Effect of treatment on the treated

As explained in Causal Inference for Data Science

The average treatment effect on the treated is the average difference between treated outcomes and their untreated potential outcomes among treated units.

The effect of treatment on the treated, usually called ATT or ATET, asks a focused causal question: among people who actually received a treatment, how much did it change their outcome? It averages the difference between their observed treated outcomes and the outcomes those same people would have had without treatment. The latter outcome is counterfactual, so it is not directly observed. section 11.4.2 section 11.4.4

This differs from the average treatment effect (ATE), which targets a broader population. ATT restricts attention to treated units. That focus is useful when available controls can represent every treated unit but cannot represent every control unit; in that case, ATT may be estimable while the reverse estimand, the average treatment effect on controls (ATC), is not. section 5.3.3 section 5.3.4

Comparable patients

Suppose treated patients have propensity scores from about 0.6 to 1, while controls range from about 0.3 to 1. Every treated patient has a comparable control, so treatment effects can be estimated for treated patients. But some controls lack a comparable treated patient, preventing estimation of an effect for all controls. section 5.3.3

Figure 5.12 The distribution overlap consists of the treated. In this case, we can calculate the (ATT).

Use the overlap plot to check the special case where the common support covers the treated group, supporting an ATT target. section 5.3.3

Matching naturally produces ATT when it pairs each treated unit with one or more controls and then averages treated-versus-matched-control differences. With unequal group sizes, controls may be reused when treated units outnumber them. Using only one match can be unstable when outcomes vary, motivating k-nearest-neighbor matching rather than reliance on a single control. section 5.3.4

A time-related event

For a movie release, ATET is the effect of the release on movies that received it, compared with the hypothetical outcome those movies would have had without a release. In difference-in-differences, the treated group’s before-to-after change is adjusted by the untreated group’s before-to-after change to recover this target under the parallel paths assumption. section 11.4.2 section 11.4.4

Practical routes to estimating ATET include:

• Apply the difference-in-differences direct formula to treated and untreated group means before and after the event. section 11.4.5
• Fit a linear model with treatment, time, and their interaction; the interaction estimates ATET in the stated specification. section 11.4.5
• Use bootstrap resampling to form confidence intervals, or use DiD-oriented R and Python packages for richer specifications. section 11.4.5

ATT does not license claims about untreated people. Under heterogeneous treatment effects, an estimate for chatbot users says how use affected users, not how nonusers would respond if they began using it. The estimand’s population is therefore part of the conclusion, not merely an implementation detail. section 10.4

How Causal Inference for Data Science covers it

How deep it goes

Defines ATT through potential outcomes and derives DiD estimation from observed data under the parallel paths assumption.

Examples

Uses overlapping patient propensity scores, chatbot engagement, movie releases, synthetic DiD data, and R and Python estimators.

What it assumes

Assumes familiarity with potential outcomes for formal DiD derivation while introducing ATT as a treated-subpopulation variation of ATE.

What you can do after

Apply it via matching or difference-in-differences formulas, linear models, bootstrapping, and named R or Python libraries.

How it connects

Connects ATT with average treatment effect, average treatment effect on controls, propensity scores, matching, instrumental variables, and difference-in-differences.

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Also explained in

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  Causal AIThe effect of treatment on the treated is the average causal effect among units that received treatment, comparing their treated outcomes with the outcomes they would have had under no treatment.

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Related concepts

• average treatment effect estimationkind of · Average treatment effect estimation quantifies the population-average difference in outcomes that would result from two alternative treatments or interventions.
• counterfactual outcomekind of · A counterfactual outcome is a hypothetical result that would have occurred under a condition, action, or intervention different from the one observed.
• treatment effectkind of · A treatment effect is the difference in an outcome attributable to receiving an intervention or exposure rather than a comparison condition.
• causal identificationaddressed by · Causal identification is the process of determining whether a causal quantity can be uniquely computed from available observational or interventional information and model assumptions.
• synthetic controlproduced by · Synthetic control is a causal inference method that estimates a treated unit’s counterfactual outcome using a weighted combination of comparison units.

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.