Concept Architecture
Concept
Theoretically, Average Treatment Effect (ATE) is the expected difference in outcomes that would occur if every individual in a target population received an intervention compared with if every individual received an alternative intervention or control. It is a fundamental estimand in causal inference, based on the potential outcomes framework, and quantifies the average causal effect of treatment at the population level. In health economics, the ATE is used to estimate treatment effects that inform cost-effectiveness analyses, health technology assessments and policy decisions.
Mathematically, the Average Treatment Effect is defined as the expectation of the difference between two potential outcomes for each individual, one under treatment and one under control. Because only one potential outcome can be observed for any individual, the ATE is estimated using randomisation, statistical adjustment or causal inference methods that account for confounding and selection bias.
In practice, the ATE is estimated from randomised controlled trials or observational studies using regression adjustment, inverse probability weighting, matching, instrumental variables or doubly robust estimators. Estimated treatment effects are frequently incorporated into health economic models to quantify differences in survival, quality-adjusted life-years, healthcare utilisation and costs between competing interventions.
Purpose
Used to estimate the average causal effect of an intervention across a target population for comparative effectiveness research, health technology assessment and economic evaluation.
Mathematical Formulae
Primary Formula
ATE = E[Y(1) ? Y(0)]
where:
- Y(1) = potential outcome under treatment
- Y(0) = potential outcome under control
- E(�) = expected value over the target population
Supporting Formulae
ATE = E[Y | T = 1] ? E[Y | T = 0] (valid under randomisation)
ATE = (1/n) ? ?(Y?(1) ? Y?(0))
Related Mathematical Methods
- Potential outcomes framework
- Causal inference
- Regression adjustment
- Propensity score matching
- Inverse probability weighting
- Instrumental variable analysis
- Doubly robust estimation
Example
A randomised trial evaluates a new antihypertensive treatment. The mean QALYs over five years are 4.25 for treated patients and 4.05 for controls.
ATE = 4.25 ? 4.05 = 0.20 QALYs
The intervention therefore produces an average gain of 0.20 QALYs per patient compared with standard care. This estimate can subsequently be incorporated into a cost-effectiveness analysis.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| AVERAGE | =AVERAGE(B2:B501)-AVERAGE(C2:C501) | Estimates the average treatment effect from trial outcomes |
| SUM | =SUM(B2:B501-C2:C501)/COUNT(B2:B501) | Calculates the average individual treatment effect when paired outcomes are available |
| LINEST | =LINEST(Y2:Y501,X2:X501,TRUE,TRUE) | Estimates adjusted treatment effects using linear regression |
VBA (Optional)
VBA can automate estimation of the Average Treatment Effect across multiple intervention groups and export results directly into health economic evaluation models.
Sources
- Rubin DB. Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies. Journal of Educational Psychology.
- Rosenbaum PR, Rubin DB. The Central Role of the Propensity Score in Observational Studies for Causal Effects. Biometrika.
- Hern�n MA, Robins JM. Causal Inference: What If.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Interpreting Indirect Treatment Comparisons and Network Meta-Analysis for Health-Care Decision Making: ISPOR Task Force on Indirect Treatment Comparisons Good Research Practices, Part 1 — Jansen, Fleurence, Devine, Itzler, Barrett, Hawkins, Lee, Boersma, Annemans & Cappelleri, Vol. 14, No. 4 ed., 2011 (Value in Health)
The ISPOR good-practice guidance on interpreting indirect treatment comparisons, network and mixed treatment comparisons for decision making — terminology, assumptions, validity and how to critically appraise an ITC/NMA when head-to-head trial evidence is unavailable.
Journal ArticleView source →
Frequently Asked Questions (6)
What is the average treatment effect?
The mean difference in outcomes that would occur if every member of a population received a treatment versus a comparator instead.
Source: Rubin 1974
Why is the average treatment effect an average across a population?
The average treatment effect is the mean difference in outcome that would result if a whole population received the treatment rather than the comparator. It is an average because the effect varies from person to person, and no study can observe both what happens to an individual with the treatment and what would have happened without it. Averaging over the population sidesteps this, since randomisation lets the treated and untreated groups stand in for one another. It describes the typical effect, not any one person's. Hernan and Robins (2020) define this quantity.
Source: Hernan & Robins 2020
How is the average treatment effect defined in potential outcomes?
In the potential outcomes framework, each individual has a potential outcome under treatment and a potential outcome under the comparator, and their individual treatment effect is the difference between these, though only one is observed for each person. The average treatment effect is the mean of these individual differences across the population, equivalently the difference between the average outcome if all were treated and the average if all received the comparator. This framing defines the causal effect clearly, and estimating it requires methods that address the fact that only one potential outcome is observed per individual.
Source: Rubin 1974
How is the average treatment effect estimated?
The average treatment effect is estimated most reliably by randomised trials, where randomisation makes the treated and comparator groups comparable, so the difference in their average outcomes estimates the average treatment effect without bias from confounding. In observational data, estimating it requires methods to address confounding, such as adjustment, matching, propensity scores, or instrumental variables, which aim to approximate the comparability that randomisation provides. Because only one potential outcome is observed per person, estimation relies on comparing groups assumed comparable, so the validity of the estimate depends on that comparability holding.
Source: Hernán & Robins 2020
Why is the average treatment effect important?
The average treatment effect is important because it summarises the overall causal effect of a treatment across a population, answering how much the treatment changes outcomes on average, which is the quantity most relevant to decisions about whether to use it. It is what randomised trials are designed to estimate and a central target of causal inference. By representing the population-level effect of treatment versus comparator, the average treatment effect provides the basis for judging a treatment's benefit and for economic evaluation, making it a foundational concept in evaluating interventions.
Source: Rubin 1974
How does the average treatment effect relate to individual effects?
The average treatment effect is the mean of the individual treatment effects across the population, so it summarises how the treatment affects people on average, but it does not reveal how effects vary between individuals, who may benefit more, less, or not at all. Because individual effects cannot be observed directly, the average treatment effect is what is typically estimated, while variation in effects is explored through subgroup or heterogeneity analysis. So the average treatment effect captures the overall effect, and understanding differences among individuals requires additional analysis beyond the average.
Source: Hernán & Robins 2020
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 20 Nov 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-ES-CER-003
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