Treatment Effect

The change in an outcome attributable to a specific treatment, distinguished from changes that would have occurred regardless due to other factors.

Source: Rubin 1974

A patient's outcome after treatment reflects the treatment together with the natural course of their illness, other care, and chance, so simply observing improvement does not reveal the treatment's own contribution. The treatment effect is the part of the change caused specifically by the treatment, the difference between what happened and what would have happened without it. Isolating it requires a comparison, ideally a randomised control, that shows the counterfactual course. Without separating it out, a treatment could be credited with change it did not cause. Hernan and Robins (2020) define this quantity.

Source: Hernan & Robins 2020

In the potential outcomes framework, a treatment effect for an individual is the difference between their potential outcome under the treatment and their potential outcome without it, though only one is observed for each person. Because the counterfactual, the unobserved outcome, cannot be seen for the same individual, the treatment effect is estimated by comparing groups. At the population level, the average treatment effect is the mean of these individual differences. This framing defines the treatment effect as a causal contrast, clarifying that it is the difference the treatment makes relative to its absence.

Source: Rubin 1974

A treatment effect is estimated most reliably by randomised trials, where randomisation makes the treated and untreated groups comparable, so the difference in their outcomes estimates the treatment effect without confounding. In observational data, estimation requires methods to address confounding, such as adjustment, matching, propensity scores, or instrumental variables, which aim to approximate the comparability randomisation provides. Because the counterfactual is unobserved for each individual, estimation relies on comparing groups assumed comparable, so the validity of the estimate depends on that comparability holding, which randomisation ensures and observational methods approximate.

Source: Hernán & Robins 2020

Isolating the treatment effect is important because outcomes are influenced by many factors besides the treatment, such as the natural course of the condition, other interventions, and chance, so a change observed after treatment is not necessarily caused by it. Attributing the outcome change to the treatment requires distinguishing its effect from these other influences. Only by isolating the treatment effect can one judge whether the treatment works and how much benefit it provides, which is what decisions require. So isolating the treatment effect is central to valid evaluation of interventions.

Source: Rubin 1974

An individual treatment effect is the difference a treatment makes for a specific person, comparing their outcome with and without treatment, while the average treatment effect is the mean of these individual effects across a population. Because the counterfactual outcome for an individual cannot be observed, individual effects are generally not directly measurable, so the average treatment effect is what is typically estimated. Individual effects may vary, a heterogeneous treatment effect, so the average does not describe every person. So the two differ in scope, individual versus population, with the average usually estimated and individual variation explored separately.

Source: Rubin 1974