DSC6008 Chap.9 Causal Effects and Potential Outcomes
Causal Effects and Potential Outcomes
Name the missing outcome
A unit has a potential outcome under each treatment condition, but only the outcome under the received treatment can be observed. A causal effect compares those potential outcomes.
This fundamental missing-outcome problem explains why an observed difference between two units is not automatically an individual treatment effect.
Define the target effect before fitting a model
An average treatment effect concerns all units in a target population, while an effect among treated units concerns a different group. These quantities can differ when responses to treatment vary.
Matching, weighting or restricting to overlap may also change which population is represented. The estimand should therefore be stated before the method, not inferred afterward from the available software output.
Use random assignment as a design argument
Random assignment makes treatment independent of potential outcomes in expectation under the implemented mechanism.
Group averages can then stand in for missing counterfactual averages, subject to adherence, missing outcomes and interference. It does not reveal both outcomes for any individual and does not guarantee identical realised groups.
Its force comes from known assignment probabilities rather than from a balance table alone.
Locate confounders before treatment
A confounder is a pre-treatment common cause of treatment choice and outcome. Timing matters. A variable caused by treatment can be a mediator or collider, and controlling for it may remove part of the effect or create a spurious association.
Drawing the sequence of causes before choosing adjustment variables helps prevent a predictive model from being mistaken for a causal design.
Treat adjustment as an argument
Propensity scores summarize the probability of treatment conditional on measured pre-treatment covariates. Matching, stratification or weighting can improve measured balance, but a highly predictive treatment model is not the goal by itself.
Check balance after adjustment and report which observations receive extreme weights or are discarded. Unmeasured common causes remain an assumption rather than a problem solved by the score.
Check overlap before trusting weighted results
If some covariate profiles appear only under one treatment, the other potential-outcome mean is unsupported there.
Extreme propensity weights signal reliance on a few unusual observations and can make estimates unstable. Restricting to a common-support population may produce a narrower but more defensible target.
That change belongs in the causal conclusion, not only in a technical appendix.
Ask whether treatments interfere across units
The usual unit-level effect assumes one unit's outcome is unaffected by another unit's assignment and that each treatment label has a well-defined version. Spillovers, contamination or inconsistent treatment delivery violate that simplification.
The remedy may be cluster assignment, wider spacing, an exposure mapping or a redefined unit, depending on the mechanism.
Expose the assumption carrying the claim
For an experiment, name the assignment and departures from it. For an observational study, name measured-confounding control, overlap, consistency and the assumption about important unmeasured causes. Report the target population and outcome timing.
A causal conclusion becomes auditable when the reader can see both the missing comparison and the reason the observed substitute is credible.
What this chapter covers
- 01
Potential outcomes
- 02
Counterfactuals
- 03
Average treatment effects
- 04
Random assignment
- 05
Confounding
- 06
Covariate balance
Worked example · free
Separate observed difference from individual effect
- 2Define the first unit's causal effect as its treated outcome minus its own untreated potential outcome.
- 2Identify that the first unit's untreated potential outcome is missing.
- 2Explain why the second unit's outcome is not automatically that counterfactual.
Key terms
- Potential Outcome
- The response a unit would have under one specified treatment condition.
- Counterfactual Outcome
- A potential outcome not observed because the unit received another treatment.
- Confounder
- A pre-treatment common cause of treatment assignment and outcome.
Causal Effects and Potential Outcomes FAQ
Why can only one potential outcome be observed?
A unit experiences one treatment condition at the relevant time, so its response under the alternative remains counterfactual. Experimental design addresses this missing-data problem by making groups comparable and estimating average effects, rather than revealing both outcomes for the same unit.
What does randomization contribute to causal inference?
It makes treatment assignment independent of the units' potential outcomes in expectation under the implemented mechanism. That breaks systematic confounding and justifies comparing treatment-group averages, subject to issues such as noncompliance, missing outcomes, interference and the exact effect being estimated.
Can propensity scores remove all confounding?
They can help balance measured pre-treatment covariates when the model and overlap are adequate. They cannot balance variables that were not measured, repair positivity failures or justify controlling for consequences of treatment. The causal assumptions still need to be stated and defended.
Assessment move
Draw two potential-outcome slots for a single unit and cross out the unobserved one. Then state which design feature or assumption lets a group supply information about the missing average. For adjustment questions, classify every variable as pre-treatment, treatment, outcome or post-treatment before deciding whether it belongs in the model.
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