The last exercise brought up one assumption used throughout causal inference: conditional exchangeability. In this lesson, we will learn a few more assumptions.
A second assumption made in causal inference is Stable Unit Treatment Value Assumption (SUTVA). The name is a mouthful, but it’s a pretty simple assumption that can be broken down into two components:
- An individual’s treatment assignment doesn’t impact the outcome of other individuals. Using the example of the hospital patients, this would mean that one individual getting therapy animal services doesn’t impact the stress level of other individuals in the hospital.
- The treatment (or control) is applied exactly the same way to all patients. For example, the patients receiving therapy animal services should receive therapy for the same amount of time and ideally from the same exact animal to ensure consistent treatment.
The next assumption we need to familiarize ourselves with is overlap. The assumption of overlap means that all subgroups of patients divided by their characteristics have a positive, non-zero probability of getting either treatment assignment. Overlap is also referred to as the common support or positivity assumption.
Take a look at the plot in the learning environment. The left half of the plot shows an example of when the assumption of overlap is met. For individuals of all ages, there is a positive probability of being assigned to either the treatment or control group. No age has a 100% probability of being assigned to treatment and a 0% probability of being in the control group or vice versa. The area of overlap is called the region of common support.
In contrast, the right half of the plot shows when the assumption of overlap is NOT met.
- Patients under the age of about 38 have zero probability of being assigned to the control group.
- Patients above the age of 38 have no probability of being assigned to the treatment group.
If we try to make inferences based on the groups with no overlap, we are comparing a group of treated younger individuals to a group of untreated older individuals. We cannot reasonably assume age does not also affect our outcome.