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

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Apr-15H.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

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Apr-15H.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 ED C

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Apr-15H.S.4 Example Exposure –Pysical Activity: PA Disease –Diabetes type 2: D2 Covariates –Smoking: S –Health Conscious:HC –Overweight: Ov –Blood Pressure: BP

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Apr-15H.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. 0

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Apr-15H.S.6 No influence of C ED C ED C ED C

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Apr-15H.S.7 Confounder: Smoking Should adjust for Smoking –Stratify –Regression D2 PA S +- 0 biased true Negative bias -2 -3

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Apr-15H.S.8 Confounder 2 Adjust for Smoking or for Health Consciousness Assume all following models are adjusted for smoking D2 PA S Negative bias HC biased true -2 -3

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Apr-15H.S.9 Intermediate (in 2. path): Overweight Alt 1: Ignore Overweight Total-2.0 D2 PA Ov +- PA Ov Alt 2: Two models: Directc2-1.5 Indirectb1*c1-0.5 Totalc2+ b1*c1-2.0 D2 PA Ov c2 b1 c1 Simply adjusting for Overweight is not OK!

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Apr-15H.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 ++

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Apr-15H.S.11 Collider: Blood Pressure Should not adjust for Blood Pressure Problem if selection is connected to BP D2 PA BP +- 0 biased true Positive bias if we adjust

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Apr-15H.S.12 Best model (so far) Model 2 is best Used extra info in graphs to decide

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Apr-15H.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) Alt 3 : Ignore Sex

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Apr-15H.S.14 Effect modifier: Sex Model with interaction term Test for interaction –Wald test on b 3 =0 If significant interaction –Sex is coded 0 for Males and 1 for Females –The effect of PA (1 unit increase) Linear model

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Apr-15H.S.15 Examples

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Apr-15H.S.16 Smoking and LRTI The truth is out there? LRTI Smoke Educ -- S 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? Education is a confounder Selection represents partial adjustment

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Apr-15H.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

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Apr-15H.S.18 Ethnicity and lung function ExposureEthnic group OutcomeLung function CovariatesHemoglobin, height Draw DAG Suggest analyzes/models Model with all covariates meaningful? Lung func Hemo HeightEthnic

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Apr-15H.S.19 Models Model 1 Lung func Ethnic Model 2 Lung func Hemo Height Lung func Hemo HeightEthnic Hart rate Model 3Model 4 Lung func Hemo Height Ethnic

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Apr-15H.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

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