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Confounding and DAGs (Directed Acyclic Graphs)

Confounding and DAGs (Directed Acyclic Graphs). Hein Stigum. Agenda. Confounder Collider. Causal Knowledge as a Prerequisite for Confounding Evaluation… Hernán et al. AJE, 2002. Confounder definition. Associations. E and D associated E causes D E and D have common cause Both

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Confounding and DAGs (Directed Acyclic Graphs)

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  1. ConfoundingandDAGs(Directed Acyclic Graphs) Hein Stigum H.S.

  2. Agenda • Confounder • Collider Causal Knowledge as a Prerequisite for Confounding Evaluation… Hernán et al. AJE, 2002 H.S.

  3. Confounder definition H.S.

  4. Associations • E and D associated • E causes D • E and D have common cause • Both • Overall E-D association = spurious effect from C + causal E-D effect E D C E D C E D H.S.

  5. Adjusting is OK Confounder examples H.S.

  6. biased true  0 1 Classic confounder C is the confounder RRED is biased RRED|C is unbiased RRED =0.8 positive bias, towards the null Adjust for age: RRED|C=0.5 is unbiased C E D age + + - vitamins birth defects H.S.

  7. Mediated confounder U is the confounder C is a confounder mediator Effect on D is mediated RRED is biased RRED|C is unbiased RRED =0.8 positive bias, towards the null Adjust for obesity: RRED|C=0.5 is unbiased obesity C age U vitamin E birth defects D + + - + H.S.

  8. Mediated confounder 2 U is the confounder C is a confounder mediator Effect on E is mediated RRED is biased RRED|C is unbiased RRED =0.8 positive bias, towards the null Adjust for earlier malformations: RRED|C=0.5 is unbiased U C E D gene + + + - earlier malform birth defects vitamin H.S.

  9. gene folate neural tube enzyme biased true  0 1 Marker for confounder U is the confounder C is a confounder marker RRED is biased RRED|C is less biased RRED =0.3 negative bias, away from the null Adjust for enzyme: RRED|C=0.5 is less biased U E D C + - - H.S. +

  10. Collider definition H.S.

  11. Definition • Confounder • Common cause for E and D • Collider • Common effect of E and D C C E E D D H.S.

  12. + + Definition cont. • Classic C is a collider, no confounding RRED is unbiased RRED|C is biased • Example RRED =1.0 cancer not diet related Positive collider=negative bias? Adjust for weight loss: RRED|C=0.8 is biased E diet cancer D weight loss C H.S.

  13. Adjusting is not OK Collider examples H.S.

  14. E D C - - + folate preterm LBW Classic collider C is a collider, There is no confounding RRED is unbiased RRED|C is biased RRED =0.5 is unbiased Negative collider=positive bias? Adjust for low birth weight (LBW): RRED|C=0.8 is biased H.S.

  15. Shared cause C is a collider of U and D C and E has a shared cause RRED is unbiased RRUD|C is biased RRED|C is biased RRED =0.8 is unbiased Adjust for low birth weight (LBW): Positive bias, towards the null? RRED|C=1.0 is biased U E D C Low age + - birth defects - + vitamin LBW H.S.

  16. Shared cause 2 C is a collider of U and E C and D has a shared cause RRED is unbiased RREU|C is biased RRED|C is biased RRED =0.8 is unbiased Adjust for maternal weight gain: Negative bias, away from the null? RRED|C=0.5 is biased U E D C gene + + maternal weight gain birth defects - vitamin + H.S.

  17. Folate-neural tube study • Case Control study • Exposure: folate intake • Disease: neural tube defects • ORED=0.65 Should we restrict analysis to live births? • ORED|C=0.80 H.S.

  18. Graph 1, collider RRED =0.65 is unbiased Adjust for stillbirth: Positive bias, towards the null RRED|C=0.8 is biased - - + folate neural tube stillbirth H.S.

  19. Graph 2, confounder marker RRED =0.65 is biased Adjust for stillbirth: Positive bias, towards the null RRED|C=0.8 is unbiased Opposite conclusion as graph 1 stillbirths folate neural tube stillbirth + - + H.S. +

  20. Summing up H.S.

  21. Confounder versus Collider • Confounder • Common cause for E and D • or some variant thereof • Adjust • Collider • Common effect of E and D • or some variant thereof • Not adjust C C E E D D H.S.

  22. E D C U E D C U E C D Collider • Common effect of: E and D cause of E and D E and cause of D

  23. Reasons not to adjust for C • C is a collider • C is a weak confounder and • C has missing • C has errors • C is highly correlated with other cofactors H.S.

  24. The birth weight “paradox” uncovered, Hernández-Díaz at al. AJE, 2006 Collider Example H.S.

  25. Birth weight distribution H.S.

  26. Infant mortality H.S.

  27. To adjust or not adjust • Crude • RRsmoke=1.55 (1.50, 1.59) • Adjusted for birth weight • RRsmoke=1.09 (1.05, 1.12) Should we adjust for birth weight? H.S.

  28. A likely DAG C is a collider of U and E C and D has a shared cause RRED is unbiased RREU|C is biased RRED|C is biased U: malnutrition, malformation U E C D U + + smoke LBW mort + + + H.S.

  29. biased true DAG simplified RRED is unbiased =1.0 RREU|C is biased <1.0 RRED|C is biased <1.0 Negative bias Same direction of bias U U + + + + smoke smoke LBW LBW mort mort + + + + 1.09 0 1.55 H.S.

  30. Summing up • Confounding • “Yellow fingers”-”lung cancer” association is useful • not causal • Collider • Among Low Birth Weight children “smokers” do better, less likely that the cause of LBW is malformation • “smoking” does not protect against mortality smoke yellow fingers lung cancer U + + smoke LBW mort + + + H.S.

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