# Causal inference --- ## From internal validity to causal inference - Causal inference based on criteria - Causal pie or apportionment - Explore causation using DAGs - Counterfactual theories of causation --- ## Simpson's paradox: why we need to study causality  --- ## Sir Austin Bradford-Hill (1965 Hill's Criteria)  --- ## Bradford-Hill Criteria - 1 - Strength of Association - Consistency of findings - Specificity - Temporality --- ## Bradford-Hill Criteria - 2 - Biological gradient - Plausibility - Coherence - Experiment - Analogy --- ## Strength - Stronger an association, more likely it is due to cause and effect - A **stronger** association would mean confounding - Strong associations also mean high PAF% with identical prevalence of exposure - pE = 0.20,RR: 3.0, PAF: 28.57% - pE = 0.20, RR: 10, PAF: 64.28% --- ## Temporality - Cause must precede Effect --- ## Biological Gradient - As dose of exposure increases, - So does effect size --- ## Sufficient and Component Cause Model  --- ## Directed Acyclic graphs for causal inference - Go to [http://dagitty.net/dags.html#](http://dagitty.net/dags.html#) - Take out your papers and pencils and follow along (you may work in groups) - You must close all open backdoor paths - You must not open any closed backdoor paths --- ## Backdoor paths - Backdoor paths are open if they have confounders or mediators - Backdoor paths are closed if they have colliders - Conditioning on colliders open closed backdoor paths --- ## Counterfactual causality concept 1 - Imagine A and Y are both binary, 1 and 0 - For A, we say a is counterfactual - a = 0 or a = 1, --- ## Counterfactual causality concept 2 - If everyone in the study were to - receive treatment or be exposed - simultaneously, and - what would the outcome? - P[Y_(a = 1) = 1] - Probability of the outcome Y under - a = 1 --- ## Counterfactual causality concept 3 - If everyone in the study were to - receive the control condition or non-exposed - simultaneously, - What would be the outcome? - P[Y_(a = 0) = 1] - Probability of the outcome Y under - a = 0 --- ## Causal Risk Ratio - P[Y_(a = 1)] / P[Y_(A = 0)] --- ## What do our observations show us? - But we do not get to see this, instead - We see P[Y = 1 | A = 1] - That is probability of the outcome given intervention or exposure - And, - P[Y = 1 | A = 0] - That is probability of outcome given control --- ## Associational Risk Ratio - P[Y = 1 | A = 1] / P[Y = 1 | A = 0] - if causal ratio = associational ratio, then - association == causation, otherwise not --- ## How do we measure counterfactuals? - Inverse probability weighting - Standardisation - g-methods - Instrumental variables --- ## Conclusions - Moving from internal validity to causality is complex - Criteria based - Counterfactual theories of causation - Cause can be conceptualised in sufficient and component causes - Next up: Study designs that best capture these relationships