Assumptions in Causal Inference
- Consistency
- Exchangeability
- Positivity
Consistency
- We assume that the causal question you claim you are answering is consistent with the one you are actually answering with your analysis.
- Mathematically: \(Y_{obs} = (X)Y(1) + (1-X)Y(0)\)
- Well defined exposure
- No interference
Well defined exposure
- We assume that for each value of the exposure, there is no difference between subjects in the delivery of that exposure
- Put another way, multiple versions of the treatment do not exist
Application exercise
- Think of an example where this might be violated
- Turn to the person next to you and tell them your example
- Pick your favorite between the two of you, we’ll share them with the class
No interference
- We assume that the outcome (technically all potential outcomes, regardless of whether they are observed) for any subject does not depend on another subject’s exposure
Application exercise
- Think of an example where this might be violated
- Turn to the person next to you and tell them your example
- Pick your favorite between the two of you, we’ll share them with the class
Exchangeability
- We assume that within levels of relevant variables (confounders), exposed and unexposed subjects have an equal likelihood of experiencing any outcome prior to exposure
- i.e. the exposed and unexposed subjects are exchangeable
- This assumption is sometimes referred to as no unmeasured confounding.
Application exercise
- Think of an example where this might be violated
- Turn to the person next to you and tell them your example
- Pick your favorite between the two of you, we’ll share them with the class
Positivity
- We assume that within each level and combination of the study variables used to achieve exchangeability, there are exposed and unexposed subjects.
- Said differently, each individual has some chance of experiencing every available exposure level.
- Sometimes this is referred to as the probabilistic assumption.
Application exercise
- Think of an example where this might be violated
- Turn to the person next to you and tell them your example
- Pick your favorite between the two of you, we’ll share them with the class