Estimands: ATE, ATT, and CATE

An estimand is the precise quantity a study aims to learn. It fixes the treatment contrast, outcome and time, population, and population-level summary. An estimator is a rule applied to data; an estimate is the resulting number.

Prerequisites

Complete Potential Outcomes. Continue using assignment to Study Sprint access versus usual resources and the six-week exam score.

Learning goals

• Distinguish an estimand, estimator, and estimate.
• Match ATE, ATT, and CATE to different decisions and populations.
• State outcome scale, horizon, support, and transport limits.

Three common averages

For eligible students:

• Average treatment effect (ATE): $E[Y(1)-Y(0)]$. This supports a decision about assigning access across the target eligible population.
• Average treatment effect among the treated (ATT): $E[Y(1)-Y(0)\mid A=1]$. This asks what the effect was for those who in fact received treatment in the assignment regime being studied.
• Conditional average treatment effect (CATE): $E[Y(1)-Y(0)\mid X=x]$. This describes the average effect in a prespecified subgroup or at covariate value $x$.

These can differ under effect heterogeneity. Suppose the effect averages 8 points for students with low prior preparedness and 2 points for students with high preparedness. If eligible students are evenly split, the ATE is 5 points. If 80% of actual participants are highly prepared, their weighted subgroup effect is $0.2(8)+0.8(2)=3.2$ points. Neither target is universally “the effect.”

Match the estimand to the decision

Decision	Candidate estimand	Additional requirement
Offer the program to all eligible students	ATE in next term's eligible population	Evidence transports to that population and implementation
Evaluate impact on this term's participants	ATT for this term's treated group	Untreated outcomes for treated students are identified
Decide whether to tailor offers by preparedness	Prespecified CATEs	Adequate support and uncertainty within every subgroup

CATE is an average, not an individual treatment effect. Searching many subgroups after seeing outcomes creates noisy, selected findings. Subgroup boundaries, multiplicity, sample size, and whether $X$ is measured before treatment all matter.

Scale and outcome matter

A mean difference, risk difference, risk ratio, and odds ratio are different summaries. Effects can also vary by follow-up time. State the scale rather than saying only “ATE.” For Study Sprint, the target is a mean score difference after six weeks, not a probability of passing or a long-term retention effect.

If post-assignment events such as dropout affect whether an outcome is observed, define how the scientific question treats them before analysis. Otherwise an estimator silently chooses a different target.

Assumptions and limits

Each estimand still needs consistency, exchangeability, positivity, an interference definition, measurement validity, and any transport assumptions. The ATT may have better observed support than the ATE in self-selected data, but it is not automatically identified. A CATE requires positivity within each target stratum and enough information for useful uncertainty.

Common mistakes

• Choosing the estimand because software reports it by default.
• Calling an estimator or regression coefficient “the ATE” without an identification argument.
• Interpreting a CATE as a certain benefit for every person in the subgroup.
• Switching outcome scale or subgroup after seeing favorable results.
• Transporting a sample ATE to a different population without justification.

Practice

Write estimands for a college deciding universal access, a tutor evaluating current participants, and an advisor considering a low-preparedness subgroup. For each, name one positivity or transport concern.

Next steps

Identification and Assumptions separates a well-defined target from what the observed data can reveal.

Primary sources

Checked 2026-10-15: Rubin, “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies”, ICH E9(R1), “Estimands and Sensitivity Analysis in Clinical Trials”, and Hernán and Robins, Causal Inference: What If.