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Conditional effect (subject-specific effect)

It represents the mean effect at the individual level, i.e. the mean effect if an exposed subject was non-exposed. In presence of confounders, this effect is often estimated by using multivariate regressions.

Marginal effect (population-average effect)

It represents the mean effect at the population level, i.e. the mean effect if all the subjects of entire population were exposed instead of non-exposed (or inversely). In presence of confounders, this effect is often estimated by using propensity scores. More precisely, two types of marginal effects are distinguished  (Pirracchio et al. 2013) :​​
The average treatment effect in the entire population (ATE) is the mean effect if all the subjects of entire population were exposed instead of non-exposed (or inversely).
The average treatment effect on the treated (ATT) is the mean effect if all the exposed subject were non-exposed (or inversely).

Differences between conditional and marginal effects

The two effect are equaled when the link between the exposure and the outcome is linear, or when there is no effect. In contrast, in case of non-linearity  (odds-ratio or hazards-ratio for instance), the conditional and marginal effects can differ.