Causal Graphs, epi forum Endringer: Litt lite tid til seleksjon Ta ut vitamin eks., kan også hoppe over konfounding def. Hein Stigum http://folk.uio.no/heins/ talks Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. H.S. H.S. 1 1 1 1 1

Agenda Motivating examples Concepts Analyzing DAGs Examples Confounder, Collider Analyzing DAGs Paths Examples Confounding Mixed (confounders and mediators) Selection bias Define a few main concepts More as we go along Surprisingly few needed With exercises, difficult to guess time Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. H.S. H.S. 2 2 2 2 2

Why causal graphs? Problem Understanding Analysis Discussion Association measures are biased Understanding Confounding, selection bias, mediators Analysis Adjust or not Discussion Precise statement of prior assumptions Apr-17 H.S.

Motivating examples Statins and coronary heart disease Disease risk: lifestyle, cholesterol Diabetes and fractures Disease risk: fall, bone density Exposure risk: BMI, Physical activity Analyze among hospital patients Exclude hospital patients Adjust or not? Exclude or not? Apr-17 H.S.

Concepts Causal versus casual Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 Informal, no strict notation/def Casual about the causal! Concepts Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. H.S. H.S. 5 5 5 5 5 5

DAG=Directed Acyclic Graph god-DAG DAG=Directed Acyclic Graph C age U obesity Node = variable Arrow = cause, (at least one individual effect) E vitamin D birth defects Arrows=lead to or causes Time E- exposure D- disease C, V - cofactor, variable U- unmeasured Directed= arrows Acyclic = nothing can cause itself Read of the DAG: Causality = arrows Associations = paths Questions on the DAG: E-D effect biased? Adjust for age? Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. 6 6 6

Possible causal structure Association and Cause Association Possible causal structure Lung cancer Yellow fingers Cause Lung cancer Yellow fingers Confounder Smoke Yellow fingers Lung cancer Assume E precedes D in time Association: observe Cause: infer (extra knowledge) Causal structure force on the data Basic structures, may generalize with many more variables: use paths Lung cancer Yellow fingers Collider Hospital Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. 7 7 7

Confounder idea + A common cause Adjust for smoking Yellow fingers Lung cancer + Smoking + + Yellow fingers Lung cancer + A confounder induces an association between its effects Conditioning on a confounder removes the association Condition = (restrict, stratify, adjust) “+” (assume monotonic effects) Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. H.S. 8 8 8 8 8

Collider idea or + and Two causes for coming to hospital Yellow fingers Hospital Lung cancer Select subjects in hospital + Hospital + + Yellow fingers Lung cancer or + and Conditioning on a collider induces an association between its causes “And” and “or” selection leads to different bias “+” (assume monotonic effects) Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. H.S. 9 9 9 9 9

Data driven analysis C E D C C C E D E D E D 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 Hirotugu Akaike 赤池 弘次 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 Apr-17 H.S.

Analyzing DAGS: Paths The Path of the Righteous Apr-17 Apr-17 Apr-17 Ezekiel 25:17. "The Path of the Righteous Man Is Beset on All Sides by The inequities of the Selfish and the Tyranny of Evil Men." (Pulp Fiction version) Analyzing DAGS: Paths Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. 11 11

Path definitions Path: any trail from E to D (without repeating or crossing itself) Type: causal, non-causal State: open, closed K   Path 1 E®D 2 E®M®D 3 E¬C®D 4 E®C¬D C Four paths: E D M Goal: Keep causal paths of interest open Close all non causal paths Apr-17 Apr-17 H.S. H.S. 12

Four rules K C 1. Causal path: ED E D M K 2. Closed path: K C E D 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 Apr-17 H.S.

Confounding Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. Informal, no strict notation/def Casual about the causal! Confounding Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. H.S. H.S. 14 14 14 14 14 14

Physical activity and Coronary Heart Disease (CHD) age We want the total effect of Physical Activity on CHD. What should we adjust for? E Phys. Act. D CHD C2 sex Unconditional   Path Type Status 1 E®D Causal Open 2 E¬C1®D Noncausal 3 E¬C2®D Bias Noncausal open=biasing path Conditioning on C1 and C2   Path Type Status 1 E®D Causal Open 2 E¬[C1]®D Noncausal Closed 3 E¬[C2]®D No bias Apr-17 Apr-17 Apr-17 H.S. H.S. 15 15

Vitamin and birth defects Bias in E-D? Adjust for C? C age U obesity E vitamin D birth defects Unconditional   Path Type Status 1 E®D Causal Open 2 E¬C®U®D Non-causal Bias Noncausal open=biasing path Both C and U are confounders Problem that we have ”forgotten” arrow C->D? Conditioning on C   Path Type Status 1 E®D Causal Open 2 E¬[C]®U®D Non-causal Closed No bias This example and previous slide are both confounding Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. 16 16 16

Mixed Confounders and mediators Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. H.S. H.S. 17 17 17 17 17 17

Diabetes and Fractures prone to fall We want the total effect of diabetes on fractures V BMI E diabetes D fracture P physical activity B bone density Conditional   Path Type Status 1 E→D Causal Open 2 E→F→D 3 E→B→D 4 E←[V]→B→D Non-causal Closed 5 E←[P]→B→D Unconditional   Path Type Status 1 E→D Causal Open 2 E→F→D 3 E→B→D 4 E←V→B→D Non-causal 5 E←P→B→D Mediators Confounders Apr-17 H.S.

Statin and CHD U lifestyle 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)? C cholesterol E statin D CHD No adjustments gives the total effect Mixed because C is both a mediator and a collider Is C a collider? Adjusting for C opens the collider path must also adjust for U to get the direct effect Apr-17 H.S.

Selection bias Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. 20 20 20 20 20 20

Diabetes and Fractures Convenience: Conduct the study among hospital patients? H hospital E diabetes D fracture 2. Homogeneous sample: Exclude hospital patients Conditional   Path Type Status 1 E→D Causal Open 2 E→[H]←D Non-Causal Unconditional   Path Type Status 1 E→D Causal Open 2 E→H←D Non-causal Closed Collider, selection bias Collider stratification bias: at least on stratum is biased Apr-17 H.S.

Selection bias: size and direction Hospital risk: Apr-17 H.S.

Adjusting for selection bias prone to fall H hospital E diabetes D fracture   Path Type Status 1 E→D Causal Open 2 E→F→[H] ←D Non-causal Adjust for F to close this path Apr-17 H.S.

Better discussion based on DAGs 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. Better discussion based on DAGs Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. 24 24

References Hernan and Robins, Causal Inference (coming) 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) Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S. 25 25 25