1. Oct-15H.S.1Oct-15H.S.1Oct-151 H.S.1Oct-15H.S.1Oct-15H.S.1 Causal Graphs, epi forum Hein Stigum http://folk.uio.no/heins/talks

2. Oct-15H.S.2Oct-15H.S.2Oct-152 H.S.2Oct-15H.S.2Oct-15H.S.2 Agenda Motivating examples Concepts –Confounder, Collider Analyzing DAGs –Paths Examples –Confounding –Mixed –Selection bias

3. Oct-15H.S.3 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?

4. Oct-15H.S.4Oct-15H.S.4 Concepts Causal versus casual Oct-15H.S.4Oct-154 H.S.4Oct-15H.S.4

5. Oct-15H.S.5Oct-15H.S.5Oct-155 H.S.5 god-DAG E vitamin D birth defects C age U obesity Read of the DAG: Causality= arrows Associations= paths Node = variable Arrow = cause, (at least one individual effect) DAG=Directed Acyclic Graph Questions on the DAG: E-D effect biased? Adjust for age?

6. Oct-15H.S.6Oct-15H.S.6Oct-156 Association and Cause Lung cancer Yellow fingers Association Possible causal structure Lung cancer Yellow fingers Cause Lung cancer Yellow fingers Confounder Smoke Lung cancer Yellow fingers Collider Hospital H.S.

7. Oct-15H.S.7Oct-15H.S.7Oct-157 H.S.7Oct-15H.S.7 Confounder idea A confounder induces an association between its effects Conditioning on a confounder removes the association Condition = (restrict, stratify, adjust) Yellow fingers Smoking Lung cancer A common cause + ++ Adjust for smoking Yellow fingers Smoking Lung cancer ++

8. Oct-15H.S.8Oct-15H.S.8Oct-158 H.S.8Oct-15H.S.8 Collider idea Conditioning on a collider induces an association between its causes “And” and “or” selection leads to different bias Yellow fingers Hospital Lung cancer Two causes for coming to hospital - or + and ++ Yellow fingers Hospital Lung cancer Select subjects in hospital ++

9. Oct-15H.S.9 Data driven analysis ED C ED C ED C ED C 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) The undirected graph above is compatible with three DAGs: 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

10. Oct-15H.S.10Oct-15H.S.10 Analyzing DAGS: Paths The Path of the Righteous Oct-15H.S.10

11. Oct-15H.S.11 Paths Oct-15H.S.11 Goal: Keep causal paths of interest open Close all non causal paths Path: Any trail from E to D (without repeating or crossing itself) Types: Causal, Non causal States: Open, Closed 1. Causal path: E . .  D (all arrows in the same direction) Before conditioning: 2. Closed path:  C  Conditioning on: 3. a non-collider closes:  [C]  or  [C]  4. a collider opens:  [C]  (or a descendant of a collider)

12. Oct-15H.S.12Oct-15H.S.12 Confounding Oct-15H.S.12Oct-1512Oct-15H.S.12Oct-15H.S.12

13. Oct-15H.S.13Oct-1513Oct-15H.S.13 Physical activity and Coronary Heart Disease (CHD) E Phys. Act. D CHD C1 age Bias Conditioning on C1 and C2 PathTypeStatus 1 EDED CausalOpen 2 E  C1]  D NoncausalClosed 3 E  C2]  D NoncausalClosed No bias Unconditional PathTypeStatus 1 EDED CausalOpen 2 E  C1  D NoncausalOpen 3 E  C2  D NoncausalOpen C2 sex 1.We want the total effect of Physical Activity on CHD. What should we adjust for?

14. Oct-15H.S.14Oct-15H.S.14Oct-1514Oct-15H.S.14 Vitamin and birth defects E vitamin D birth defects C age U obesity Bias in E-D? Adjust for C? Bias Conditioning on C PathTypeStatus 1 EDED CausalOpen 2 E  C]  U  D Non-causalClosed No bias Unconditional PathTypeStatus 1 EDED CausalOpen 2 ECUDECUD Non-causalOpen This example and previous slide are both confounding

15. Oct-15H.S.15Oct-15H.S.15 Mixed Oct-15H.S.15Oct-1515Oct-15H.S.15Oct-15H.S.15

16. Oct-15H.S.16 Diabetes and Fractures E diabetes D fracture F prone to fall Unconditional PathTypeStatus 1E→DCausalOpen 2E→F→DCausalOpen 3E→B→DCausalOpen 4E←V→B→DNon-causalOpen 5E←P→B→DNon-causalOpen P physical activity B bone density V BMI Conditional PathTypeStatus 1E→DCausalOpen 2E→F→DCausalOpen 3E→B→DCausalOpen 4E←[V]→B→DNon-causalClosed 5E←[P]→B→DNon-causalClosed Mediators Confounders We want the total effect of diabetes on fractures

17. Oct-15H.S.17 Statin and CHD 1.We want the total effect of statin on CHD. What would we adjust for? 2.Can we estimate the direct effect of statin on CHD (not mediated through cholesterol)? E statin D CHD C cholesterol U lifestyle No adjustments gives the total effect Adjusting for C opens the collider path must also adjust for U to get the direct effect Is C a collider?

18. Oct-15H.S.18Oct-15H.S.18 Selection bias Oct-15H.S.18Oct-1518Oct-15H.S.18Oct-15H.S.18

19. Oct-15H.S.19 Diabetes and Fractures E diabetes D fracture H hospital Collider, selection bias 1.Convenience: Conduct the study among hospital patients? Unconditional PathTypeStatus 1E→DCausalOpen 2E→H←DNon-causalClosed Conditional PathTypeStatus 1E→DCausalOpen 2E→[H]←DNon-CausalOpen Collider stratification bias: at least on stratum is biased 2. Homogeneous sample: Exclude hospital patients

20. Oct-15H.S.20 Selection bias: size and direction Hospital risk:

21. Adjusting for selection bias Oct-15H.S.21 F prone to fall E diabetes D fracture H hospital PathTypeStatus 1E→DCausalOpen 2E→F→[H] ←DNon-causalOpen Adjust for F to close this path

22. Oct-15H.S.22Oct-15H.S.22 Summing up 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. Oct-15H.S.22 Better discussion based on DAGs

23. Oct-15H.S.23Oct-15H.S.23Oct-1523 References 1 Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3. ed. Philadelphia: Lippincott Willams & Williams,2008. 2Hernan MA, Hernandez-Diaz S, Robins JM. A structural approach to selection bias. Epidemiology 2004; 15: 615-25. 3Hernandez-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. 7Weinberg CR. Can DAGs clarify effect modification? Epidemiology 2007; 18: 569-72. Hernan and Robins, Causal Inference (coming) Oct-15H.S.23