candidate sets contain only ancestors of exposure or outcome. Variables affected by exposure or outcome are disregarded. 10
11 How to identify the minimally sufficient adjustment sets (MSAS)? How many sets have to be tested to find the MSAS? With n variables you get 2 n possible combinations of the variables. n = = 8 n = = 1,024 n = = 1,048,576 n = = You cannot compute all combinations in finite time, if the count of variables is high. 11
12 DAG Program Programming language: C++ Available as DOS command line program or Windows program (GUI): First version: Version v0.12 (Mar 31, 2010) [MS DOS program] New version: Version v0.20 (Nov 11, 2010) [WINDOWS program] Publication: Knüppel S, Stang A. Research Letter. Epidemiology, Volume 21, Number 1, January 2010, p.159 The DAG Program needs at least two input files (ASCII) Definition of the graph (adjacency matrix or adjacency list) Information about variables, if measured 12
![20 (Nov 11, 2010) [WINDOWS program] Publication: Knüppel S, Stang A. Research Letter.](/docs-images/46/21362246/images/page_12.jpg "Epidemiology, Volume 21, Number 1, January 2010, p.")
13 DAG Program example: INPUT DATA 1. Definition of causal graph A B a. Adjacency list ( edge statements ) Z edge from parent to child_1, to child_2 etc. E D A E Z B D Z Z E D b. Adjacency matrix to E D A B Z E D from A B Z E 2. Variable information Variable name E 1 D 1 A 1 B 1 Z 1? Status 1 = measured 0 = unmeasured D 1th line: exposure 2nd line: outcome Other variables 13
14 Open DAG program 14
15 Input data Variable information Adjacency list ( edge statements ) 15
16 Identifying the minimally sufficient adjustment sets (MSAS)? Find MSAS 16
17 Path summary MSAS Varifying paths 17
18 Two options to show and count paths 18
19 DAG Program example: test sets A B We would like to test four different sets of covariates, whether they are sufficient. Z Set 1 = {A} Set 2 = {A,B} E? D Set 3 = {A,B,Z} Set 4 = {A,B,Z} In addition to the variable information and graph description we need a file which specifies the test sets. Set file A A B A Z A B Z 19
20 Set summary 20
21 21
22 Issues How many paths can be covered by the DAG program? The backtracking algorithm is a fast algorithm to identify paths and can handle a high number of paths. The operating time depends on the number of existing paths. So far the upper limit for the number of paths, which can be handled, is not tested. 22
23 Issues How many covariates can be covered by the DAG program? The direct parents of both exposure and outcome are always part of the MSAS. To identify the MSAS we are able to restrict the searching to variables which are ancestors of exposure and outcome which lie on open back-door paths. (Johannes Textor will talk about that more detailed.) 23
24 Lutz Breitling: dagr 24
25 Summary Directed acyclic graphs are useful to visualize causal relationships. DAGs can contain thousands or more paths. The DAG program, DAGitty and dagr follows the strict DAG rules and suggests one or more MSAS. It is possible to test different covariate sets. 25
26 Thank you for your attention Sven Knüppel Department of Epidemiology Deutsches Institut für Ernährungsforschung German Institute of Human Nutrition Potsdam-Rehbrücke DAG Program: Johannes Textor s DAGitty: Thanks to Juliane Hardt, Dagmar Drogan, and Karina Meidtner for helpful comments. Special thanks to Andreas Stang and Charles Poole 26
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