Apr-15H.S.1 Simple Causal Graphs Hein Stigum Presentation, data and programs at: Simple Casual Graphs.

04/21/23 H.S. 1

Simple Causal Graphs

Hein Stigum

Presentation, data and programs at:

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

Simple Casual Graphs

04/21/23 H.S. 2

Causal graphs

• Simple causal graphs– Proper analysis (adjust or not)

– Direction of bias

• Directed Acyclic Graphs (DAGs)– Formal tool

– Inventory of variables

– Proper analysis (adjust or not)

– Causal inference

04/21/23 H.S. 3

Exposure-Disease influenced by C

• C can be:– Confounder

– Intermediate (in 2. Path)

– Collider

– Effect modifier

• Use graphs– Determine C-type

– Choose analysis

E D

C

04/21/23 H.S. 4

Example

• Exposure– Pysical Activity: PA

• Disease– Diabetes type 2: D2

• Covariates– Smoking: S

– Health Conscious: HC

– Overweight: Ov

– Blood Pressure: BP

04/21/23 H.S. 5

Linear models

• Best model?– Likelihood ratio tests or Akaike criteria mod 4

– All changes in PA effect considered important mod 4

– Claim mod 2.

• Model choice can not be based on data only.

• Need extra info or assumptions.

0Diabetes type 2

mod 1 mod 2 mod 3 mod 4Pysical Activity -3 pp -2 pp -1.5 pp -0.5 ppSmokingOverweightBlood Pressure

04/21/23 H.S. 6

No influence of C

E D

C

E D

C

E D

C

04/21/23 H.S. 7

Confounder: Smoking

• Should adjust for Smoking– Stratify

– Regression

D2 PA

S

+-

0

biased true

Negative bias

-2-3

04/21/23 H.S. 8

Confounder 2

Adjust for Smoking or

for Health Consciousness

Assume all following models are adjusted for smoking

D2 PA

SNegative bias

HC

+

-

+

0

biased true

-2-3

04/21/23 H.S. 9

Intermediate (in 2. path): Overweight

Alt 1: Ignore OverweightTotal -2.0D2 PA

Ov

+-

PA

Ov Alt 2: Two models:Direct c2 -1.5

Indirect b1*c1 -0.5

Total c2+ b1*c1 -2.0D2 PA

Ov

c2

b1 c1

Simply adjusting for Overweight is not OK!

04/21/23 H.S. 10

Collider idea

• Conditioning on a collider induces an association between the causes

• Condition = (restrict, stratify, adjust)• Bias direction?

Hip arthritis

Limp

Knee injury

Two causes for limping

-

++

Hip arthritis

Limp

Knee injury

Select limping subjects

++

04/21/23 H.S. 11

Collider: Blood Pressure

• Should not adjust for Blood Pressure

• Problem if selection is connected to BP

D2 PA

BP

+-

0

biasedtrue

Positive bias if we adjust

04/21/23 H.S. 12

Best model (so far)

• Model 2 is best

• Used extra info in graphs to decide

Diabetes type 2mod 1 mod 2 mod 3 mod 4

Pysical Activity -3 pp -2 pp -1.5 pp -0.5 ppSmoking ConfounderOverweight IntermediateBlood Pressure Collider

04/21/23 H.S. 13

Effect modifier: Sex

• Alt 2: Model with interaction– Technical

– Test for interaction

– Efficient (7 estimates)

D2 PA

Sex

• Alt 1 : Two models– Easy

– No test for interaction

– Inefficient (12 estimates)

Two modelsMales Females

PA -2.5 -1.5Co 1Co 2Co 3Co 4const

Model with interactionMales Females

PA -2.5 -1.5Co 1Co 2Co 3Co 4const

• Alt 3 : Ignore Sex

04/21/23 H.S. 14

Effect modifier: SexModel with interaction term

• Test for interaction– Wald test on b3=0

• If significant interaction– Sex is coded 0 for Males and 1 for Females

– The effect of PA (1 unit increase)

...2 3210 SexPAbSexbPAbbD

31

1

:Femalesfor

:Malesfor

bb

b

• Linear model

-2.5

-1.5

04/21/23 H.S. 15

Examples

04/21/23 H.S. 16

Smoking and LRTIThe truth is out there?

LRTI Smoke

Educ

--

S

LRTI=Lower Resperatory Tract InfectionsWant: effect of smoking in pregnancy on LRTI in childrenHave: 40% response, high education is overrepresented

Best causal estimate:Crude smoke-LRTI under 100% response?Crude smoke-LRTI under 40% response?

Education is a confounderSelection represents partial adjustment

04/21/23 H.S. 17

Smoking and LRTI, ex 2

LRTI Smoke

Educ S

• Education is a not a confounder• Crude smoke-LRTI in population is unbiased• Crude smoke-LRTI in sample is biased, S is a collider• Adjusted smoke-LRTI in sample is unbiased

04/21/23 H.S. 18

Ethnicity and lung function

• Exposure Ethnic group• Outcome Lung function• Covariates Hemoglobin, height

• Draw DAG• Suggest analyzes/models• Model with all covariates meaningful?

Lung func Hemo

HeightEthnic

04/21/23 H.S. 19

ModelsModel 1

Lung func Ethnic

Model 2

Lung func Hemo

Height

Lung func Hemo

HeightEthnic

Hart rate

Model 3 Model 4

Lung func Hemo

Height

Ethnic

04/21/23 H.S. 20

Summing up

• In a study of 2 variables, a 3. variable may have 4 effects:Confounder, Intermediate, Collider, Effect modifier

• Not distinguished from data, need extra info

• Casual graphs help use the extra info