Thread by @THilalMD

Let's talk broad concepts - Causality. #thread

Suppose Jack took LSD and then got into a car accident. Did the LSD cause the car accident?

In a parallel universe where Jack did not take the LSD:
- If he gets into a car accident, then the LSD was probably incidental
- If he does not get into a car accident, then the LSD was probably the cause

That's a counterfactual view of causality.

Let's add another layer to it.

What if Jim was drinking alcohol too. Would he had suffered a car accident if he did not take LSD, even if he was drinking?

So, when establishing causality, ask yourself "what are the potential variables involved"?

In Jim's case, compared to:
- No LSD or alcohol?
- No LSD, but with alcohol?

Defining your question is important (well-specified counterfactual).

But you cannot create a parallel universe. Meaning, you cannot directly obseve counterfactuals. So how do you establish causality?

A few key concepts/assumptions you have to make:
- Consistency
- Positivity
- Exchangeability

Consistency refers to the route you take to acheive a desired goal.

For example, you want to lower the number of cigarettes smoked/day and examine the effect on risk of MI.

How will you do that?
- Will you force cigs out of the participants hands everyday?
- Will you use nicotine replacement methods?
- Will you use bupropion?

The route you take will have a different effect on acheiving your desired goal (lowering number of cigs/day)

Positivity refers to the positive probability that all individuals get all available interventions (even if unlikely)

If only individuals >50 years smoke, and no individuals <50 years smoke, then can't seperate the effects of smoking on MI

Exchangeability is an assumption about the nature of data. It refers to variables being independent from each other. Meaning, the actual exposure between groups does not predict the counterfactual outcome.

This concept is closely related to correlation. Just because older people get MIs and older people take aspirin doesn't mean aspirin caused the MIs.

So how do we assess causality taking these assumptions into cnsideration?

Randomized controlled trials

Consistency and positivity is acheived by design (i.e. randomization). Everyone who enters the trial will get the exposure in the same way, using the same method and there will be equal chance for everyone in the trial to get one intervention or the other.

But since we can't conduct randomized trials for everything to establish causality, and since they are not without their limitations (random error, drop-out, lack of generalizability)..

..we turn to observational data. Observational data forms the basis of much of the literature relating to establishing causality (e.g. smoking and lung cancer).

Now, to make this topic even more complicated, I will copy @venkmurthy @bogdienache @raj_mehta @rwyeh to shed more light on some of these concepts.