1. Using Directed Acyclic Graphs (DAGs) to assess confounding Glenys Webster & Anne Harris May 14, 2007 St Paul’s Hospital Statistical “Rounds”

2. The Issue Confounding introduces bias into effect estimates Common methods to assess confounding can –Fail to identify confounders  residual bias –Introduce bias by adjusting for non-confounders Graphical causal models (e.g. DAGs) can help Hernan, MA 2002. Am J of Epidemiol 155 (2): 176-184

3. Objective Introduce a graphical method to help assess potential confounders –Directed Acyclic Graphs (DAGs) –Useful during Study design (which variables to measure?) Data analysis (which variables to adjust for?)

4. Has anyone used DAGs before?

5. Overview Review common methods to assess confounding Introduce Directed Acyclic Graphs (DAGs) Exercise: Spot the confounders! Example: Folate vs neural tube defects –Why incorporating a priori knowledge (using DAGs) matters Conclusions & Discussion

6. What is confounding?

7. Occurs when the relationship observed between E & D is at least partly due to another variable (C) Occurs when E & D share a common cause CED E.g. E = yellow fingers, D = lung cancer, C = smoking

8. How to assess confounding? 3 commonly used methods: 1.Automatic variable selection (p values) 2.Compare adjusted vs unadjusted ORs 3.Check criteria for confounding Confounders are: Associated with E Associated with D (in unexposed) Not in the causal pathway between E & D

9. BUT! These methods may lead to bias 1-4 by: –Omitting important confounders –Adjusting for non-confounders Limited consideration of causal mechanisms Graphical models (e.g. DAGs) can help 1.Weinberg CR 1993. Am J Epidemiol 137: 1-8 2.Greenland S et al. 1999. Epidemiology 10: 37-48 3.Robins JM. 2001. Epidemiology 12: 313-320 4.Pearl J. 2000. Causality. Cambridge University Press

10. Directed Acyclic Graphs (DAGs) Picture showing relationships among variables Incorporate a priori knowledge Clearly state assumptions Helps to identify: –Which variables to measure –Confounders & Non-confounders Proper control for confounding reduces bias

11. Directed Acyclic Graphs (DAGs) Nodes (variables) and arrows Arrows indicate “causal direction” Arrows say nothing about the magnitude, shape or the mathematical direction of the association (i.e. positive, negative) CED

12. Directed Acyclic Graphs (DAGs) Directed: Arrows show “causal direction” of association Acyclic: No feedback loops between E & D (following direction of arrows) CEDCED

13. Variable definitions E = Exposure D = Disease C = Potential confounder U = Unmeasured variable CED U

14. DAGs terminology Ancestor, Parent Descendent, Child Common ancestor = Common cause = Confounder Common descendent = Common effect = Collider CEDEDC

15. Using DAGs to assess confounding Draw a DAG Remove arrow between E  D Are there any open “backdoor pathways” to get from E to D? If yes  confounding  need to adjust If no  no confounding  do not adjust! Rules:  Can follow arrows in any direction  Colliders (common effects) BLOCK a path  Adjusting for a non-collider BLOCKs the path  Adjusting for a collider OPENs the path

16. Example 1: C = common cause CED Step 1: Remove arrow between E  D

17. Example 1: C = common cause CED Step 2: Look for backdoor pathways between E & D

18. Example 1: C = common cause CED Backdoor path exists!  need to adjust for C

19. Example 1: C = common cause CED Adjusting for C blocks the backdoor pathway from E to D. There is no more confounding. Observed E  D relationship is free of bias

20. Example 2: C = common effect (collider) EDC Step 1: Remove arrow between E  D

21. Example 2: C = common effect (collider) EDC Step 2: Look for backdoor pathways between E & D

22. Example 2: C = common effect (collider) EDC C is a collider  Blocks the path No backdoor pathway  do not adjust for C Adjusting for C would open the pathway, & INTRODUCE BIAS!

23. Spot the confounders (see handout) For each graph, should we adjust for C? Remove arrow between E  D Are there any open “backdoor pathways” to get from E to D?  If yes  confounding  need to adjust  If no  no confounding  Do not adjust! Rules:  Can follow arrows in any direction  Colliders BLOCK a path  Adjusting for a non-collider BLOCKs the path  Adjusting for a collider OPENs the path

24. Fig 5 CE D

25. Fig 6 CED U

26. Fig 7 CED U

27. Fig 8 UED C

28. Fig 1 ED C

29. Fig 2 ED C U1U1

30. Fig 3 ED C U2U2

31. Fig 4 ED C U2U2 U1U1

32. Exercise results Adjust for C? FigureYESNO 1 2 3 4 5 6 7 8( ) What do these graphs have in common?

33. Incorporating a priori knowledge DAGs incorporate our a priori knowledge about how variables are related Ignoring this knowledge (e.g. using standard methods to assess confounding) may introduce bias  Example from the birth defects literature

34. Example Case-control study of folate supplementation (E) and neural tube defects (D). What should be done with mystery variable, C? Neural Tube Defect Control Defect Folate 43239 No Folate 194704 Crude OR: 0.65 (CI: 0.45-0.94)

35. Is Mystery Variable ‘C’ a confounder? Method 1: Automatic selection Build model with D, E and C If p value of ß C is < 0.1, keep C in model –p value of ß C = 0.001 Conclusion: Adjust for C

36. Is Mystery Variable ‘C’ a confounder? Method 2: Change in effect size Compare adjusted and unadjusted ORs If the difference is > 10%, adjust for C –Unadjusted OR = 0.65 –Adjusted OR = 0.80 –(0.8 - 0.65)/0.65 = 0.23 (23% difference) Conclusion: Adjust for C

37. Is Mystery Variable ‘C’ a confounder? Method 3: Check rules for confounding Is C is associated with Folate supplementation (E)? OR = 0.50 Is C is associated with Neural tube defects in people who did not take folate (D)? OR = 15.22 Is C in the causal pathway between folate and neural tube defects? No (based on a priori knowledge) Conclusion: Adjust for C

38. Adjusting for C All 3 standard methods  Adjust for C Neural Tube Defect Control Defect Folate198 No Folate10046 Neural Tube Defect Control Defect Folate24231 No Folate94658 C = 1 C = 0 OR C=1 : 1.09OR C=0 : 0.72 Adjusted OR = 0.80 (95% CI: 0.53, 1.20)

39. Compare adjusted OR to crude OR: OR adjusted = 0.80 (CI: 0.53, 1.20) OR crude = 0.65 (CI: 0.45-0.94) Was adjustment appropriate? Adjusting for C CE D

40. What is C? Stillbirth or therapeutic abortion (C=1) Live birth (C=0) CE D ED C

41. Folate Example Key Points Standard methods to assess confounding include little a priori knowledge about how variables are related Standard methods may suggest confounding when it is NOT present Adjusting for non-confounders (colliders) can introduce bias A causal model (e.g. a DAG) is required to separate colliders from confounders.

42. Conclusions Common methods to assess confounding can lead to bias by: –Omitting important confounders –Adjusting for non-confounders DAGs are used to –Identify confounders and non-confounders (colliders) –Incorporate a priori knowledge –Clearly state your mental model of how system works –Allow others to follow your reasoning DAGs are useful for study design & data analysis

43. Discussion