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Counterfactual outcome

As explained in Causal Inference for Data Science

A counterfactual is a representation of what would have happened to a unit or system under a treatment or condition different from the one actually observed.

A counterfactual outcome represents the result a person, group, or system would have had under an alternative treatment or condition. For a patient, Y1(i) is the potential outcome with treatment and Y0(i) without it. After treatment is assigned, only one can be observed: the factual outcome. The other remains unobserved, creating the central missing-data problem of causal inference. section 10.1.1

Recovery under the treatment not received

Suppose a treated patient does not recover. The observed outcome is their recovery under treatment, not proof that treatment caused failure. Their counterfactual outcome is whether that same patient would have recovered without treatment. A patient may recover under either condition, neither condition, or only one of them. section 10.1.1

Table 10.1 Hypothetical example of POs with assignment (T(i)) and observed recovery (Y(i))
Name
i
Y 0( i)
Y 1( i)
T( i)
Y( i)
Drummer
1
0
0
1
0
Burton
2
1
0
1
0
Holden
3
0
1
1
1
Avasarala
4
1
1
0
1

Compare each patient's two potential recovery outcomes with the assigned treatment and the single outcome actually observed. section 10.1.1

Counterfactual outcomes turn descriptive questions into causal ones: not merely what happened after treatment, but what would have happened otherwise. In difference-in-differences, the key missing quantity is the post-event outcome for treated units had they not been treated. It cannot be calculated directly from their observed post-event data. section 11.4.2

Common ways to estimate a counterfactual outcome include:

  • Use a synthetic control: train a predictive relationship on pre-event data, then forecast the treated series after the event as its no-event scenario. section 11.3
  • Use difference-in-differences: compare treated and untreated groups over time to estimate the treated group’s missing no-treatment post-event outcome. section 11.4.2

A credible estimate depends on assumptions. For synthetic controls, the event must not affect the control series, the outcome–control relationship must remain stable, and no nearby event should distort that relationship. Otherwise, the gap between observed and predicted outcomes cannot confidently be assigned to the focal event. section 11.3.3

The term has related but distinct uses. In the potential-outcomes framework, it usually means an unobserved potential outcome. In DAG-based reasoning, counterfactuals address what would occur for a particular situation under a different action; cases involving post-treatment mediators require more advanced treatment because intervention and subgroup selection interact. section 10.2.3 section 2.5.8

How Causal Inference for Data Science covers it

How deep it goes
Defines individual and group counterfactuals, then introduces DAG counterfactuals as advanced and mathematically subtle.
Examples
Uses patient recovery, movie-release viewing series, and treated-versus-untreated post-event outcomes.
What it assumes
Introduces potential-outcome notation from zero while treating DAG counterfactuals and post-treatment selection as advanced.
What you can do after
Evaluate/understand whether an observed outcome can answer a causal question and which missing alternative outcome must be estimated.
How it connects
Connects potential outcomes, causal inference, difference-in-differences, synthetic controls, DAGs, mediators, and conditional intervention.
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This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.