DAGs intro without exercises 1h Directed Acyclic Graph Hein Stigum http://folk.uio.no/heins/ courses Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. H.S. H.S. 1 1 1 1 1

Motivating example C E D C C E D E D Want the effect of E on D (E precedes D) C Observe the two associations C-E and C-D E D Not enough information! Different analyses for: C C Causal information E D E D Confounder Mediator Need causal information from outside the data to do a proper analysis! Feb-19 H.S.

Agenda Background DAG concepts Analyzing DAGs Association, Cause Confounder, Collider Paths Analyzing DAGs Examples DAG concepts Define a few main concepts Paths: Surprisingly few rules needed Analyzing DAGs Examples: conf, intermediate, collider Selection bias, Information bias Rand, Mend Rand The two former: manual for use More on DAGs Deeper thoughts and problems With exercises, difficult to guess time Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. H.S. H.S. 3 3 3 3 3

Why causal graphs? Problem Causal graphs help: Association measures are biased Causal graphs help: Understanding Confounding, mediation, selection bias Analysis Adjust or not Discussion Precise statement of prior assumptions Feb-19 H.S.

Causal versus casual CONCEPTS Feb-19 H.S.

god-DAG Causal Graph: Read of the DAG: Causality = arrows Estimations: Node = variable Arrow = cause E=exposure, D=disease DAG=Directed Acyclic Graph Read of the DAG: Causality = arrows Associations = paths Independencies = no paths Estimations: E-D association has two parts: ED causal effect keep open ECUD bias try to close Arrows=lead to or causes Time E- exposure D- disease C, V - cofactor, variable U- unmeasured Directed= arrows Acyclic = nothing can cause itself E[C]UD Condition (adjust) to close Feb-19 Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. 6 6 6

Association and Cause Association 3 possible causal structure E D (Reversed cause) E D 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 + more complicated structures Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. 7 7 7

Confounder idea + A common cause Adjust for smoking Smoking Yellow fingers Smoking Lung cancer + + + Yellow fingers Lung cancer + A confounder induces an association between its effects Conditioning on a confounder removes the association Condition = (restrict, stratify, adjust) Simplest form “+” (assume monotonic effects) Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. H.S. 8 8 8 8 8

Collider idea or + and Two causes for selection to study Selected subjects Selected Yellow fingers Selected Lung cancer + + + Yellow fingers Lung cancer or + and Conditioning on a collider induces an association between its causes “And” and “or” selection leads to different bias Simplest form “+” (assume monotonic effects) Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 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 C-E and C-D - Assume statistical criteria dictates adjusting for C (likelihood ratio, Akaike (赤池 弘次) or 10% 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. Direct: adjust 3. Total: not adjust 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 Feb-19 H.S.

Paths The Path of the Righteous Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. 11 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) Paths Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. 11 11

Path definitions Path: any trail from E to D (without repeating itself) Type: causal, non-causal State: open, closed   Path 1 E®D 2 E®M®D 3 E¬C®D 4 E®K¬D Four paths: Notice: path with or against the arrows Paths show potential association Goal: Keep causal paths of interest open Close all non-causal paths Feb-19 Feb-19 H.S. H.S. 12

Four rules 1. Causal path: ED 2. Closed path: K (all arrows in the same direction) otherwise non-causal Before conditioning: 2. Closed path: K (closed at a collider, otherwise open) Conditioning on: 3. a non-collider closes: [M] or [C] 4. a collider opens: [K] (or a descendant of a collider) Feb-19 H.S.

ANALYZING DAGs Feb-19 H.S.

Confounding examples Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 H.S. Informal, no strict notation/def Casual about the causal! Confounding examples Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. H.S. H.S. 15 15 15 15 15 15

Physical activity and Coronary Heart Disease (CHD) We want the total effect of Physical Activity on CHD. What would we adjust for? Unconditional   Path Type Status 1 E®D Causal Open 2 E¬C1®D Non-causal 3 E¬C2®D This is an example of confounding Bias Noncausal open=biasing path Conditioning on C1 and C2   Path Type Status 1 E®D Causal Open 2 E¬[C1]®D Non-causal Closed 3 E¬[C2]®D No bias Feb-19 Feb-19 Feb-19 H.S. H.S. 16 16

Intermediate variables Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. H.S. H.S. 17 17 17 17 17 17

Tea and depression Total effect: Direct effect: Caffeine intermediate or confounder? adjust for O adjust for C (and O) Caffeine is both intermediate and part of a confounder path.   Path Type Status 1 E→D Causal Open 2 E→C→D 3 E←O→C→D Non-causal Tea and depression: Finnish study Caffeine reduces depression: Nurses Health Study direct total indirect Feb-19 H.S.

Statin and CHD We want the total effect of statin on CHD. What would you adjust for? Can we estimate the direct effect of statin on CHD (not mediated through cholesterol)? Nothing No, U is unmeasured No adjustments gives the total effect Adjusting for C will close path 2 but will open path 3 and give bias! C is a collider on path 3 Feb-19 H.S.

Selection bias Two concepts Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. H.S. H.S. 20 20 20 20 20 20

Convenience sample, homogenous sample hospital Convenience sample: Conduct the study among hospital patients? E diabetes D fractures 2. Homogeneous sample: Population data, 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 This type of selection bias can be adjusted for! Feb-19 H.S.

Summing up Better discussion based on DAGs Draw your assumptions 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 Draw your assumptions before your conclusions Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. 22 22

Recommended reading Books Papers Hernan, M. A. and J. Robins. Causal Inference. Web: Rothman, K. J., S. Greenland, and T. L. Lash. Modern Epidemiology, 2008. Morgan and Winship, Counterfactuals and Causal Inference, 2009 Pearl J, Causality – Models, Reasoning and Inference, 2009 Veierød, M.B., Lydersen, S. Laake,P. Medical Statistics. 2012 Papers Greenland, S., J. Pearl, and J. M. Robins. Causal diagrams for epidemiologic research, Epidemiology 1999 Hernandez-Diaz, S., E. F. Schisterman, and M. A. Hernan. The birth weight "paradox" uncovered? Am J Epidemiol 2006 Hernan, M. A., S. Hernandez-Diaz, and J. M. Robins. A structural approach to selection bias, Epidemiology 2004 Berk, R.A. An introduction to selection bias in sociological data, Am Soc R 1983 Greenland, S. and B. Brumback. An overview of relations among causal modeling methods, Int J Epidemiol 2002 Weinberg, C. R. Can DAGs clarify effect modification? Epidemiology 2007 Hernan and Robins Causal inference (web) Hernan a struct approach Hernandez- From causal Shahar Rothman Feb-19 Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. 23 23 23