A Crash In Causal Inference
I leaned Causal Inference in my master program and found it’s interesting and used frequently in business world. I am pretty interested in it and decided to take another causal course.
This is my notes for the course A Crash In Causal Inference at Coursera.
- Course Name: A Crash Course in Causality: Inferring Causal Effects from Observational Data
- Platform: Coursera
- University: by University of Pennsylvania
- Professor: Jason A. Roy, Ph.D.
Hypothetical Interventions
There are something you could manipulate while others not.
For example,
Intervention like Region, whether to have a drug a things that you can change.
If you care about whether the race has a causal impact of people getting a job, you cannot assign race to one person. Instead, you can do like what are listed in the table:
| No Direct Intervention | Manipulate Intervention |
|---|---|
| Race | Name on Resume |
| Obesity | Bariatric Surgery |
| Socioeconomics Status | Gift of Money |
This course/notes primarily focus on treatments/exposures that could be thought of as interventions
- Treatment that we can imagine being randomized (manipulated) in a hypothetical trial.
Because their meaning is well defined and potentially actionable.
The Fundamental Problem of Causal Inference is that we can only observe one potential outcome for each person.
However, with certain assumptions, we can estimate population level (average) causal effects.
Average Causal Inference Effects
How to estimate causal inference effects?
Example: Regional (A=1) versus genreal (A=0_ anesthesia for hip fracture surgery on risk of major pulmonary complications
- Suppose E(Y_1 - Y_0) = 1
- Probability of major pulmonary complications is lower by 0.1 if given regional anesthesia compared with general anesthesia.
- If 1000 people were going to have hip fracture surgery, we would expect 100 fewer people to have pulmonary complications under regional anesthesia compared with general anesthesia.
In General
E(Y_1 - Y_0) ≠ E(Y|A=1) - E(Y|A=0)
It’s changing the original population which is not true.
| E(Y | A=1) - E(Y | A=0) is genially NOT a causal effect. Because it is comparing two different populations of people |
E(Y_1 - Y_0) is a causal effect because it is comparing what would happen if the same people treated with A=1 versus if the SAME PEOPLE were treated with A = 0.
