Causal Inference

Prediction versus Intervention. Former: “Among patients who got the treatement, what is $Y$?”

$$P(Y|T=1)$$

If we intervene to assign treatment, what happens to $Y$?

$$P(Y|\text{do}(T=1))$$

In general, $P(Y|T=1) \ne P(Y|\text{do}(T=1))$. That is, Prediction is not Intervention.

DAG Patterns

Confounders, Mediators, Colliders. Bread ‘n Butter.

Pattern	Problem
Confounder	Simpson’s Paradox
Collider	Berkson’s Paradox, Healthy Volunteer Effect
Mediator	Overadjustment Bias

Source