Causal inference

Builds on Rubin causal model Statistical inference

Definition

Causal inference is the branch of statistical inference whose targets are causal quantities. These are the values an outcome would take under interventions that set a treatment or exposure to given values. In the potential outcomes framework, a typical target is the average treatment effect $E[Y(1) - Y(0)]$ . Here $Y(w)$ is the outcome a unit would have under treatment level $w$ . A causal quantity is identified if, under stated assumptions, it is a function of the distribution of the observed variables.

Remarks

Causal inference has two steps: identification, which shows that the target is a function of the observed distribution under assumptions, and estimation of that function from data.

Example: in a completely randomised experiment with treatment $W \in \set{0, 1}$ , randomization makes $W$ independent of $(Y(0), Y(1))$ . Then $E[Y(1) - Y(0)] = E[Y \mid W = 1] - E[Y \mid W = 0]$ , so the average treatment effect is identified and estimated by the difference of group means.

Non-example: estimating $E[Y \mid W = 1] - E[Y \mid W = 0]$ in observational data, with no assumption linking it to $Y(1)$ and $Y(0)$ , is a description of an association, not causal inference. If sicker patients choose the treatment, this difference may even have the opposite sign to the causal effect.

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Tag	`FPKRV34TBV`
URI	`m2://FPKRV34TBV`
Kind	definition
Writing	W0 stub
MSC	62D20, 62A01
Defines	Causal inference
Uses	Rubin causal model, Statistical inference

Causal inference

Definition

Remarks

Reading path

Further reading

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