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Causal Graphs, epi forum

Causal Graphs, epi forum. Hein Stigum http://folk.uio.no/heins/ talks. Nov-14. Nov-14. Nov-14. Nov-14. Nov-14. H.S. H.S. H.S. H.S. 1. 1. 1. 1. 1. Agenda. Motivating examples Concepts Confounder, Collider Analyzing DAGs Paths Examples Confounding

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Causal Graphs, epi forum

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  1. Causal Graphs, epi forum Hein Stigum http://folk.uio.no/heins/ talks Nov-14 Nov-14 Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. H.S. H.S. 1 1 1 1 1

  2. Agenda • Motivating examples • Concepts • Confounder, Collider • Analyzing DAGs • Paths • Examples • Confounding • Mixed (confounders and mediators) • Selection bias Nov-14 Nov-14 Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. H.S. H.S. 2 2 2 2 2

  3. Why causal graphs? • Problem • Association measures are biased • Understanding • Confounding, selection bias, mediators • Analysis • Adjust or not • Discussion • Precise statement of prior assumptions H.S.

  4. Motivating examples • Statins and coronary heart disease • Disease risk: lifestyle, cholesterol • Diabetes and fractures • Disease risk: fall, bone density • Exposure risk: BMI, Physical activity • Diabetes and fractures • Analyze among hospital patients • Exclude hospital patients Adjust or not? Exclude or not? H.S.

  5. Concepts Causal versus casual Nov-14 Nov-14 Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. H.S. H.S. 5 5 5 5 5

  6. god-DAG DAG=Directed Acyclic Graph C age U obesity Node = variable Arrow = cause, (at least one individual effect) E vitamin D birth defects Read of the DAG: Causality = arrows Associations = paths Questions on the DAG: E-D effect biased? Adjust for age? Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. 6 6 6

  7. Association and Cause Yellow fingers Lung cancer Cause Smoke Yellow fingers Lung cancer Confounder Hospital Collider Yellow fingers Lung cancer Possible causal structure Association Yellow fingers Lung cancer Nov-14 Nov-14 H.S. H.S. H.S. 7 7

  8. A confounder induces an association between its effects Conditioning on a confounder removes the association Condition = (restrict, stratify, adjust) Confounder idea Adjust for smoking Smoking + + Yellow fingers Lung cancer + A common cause Smoking + + Yellow fingers Lung cancer Nov-14 Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. H.S. 8 8 8 8

  9. Conditioning on a collider induces an association between its causes “And” and “or” selection leads to different bias Collider idea Select subjects in hospital Hospital + + Yellow fingers Lung cancer • or • + and Two causes for coming to hospital Hospital + + Yellow fingers Lung cancer Nov-14 Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. H.S. 9 9 9 9

  10. Data driven analysis Want the effect of E on D(E precedes D) Observe the two associations E-C and D-C Assume criteria dictates adjusting for C (likelihood ratio, Akaike (赤池 弘次) or change in estimate) C E D The undirected graph above is compatible with three DAGs: C C C E D E D E D Confounder 1. Adjust Mediator 2. Adjust (direct) 3. Not adjust (total) Collider 4. Not adjust Conclusion: The data driven method is correct in 2 out of 4 situations Need information from outside the data to do a proper analysis H.S.

  11. Analyzing DAGS: Paths The Path of the Righteous Nov-14 Nov-14 H.S. H.S. H.S. 11 11

  12. Path definitions Path: any trail from E to D (without repeating or crossing itself) Type: causal, non-causal State: open, closed K C Four paths: E D M Goal: Keep causal paths of interest open Close all non causal paths Nov-14 H.S. H.S. 12

  13. Four rules K non-causal C 1. Causal path: ED (all arrows in the same direction) otherwise non-causal E D causal M K closed Before conditioning: 2. Closed path: K (closed at a collider, otherwise open) C E D open M K Conditioning on: 3. a non-collider closes: [M] or [C] 4. a collider opens: [K] (or a descendant of a collider) C E D M H.S.

  14. Confounding Nov-14 Nov-14 Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. H.S. H.S. 14 14 14 14 14

  15. Physical activity and Coronary Heart Disease (CHD) C1 age • We want the total effect of Physical Activity on CHD. What should we adjust for? E Phys. Act. D CHD C2 sex Bias No bias Nov-14 Nov-14 H.S. H.S. 15 15

  16. Vitamin and birth defects Bias in E-D? Adjust for C? C age U obesity E vitamin D birth defects Bias This example and previous slide are both confounding No bias Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. 16 16 16

  17. Mixed Confounders and mediators Nov-14 Nov-14 Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. H.S. H.S. 17 17 17 17 17

  18. Diabetes and Fractures F prone to fall We want the total effect of diabetes on fractures E diabetes D fracture V BMI P physical activity B bone density Mediators Confounders H.S.

  19. Statin and CHD U lifestyle C cholesterol E statin D CHD No adjustments gives the total effect Is C a collider? Adjusting for C opens the collider path must also adjust for U to get the direct effect • We want the total effect of statin on CHD. What would we adjust for? • Can we estimate the direct effect of statin on CHD (not mediated through cholesterol)? H.S.

  20. Selection bias Nov-14 Nov-14 Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. H.S. H.S. 20 20 20 20 20

  21. Diabetes and Fractures • Convenience: • Conduct the study among • hospital patients? H hospital E diabetes D fracture 2. Homogeneous sample: Exclude hospital patients Collider, selection bias Collider stratification bias: at least on stratum is biased H.S.

  22. Selection bias: size and direction Hospital risk: H.S.

  23. Adjusting for selection bias F prone to fall H hospital E diabetes D fracture Adjust for F to close this path H.S.

  24. Summing up Better discussion based on DAGs Nov-14 Data driven analyses do not work. Need (causal) information from outside the data. DAGs are intuitive and accurate tools to display that information. Paths show the flow of causality and of bias and guide the analysis. DAGs clarify concepts like confounding and selection bias, and show that we can adjust for both. Nov-14 H.S. H.S. H.S. 24 24

  25. References 1 Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3. ed. Philadelphia: Lippincott Willams & Williams,2008. Hernan MA, Hernandez-Diaz S, Robins JM. A structural approach to selection bias. Epidemiology 2004; 15: 615-25. Hernandez-Diaz S, Schisterman EF, Hernan MA. The birth weight "paradox" uncovered? Am J Epidemiol 2006; 164: 1115-20. 4 Schisterman EF, Cole SR, Platt RW. Overadjustment Bias and Unnecessary Adjustment in Epidemiologic Studies. Epidemiology 2009; 20: 488-95. 5 VanderWeele TJ, Hernan MA, Robins JM. Causal directed acyclic graphs and the direction of unmeasured confounding bias. Epidemiology 2008; 19: 720-8. 6 VanderWeele TJ, Robins JM. Four types of effect modification - A classification based on directed acyclic graphs. Epidemiology 2007; 18: 561-8. 7 Weinberg CR. Can DAGs clarify effect modification? Epidemiology 2007; 18: 569-72. Hernan and Robins, Causal Inference (coming) Nov-14 Nov-14 Nov-14 H.S. H.S. H.S. 25 25 25

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