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Hein Stigum folk.uio.no/heins/

Summary of “Graphical and Causal Modeling in Genetics and Epidemiology” by Vanessa Didelez Nuala Sheehan. Hein Stigum http://folk.uio.no/heins/. Dec-19. H.S. 1. Graphical Models. Pedigrees Compute carrier probability Causal Reasoning Conditional independence Two main types

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Hein Stigum folk.uio.no/heins/

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  1. Summary of“Graphical and Causal Modeling in Genetics and Epidemiology”by Vanessa DidelezNuala Sheehan Hein Stigum http://folk.uio.no/heins/ Dec-19 H.S. H.S. 1

  2. Graphical Models • Pedigrees • Compute carrier probability • Causal Reasoning • Conditional independence • Two main types • Undirected graphs • Directed acyclic graphs • Medelian randomization Dec-19 H.S. H.S. 2

  3. Introduction “Close to the edge” Dec-19 H.S. H.S. 3

  4. Associations C E D E D C E D Confounder Collider Dec-19 • E and D associated if: • E causes D • C is a common cause of E and D • C is a common effect of E and D and we condition on C Dec-19 H.S. H.S. H.S. 4 4

  5. Marginal and conditional dependence Conditionally Independent | C Marginally dependent E and D are: Dec-19 H.S. H.S. 5

  6. C E D Test of H0 • Can test H0 only if • E and D are conditionally independent, given the variables we adjust for (C) C E D Not OK OK Need graphic tools! Dec-19 H.S. H.S. 6

  7. Graphic tools “We have the moral edge!” Dec-19 H.S. H.S. 7

  8. 1 4 5 2 3 Undirected Graph Definition: A and B are separated by C if all paths from A to B pass thru C Are 1 and 5 separated by 2 ? Are 1 and 5 separated by 3 ? Are 1 and 5 separated by 3 and 4 ? Yes No Yes If 1 and 5 are separated by 2, then 1 and 5 are conditionally independent given 2 Dec-19 H.S. H.S. 8

  9. T U A Example: Chewing tobacco and ulcers T and U are marginally dependent T and U are conditionally independent given A T and U are separated by A Dec-19 H.S. H.S. 9

  10. Directed Acyclic Graphs, DAGs 1 3 5 Are 1 and 4 separated by 2 ? No 2 4 • Steps: • Take ancestral graph of {1,2,4} • Moralize the graph • Look for separation Dec-19 H.S. H.S. 10

  11. Directed Acyclic Graphs, DAGs 1 3 5 Are 1 and 4 separated by 2 ? No 2 4 1 3 Take ancestral graph of {1,2,4} 2 4 1 3 Moralize the graph 2 4 Are 1 and 4 separated by 2 ? No Dec-19 H.S. H.S. 11

  12. U D A E C Estrogen and Endometrial cancer U=unknown uterine abnormality D=endometrial cancer E=estrogen C=vaginal bleeding A=ascertained cancer U D A E C Null hypothesis: E and D independent. Can we test H0? Case-control study, condition on A. Are E and D cond. independent given A? Does it help to adjust for C? 1. Take ancestral graph of {E,D,A} 2. Moralize 3. Separation by A? 4. Separation by C,A? No No Dec-19 H.S. H.S. 12

  13. Test of H0 Can test H0 only if E and D are conditionally independent, given the variables we adjust for (C) C E D C E D Not OK OK Use tools to verify! Dec-19 H.S. H.S. 13

  14. T C E E D D E D E D S Cause versus Association • Observe association, not necessarily causal: • Confounding • Reverse causation • Selection effect • Time trends Dec-19 H.S. H.S. 14

  15. C E D C do(E) D Definitions • Association • Observing E predicts D • Causation • Manipulating E predicts D Dec-19 H.S. H.S. 15

  16. Problem • Association ≠ causation • Intervention on association may be useless • Randomization not always feasible • Need causal information from observational studies Dec-19 H.S. H.S. 16

  17. Mendelian randomization Dec-19 H.S. H.S. 17

  18. Observational study all measured confounders adjusted for Randomized trial Strong effect, compliance Does not exist Does not exist RD if and only if E causes D Medelian randomization Gene/ exposure association strong, or large N Should not exist, Mendel’s 2. law Must not exist, depends on the function of the gene GD if and only if E causes D U E D Observation versus trial U 2 1 R E D 3 U 2 1 G E D 3 Dec-19 H.S. H.S. 18

  19. Observational study Alcohol use increases blood pressure Many ”lifestyle” confounders Gene: ALDH2, 2 alleles 2,2 type suffer nausea, headache after alcohol  low alcohol regardless of lifestyle (U) Medelian randomization Gene ALDH2 is highly associated with alcohol Mendel’s 2. law, no ass. to obs. confounders OK, gene function is known Result: 2,2 type BP +7.4 mmHg U A BP Ex: Alcohol and blood pressure U 2 1 G A BP 3 Dec-19 H.S. H.S. 19

  20. U 2 1 G E D 3 Violations of core conditions • Gene/exposure association • Gene rare or weak effect  large N • Compensation • and 3. Gene independent of U and D • Pleiotropy • Linkage disequilibrium • Population stratification H.S.

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