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**Presentation, data and programs at:**

Simple Causal Graphs Simple Casual Graphs Hein Stigum Presentation, data and programs at: Apr-17 H.S.

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**Causal graphs Simple causal graphs Directed Acyclic Graphs (DAGs)**

Proper analysis (adjust or not) Direction of bias Directed Acyclic Graphs (DAGs) Formal tool Inventory of variables Causal inference Apr-17 H.S.

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**Exposure-Disease influenced by C**

C can be: Confounder Intermediate (in 2. Path) Collider Effect modifier Use graphs Determine C-type Choose analysis C E D Apr-17 H.S.

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**Example Exposure Disease Covariates Pysical Activity: PA**

Diabetes type 2: D2 Covariates Smoking: S Health Conscious: HC Overweight: Ov Blood Pressure: BP Apr-17 H.S.

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**Linear models Best model? Model choice can not be based on data only.**

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. All est significant (except PA=0) 20% D2 overall. PA from 0-5. Max PA is -10 pp. Apr-17 H.S.

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No influence of C E D C E D C E D C Apr-17 H.S.

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**Confounder: Smoking Should adjust for Smoking Stratify Regression S**

Negative bias + - biased true PA D2 -3 -2 Should adjust for Smoking Stratify Regression Apr-17 H.S.

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**Confounder 2 Adjust for Smoking or for Health Consciousness**

+ - HC S Negative bias biased true PA D2 -3 -2 Adjust for Smoking or for Health Consciousness Assume all following models are adjusted for smoking Problem: if effect from HC to D2 (via diet ) If we include both, the simple pos/neg bias calc will not work unless both pathways have the same sign Could adjust for HC if measured, or for both Smoking and Diet. DAGs will not give this info, a important shortcoming. Apr-17 H.S.

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**Intermediate (in 2. path): Overweight**

+ - Alt 1: Ignore Overweight Total PA D2 Alt 2: Two models: Direct c Indirect b1*c Total c2+ b1*c1 -2.0 Ov Ov c1 Assume all these model are adjusted for smoking b1=-0.25, c1=2, b1*c1=-0.5 b1 c2 PA PA D2 Simply adjusting for Overweight is not OK! Apr-17 H.S.

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**Select limping subjects**

Collider idea Two causes for limping Hip arthritis Limp Knee injury Select limping subjects + Limp + + Hip arthritis Knee injury - Conditioning on a collider induces an association between the causes Condition = (restrict, stratify, adjust) Bias direction? Hip arthritis and knee injury are not associated Hip arthritis and knee injury are rare events Apr-17 H.S.

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**Collider: Blood Pressure**

BP Positive bias if we adjust + - true biased PA D2 Should not adjust for Blood Pressure Problem if selection is connected to BP Study of subjects with high BP, decide to analyze PA-D2 association Or, based on invitation letter advertising BP-measurement, people with high BP select into study Apr-17 H.S.

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**Best model (so far) Model 2 is best**

Used extra info in graphs to decide All est significant (except PA=0) 20% D2 overall. PA from 0-5. Max PA is -10 pp. Apr-17 H.S.

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**Effect modifier: Sex Alt 3 : Ignore Sex Alt 1 : Two models**

PA D2 Alt 1 : Two models Easy No test for interaction Inefficient (12 estimates) p=number of covariates Estimates=2(p+1) versus p+2 Alt 2: Model with interaction Technical Test for interaction Efficient (7 estimates) Apr-17 H.S.

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**Effect modifier: Sex Model with interaction term**

Linear model 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) -2.5 -1.5 Apr-17 H.S.

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Examples Apr-17 H.S.

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**Smoking and LRTI The truth is out there?**

LRTI=Lower Resperatory Tract Infections Want: effect of smoking in pregnancy on LRTI in children Have: 40% response, high education is overrepresented Best causal estimate: Crude smoke-LRTI under 100% response? Crude smoke-LRTI under 40% response? LRTI Smoke Educ - S Smoking in pregnancy Lower Respiratory Tract Infections Education a confounder? Strong selection on educ in data, effect? Education is a confounder Selection represents partial adjustment Apr-17 H.S.

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**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 Apr-17 H.S.

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**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 Height Ethnic Apr-17 H.S.

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**Models Model 1 Lung func Ethnic Model 2 Lung func Hemo Height**

Hart rate Model 3 Model 4 Lung func Hemo Height Ethnic Model 1: total effect of ethnic group on lung function Model 2: adjusted effect of hemoglobin on lung function Model 3: Add all covariates, if effect of ethnic group, then some physio variable is missing Model 4: ethnic group as a effect modifier of hemoglobin on lung function Apr-17 H.S.

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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 The 3 first situations can not be gleaned from the data Apr-17 H.S.

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