Introduction to DAGs Directed Acyclic Graphs

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1 Introduction to DAGs Directed Acyclic Graphs Metalund and SIMSAM EarlyLife Seminar, 22 March 2013 Jonas Björk (Fleischer & Diez Roux 2008)

2 Introduction to DAGs Basic terminology and principles Classification of bias in the DAG framework Concerns and limitations Examples from analysis of neighbourhood health effects

3 DAG a logical system for causal relationships Development of Western science is based on two great achievements: 1. the invention of the formal logical system by the Greek philosophers 2. the discovery of the possibility to find out causal relationships by systematic experiment during the Renaissance (Albert Einstein, 1953; adopted from Pearl 2009)

4 Directed Acyclic Graphs (DAGs) Causal diagrams - visualize causal (structural) relationships between variables Based on mathematical theory and reasoning Used in Epidemiology, social science Computer science, artificial Intelligence Economics, Business administration Cognitive science... Minimize bias - identify appropriate (and inappropriate) analytical strategies

5 DAGs - nodes and arrows Nodes represent variables Measured and unmeasured Observable and unobservable Structural Equation Models (SEMs); Directed arrows (single-headed) show direct causal effects (Hernan, Epidemiology 2004)

6 DAG Language Direct effect (only one) E affects D directly if there is an arrow from E to D E D Indirect effect (can be more than one) E affects D indirectly if there are a sequence of directed arrows starting in E and ending in D E M D Children Variables directly affected by E Descendants: directly or indirectly affected by E Parents Variables that directly affect E Ancestors: all variables that affect E directly or indirectly

7 DAG Language - Example Direct effect Indirect effect Children, Descendants Parents, Ancestors (Fleischer & Diez Roux 2008)

8 Acyclic graphs Loops not allowed: E D Temporal associations can be depicted in the following way: E 0 D E 1 Time moves from left to right in the graph

9 Path Paths (E Z D) Sequence of arrows connecting two variables, regardless of the direction of the arrows E Z D E Z D E Z D E Z D Collider (common cause within a path) Variable Z in a path that has two arrows pointing into it E Z D Blocks (breaks) the information chain between E and D Unblocked backdoor path from E to D Begins with arrow pointing into E Ends with arrow pointing into D Does not contain a collider This is the origin of confounding

10 DAG Language - Example Path Collider Unblocked backdoor path (Fleischer & Diez Roux 2008)

11 Common cause (Hernan, Epidemiology 2004) If we want to illustrate the E-D association, all common causes must be included, otherwise the DAG is not considered causal

12 Common effect Common consequence Collider on the path between E and D (Hernan, Epidemiology 2004) Conditioning ( knowing the value of ) Restriction Stratification Matching Adjustment Creates an association between E and D

13 DAG Language - Example Common cause Common effect Conditioning (Fleischer & Diez Roux 2008)

14 Bias Structural association between exposure (E) and outcome (D) that is not causal (from E to D) Reversed causality (Information bias?) Confounding Selection bias Thus, under the causal null hypothesis, exposure and outcome will still be associated

15 Association vs. causation E - D associations can have three different structural origins according to DAG theory: 1. Cause and effect (watch out for reversed causality) 2. Common cause (confounding) Chance is not a structural source of association! 3. Conditioning on a common effect (selection bias) (Hernan et al. 2004)

16 Appropriate design and analytical strategy 1. Design that avoids reversed causality 2. Control confounding by blocking backdoor paths from E to D (conditioning) 3....identify selection bias introduced by conditioning

17 Small Group Discussion DAGs Control confounding by conditioning Identify selection bias from conditioning Which variables should we adjust for in order to estimate 1) the total (direct + indirect) effect 2) the direct effect (Fleischer & Diez Roux 2008) of neighborhood violence on CVD? Motivate your answers!

18 Confounding controls in DAGs There exists formal methods (and software) to 1. Determine the set S of covariates that is necessary to control for confounding 2. Determine whether set S of covariates is minimally sufficient to control for confounding Have we discovered all unblocked backdoor paths? Is there redundancy in the set of blocking variables? (Fleischer & Diez Roux 2008)

19 Minimally sufficient? Suppose we think that S={Income, PA} is sufficient to control for when estimating the direct effect? 1. Delete all arrows starting at E (Neighbourhood violence) 2. Connect all variables that share a child or descendent in S 3. Is there any unblocked backdoor paths from E to D (CVD) that does not pass through S?

20 If you still think you can rely on your intuition... Z 1 Z 2 Z 3 Z 4 Z 5 (Adopted from Pearl 2009, p. 80) E Z 6 D Which variables should we adjust for in order to estimate the effect of E and D? Motivate your answer!

21 DAGs concerns and limitations How much should be included? All common causes must be included A complete DAG for several exposures and outcomes can be quite messy Binary nature Effect / no effect Effect size, dose-response, magnitude of interaction etc. cannot be depicted Assumes a perfect study setting Correctly specified model, no measurement errors, continuous monitoring of outcome in longitudinal settings etc. Limited guidance in the choice of analytical strategy in less perfect settings (e.g. trade-off confounding vs. selection)

22 DAGs How much should be included? (de Jong et al. 2012)

23 DAGs in longitudinal survey settings Common cause D t - 1 D t Different types of effects 1. Trigger effect 2. Effect of long-time exposure 3. Effect with long-time effect on outcome 4. Delayed effect E t - 1 E t t -1 Common consequence (collider) t Time

24 Additional Reading Pearl J. Causality models, reasoning and inference. Cambridge University Press 2009 (second edition) Fleischer NL & Diez Roux AV. Using directed acyclic graphs to guide analyses of neighbourhood health effects: an introduction. J Epidemiol Community Health 2008;62: Hernan et al. A structural approach to selection bias. Epidemiology 2004;15:

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