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Causal Inference

Notes on Causal Inference following the course by Brady Neal.

Author

Affiliation

Skip Moses

 

Published

May 31, 2022

DOI

In this post we preview the course on Causal Inference. This post will give a brief overview of the main concepts.

What is causal inference?

Motivating Example

Suppose we have some disease we are tying to treat with treatment A and treatment B. Our only goal is minimizing death. Suppose treatment B is much more scarce than treatment A.

Data at Treatment Level

Treatment Total
A 240/1500 16%
B 105/550 19%

Data at the Condition Level

Treatment Mild Severe Total
A 210/1400 15% 30/100 30% 240/1500 16%
B 5/50 10% 100/500 20% 105/550 19%

14001500(0.15)+1001500(0.30)=0.16

50550(0.10)+500550(0.20)=0.19

Which treatment should you choose?

Correlation does not imply causation

What does imply causation?

Potential Outcomes

Fundamental problem of causal inference

Work around (Average Treatment Effect ATE)

E[Yi(1)]E[Yi(0)]E[Y|T=1]E[Y|T=0] The left hand side is causal, while the right hand side is causal and confounding.

Observational Sudies

E[Y(t)|W=w]:=E[Y|do(T=t),W=w]=E[Y|t,w] - This still depends on w, so we take the marginal

E[Y(t)]:=E[Y|do(T=t)]=EWE[Y|t,W]

Example

Treatment Mild Severe Total
A 210/1400 15% 30/100 30% 240/1500 16%
B 5/50 10% 100/500 20% 105/550 19%

E[Y|do(T=t)]=EWE[Y|t,C]=cCE[Y|t,c]P(c)

14502050(0.15)+6002050(0.30)0.194

14502050(0.10)+6002050(0.20)0.129