1. Jun-16H.S.1 Confounding and DAGs (Directed Acyclic Graphs) Hein Stigum

2. Agenda Confounder Collider Jun-16H.S.2 Causal Knowledge as a Prerequisite for Confounding Evaluation… Hernán et al. AJE, 2002

3. CONFOUNDER DEFINITION Jun-16H.S.3

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 Jun-16H.S.4 ED ED C ED C

5. CONFOUNDER EXAMPLES Adjusting is OK Jun-16H.S.5

6. Classic confounder C is the confounder RR ED is biased RR ED|C is unbiased RR ED =0.8 positive bias, towards the null Adjust for age: RR ED|C =0.5 is unbiased Jun-16H.S.6 ED C birth defects vitamins age + + - 01  biased true

7. Mediated confounder U is the confounder C is a confounder mediator Effect on D is mediated RR ED is biased RR ED|C is unbiased RR ED =0.8 positive bias, towards the null Adjust for obesity: RR ED|C =0.5 is unbiased Jun-16H.S.7 ED C U vitaminbirth defects obesity age + + - +

8. Mediated confounder 2 U is the confounder C is a confounder mediator Effect on E is mediated RR ED is biased RR ED|C is unbiased RR ED =0.8 positive bias, towards the null Adjust for earlier malformations: RR ED|C =0.5 is unbiased Jun-16H.S.8 ED U C vitamin birth defects gene earlier malform + + -+

9. Marker for confounder U is the confounder C is a confounder marker RR ED is biased RR ED|C is less biased RR ED =0.3 negative bias, away from the null Adjust for enzyme: RR ED|C =0.5 is less biased Jun-16H.S.9 - + - + ED C U folateneural tube enzyme gene 01  biased true

10. COLLIDER DEFINITION Jun-16H.S.10

11. Definition Confounder –Common cause for E and D Collider –Common effect of E and D Jun-16H.S.11 ED C ED C

12. Definition cont. Classic C is a collider, no confounding RR ED is unbiased RR ED|C is biased Example RR ED =1.0 cancer not diet related Positive collider=negative bias? Adjust for weight loss: RR ED|C =0.8 is biased Jun-16H.S.12 EDC diet cancerweight loss + +

13. COLLIDER EXAMPLES Adjusting is not OK Jun-16H.S.13

14. Classic collider C is a collider, There is no confounding RR ED is unbiased RR ED|C is biased RR ED =0.5 is unbiased Negative collider=positive bias? Adjust for low birth weight (LBW): RR ED|C =0.8 is biased Jun-16H.S.14 EDC folatepretermLBW - - +

15. Shared cause C is a collider of U and D C and E has a shared cause RR ED is unbiased RR UD|C is biased RR ED|C is biased RR ED =0.8 is unbiased Adjust for low birth weight (LBW): Positive bias, towards the null? RR ED|C =1.0 is biased Jun-16H.S.15 DC U E birth defects LBW Low age vitamin + - + -

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

17. Folate-neural tube study Case Control study –Exposure:folate intake –Disease:neural tube defects –OR ED =0.65 Should we restrict analysis to live births? –OR ED|C =0.80 Jun-16H.S.17

18. Graph 1, collider RR ED =0.65 is unbiased Adjust for stillbirth: Positive bias, towards the null RR ED|C =0.8 is biased Jun-16H.S.18 folateneural tubestillbirth - - +

19. Graph 2, confounder marker RR ED =0.65 is biased Adjust for stillbirth: Positive bias, towards the null RR ED|C =0.8 is unbiased Opposite conclusion as graph 1 Jun-16H.S.19 - + + + folateneural tube stillbirth stillbirths

20. SUMMING UP Jun-16H.S.20

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 Jun-16H.S.21 ED C ED C

22. Collider Common effect of: E and D cause of E and D E and cause of D DCE DC U EDC U E

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 Jun-16H.S.23

24. COLLIDER EXAMPLE The birth weight “paradox” uncovered, Hernández-Díaz at al. AJE, 2006 Jun-16H.S.24

25. Birth weight distribution Jun-16H.S.25

26. Infant mortality Jun-16H.S.26

27. To adjust or not adjust Crude –RR smoke =1.55 (1.50, 1.59) Adjusted for birth weight –RR smoke =1.09 (1.05, 1.12) Should we adjust for birth weight? Jun-16H.S.27

28. A likely DAG C is a collider of U and E C and D has a shared cause RR ED is unbiased RR EU|C is biased RR ED|C is biased U: malnutrition, malformation Jun-16H.S.28 CD U E LBWmort U smoke + + + + +

29. DAG simplified RR ED is unbiased=1.0 RR EU|C is biased<1.0 RR ED|C is biased<1.0 Negative bias Same direction of bias Jun-16H.S.29 LBWmort U smoke + + + 01.55 biased true LBWmort U smoke + + + + + 1.09

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 Jun-16H.S.30 yellow fingers lung cancer smoke LBWmort U smoke + + + + +