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Causal Graphs, epi forum

Hein Stigum

http://folk.uio.no/heins/

talks

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Agenda

• Motivating examples

• Concepts– Confounder, Collider

• Analyzing DAGs– Paths

• Examples– Confounding– Mixed (confounders and mediators)

– Selection bias

Why causal graphs?

• Problem– Association measures are biased

• Understanding– Confounding, selection bias, mediators

• Analysis– Adjust or not

• Discussion– Precise statement of prior assumptions

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Motivating examples

• Statins and coronary heart disease– Disease risk: lifestyle, cholesterol

• Diabetes and fractures– Disease risk: fall, bone density

– Exposure risk: BMI, Physical activity

• Diabetes and fractures– Analyze among hospital patients

– Exclude hospital patients

Adjust or not?

Exclude or not?

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ConceptsCausal versus casual

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god-DAG

Evitamin

Dbirth defects

Cage

Uobesity

Read of the DAG:Causality = arrowsAssociations = paths

Node = variableArrow = cause, (at least one individual effect)

DAG=Directed Acyclic Graph

Questions on the DAG:E-D effect biased?Adjust for age?

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Association and Cause

Lungcancer

Yellowfingers

Association Possible causal structure

Lungcancer

Yellowfingers

Cause

Lungcancer

Yellowfingers

Confounder

Smoke

Lungcancer

Yellowfingers

Collider

Hospital

H.S.

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Confounder idea

• A confounder induces an association between its effects• Conditioning on a confounder removes the association• Condition = (restrict, stratify, adjust)

Yellow fingers

Smoking

Lung cancer

A common cause

+

++

Adjust for smoking

Yellow fingers

Smoking

Lung cancer

++

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Collider idea

• Conditioning on a collider induces an association between its causes

• “And” and “or” selection leads to different bias

Yellow fingers

Hospital

Lung cancer

Two causes for coming to hospital

- or+ and

++

Yellow fingers

Hospital

Lung cancer

Select subjects in hospital

++

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Data driven analysis

E D

C

E D

C

E D

C

E D

C

Want the effect of E on D (E precedes D)

Observe the two associations E-C and D-CAssume criteria dictates adjusting for C (likelihood ratio, Akaike ( 赤池 弘次 ) or change in estimate)

The undirected graph above is compatible with three DAGs:

Confounder1. Adjust

Mediator2. Adjust (direct)

3. Not adjust (total)

Collider4. Not adjust

Conclusion: The data driven method is correct in 2 out of 4 situationsNeed information from outside the data to do a proper analysis

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Analyzing DAGS: PathsThe Path of the Righteous

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Path definitions

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Path: any trail from E to D (without repeating or crossing itself)

Type: causal, non-causalState: open, closed

E D

C

M

K

Four paths:

Goal: Keep causal paths of interest openClose all non causal paths

  Path1 ED2 EMD3 ECD4 ECD

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E D

C

M

K

causal

non-causal

E D

C

M

K

open

closed

E D

C

M

K

1. Causal path: ED (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)

Four rules

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Confounding

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Physical activity and Coronary Heart Disease (CHD)

EPhys. Act.

DCHD

C1age

Bias

Conditioning on C1 and C2  Path Type Status

1 ED Causal Open2 EC1]D Noncausal Closed3 EC2]D Noncausal Closed

No bias

Unconditional  Path Type Status

1 ED Causal Open2 EC1D Noncausal Open3 EC2D Noncausal Open

C2sex

1. We want the total effect of Physical Activity on CHD. What should we adjust for?

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Vitamin and birth defects

Evitamin

Dbirth defects

Cage

Uobesity

Bias in E-D? Adjust for C?

Bias

Conditioning on C  Path Type Status

1 ED Causal Open2 EC]UD Non-causal Closed No bias

Unconditional  Path Type Status

1 ED Causal Open2 ECUD Non-causal Open

This exampleand previous slide

are both confounding

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MixedConfounders and mediators

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Diabetes and Fractures

Ediabetes

Dfracture

Fprone to fall

Unconditional  Path Type Status

1 E→D Causal Open2 E→F→D Causal Open3 E→B→D Causal Open4 E←V→B→D Non-causal Open5 E←P→B→D Non-causal Open

Pphysical activity

Bbone

density

VBMI

Conditional  Path Type Status

1 E→D Causal Open2 E→F→D Causal Open3 E→B→D Causal Open4 E←[V]→B→D Non-causal Closed5 E←[P]→B→D Non-causal Closed

Mediators

Confounders

We want the total effect ofdiabetes on fractures

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Statin and CHD

1. We want the total effect of statin on CHD. What would we adjust for?

2. Can we estimate the direct effect of statin on CHD (not mediated through cholesterol)?E

statinD

CHD

Ccholesterol

Ulifestyle

UnconditionalPath Type Status

1 E D Causal Open2 E C D Causal Open3 E C U D Non-causal Closed

No adjustments gives the total effect

Conditioning on CPath Type Status

1 E D Causal Open2 E C] D Causal Closed3 E C] U D Non-causal Open

Adjusting for C opens the collider pathmust also adjust for Uto get the direct effect

Is C a collider?

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Selection bias

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Diabetes and Fractures

Ediabetes

Dfracture

Hhospital

Collider, selection bias

1. Convenience: Conduct the study among

hospital patients?

Unconditional  Path Type Status

1 E→D Causal Open2 E→H←D Non-causal Closed

Conditional  Path Type Status

1 E→D Causal Open2 E→[H]←D Non-Causal Open

Collider stratification bias: at least on stratum is biased

2. Homogeneous sample: Exclude hospital patients

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Selection bias: size and direction

1 0 sum

1 36 64 1000 164 736 900

1000RR= 2.0

DPopulation

E1 0 sum

1 22 13 350 49 74 123

157RR= 1.6

DHospital

E1 0 sum

1 15 51 650 115 663 777

843RR= 1.5

No hospitalD

E

1 0

1 0.6 0.20 0.3 0.1

Response= 16 %

D

E

2.0 3.0

2.0E D

HHospital risk:

Adjusting for selection bias

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Fprone to fall

Ediabetes

Dfracture

Hhospital

  Path Type Status1 E→D Causal Open2 E→F→[H] ←D Non-causal Open Adjust for F to close this path

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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.

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Better discussion based on DAGs

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References1 Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3. ed. Philadelphia:

Lippincott Willams & Williams,2008.

2 Hernan MA, Hernandez-Diaz S, Robins JM. A structural approach to selection bias. Epidemiology 2004; 15: 615-25.

3 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)

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