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Causal inference. Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/ talks. Contents. Background Error Bias Define causal effect Individual Average Identify causal effect Exchangeability Positivity Consistency. Background. August 14. H.S. 3. Random error
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Causal inference Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/talks H.S.
Contents • Background • Error • Bias • Define causal effect • Individual • Average • Identify causal effect • Exchangeability • Positivity • Consistency H.S.
Background August 14 H.S. 3
Random error Source: sampling Expressed as: p-values Confidence intervals (precision) Affect All measures Systematic error Source: design Expressed as bias: Selection bias Information bias Confounding Affect: Frequency measure Association measure Error Causality field: Strong focus on bias at the expense of precision H.S.
Precision Bias True value Estimate Precision Bias Causal effect Association Precision and Bias Bias: association causal effect Objective: find effects H.S.
Define Causal Effects August 14 H.S. 6
Individual causal effect • Counterfactual outcome • Important • Clear definition • Notation mathematical proofs • Notation new methods • Estimate individual effect? • No, but Crossover design H.S.
Individual causal effects 20 subjects 12 individual causal effects H.S.
Average causal effect • Counterfactual outcome • Estimate average effect? • Yes, Randomized controlled trial H.S.
Identify Causal Effects August 14 H.S. 10
Ideal Randomized Trial • Trial • Randomize, Treat, Compare outcomes • Features • Exchangeability • Comparable groups • Positivity • Both treated and untreated • Consistency • Well defined intervention and contrast C E D H.S.
Conditional Randomized Trial • Conditional Trial • By sex: Randomize, Treat, Compare outcomes • Features • Conditional Exchangeability • Comparable groups by sex • Conditional Positivity • Both treated and untreated by sex • Consistency • Well defined intervention and contrast C E D sex C Males E D C Females E D H.S.
Observational study • Observational study Make = conditionally randomized trial • Need Features • Conditional Exchangeability • Comparable groups by all values of C • Conditional Positivity • Both treated and untreated by all values of C • Consistency • Well defined intervention and contrast C E D H.S.
Need to measure all relevant factors C E D C E D Conditional exchangeability Conditional exchangeability = No unmeasured confounding Two ways to remove confounding: Adjust: Balance: H.S.
Balance by Inverse Probability Weights • Weights • Estimate probability of exposed by C = pi • Balance • Weight exposed by 1/ pi, for plot 100/pi • Weight unexposed by 1/(1- pi) , for plot 100/(1-pi) • Effect C E D H.S.
C smoke - + E overweight D Blood pressure IPW and plots Effect of E on D: Crude: 0 biased Adjusted: 4 true Balance the data using IPW Result: all plots of D versus E are adjusted Problem: N gets large H.S.
Conditional positivity example Prior knowledge Dose response is linear Positivity problem Estimate dose response for each sex?
Conditional positivity Conditional positivity = exposed and unexposed for all values of C C E D Parametric assumption: linear “dose response” H.S.
Consistency Consistency = Well defined intervention and contrast August 14 H.S. 19
Excess mortality from air pollution? Standard method: estimate attributable fraction Implicit contrast: current levels versus zero Implicit intervention: not existent Air pollution H.S.
Body Mass Index Excess mortality from obesity? Standard method: estimate attributable fraction Implicit contrast: 30versus <25 Exercise Implicit intervention: Diet Mortality Smoking August 14 H.S. 21
Poorly defined intervention may affect exchangeability • Adjust for lung disease? C lung disease C lung disease C lung disease E diet D mortality E smoking D mortality E exercise D mortality Adjust Need not adjust Should not adjust H.S.
Poorly defined intervention may affect positivity • Confounder status unknown • Can not asses positivity H.S.
Summing up • Defined bias • Objective: find effects • Conditions to find effects • Exchangeability: comparable E+ and E- • Positivity: E+ and E- in all strata • Consistency: well defined intervention and contrast H.S.
Litterature • Hernan and Robins, Causal Inference H.S.
