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#
• 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