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Mediation analysis in causal inference has traditionally focused on binary exposures and deterministic interventions, and a decomposition of the average treatment effect in terms of direct and indirect effects.We present an analogous decomposition of the population intervention effect, defined through stochastic interventions on the exposure. Population intervention effects provide a generalized framework in which a variety of interesting causal contrasts can be defined, including effects for continuous and categorical exposures. We show that identification of direct and indirect effects for the population intervention effect requires weaker assumptions than its average treatment effect counterpart, under the assumption of no mediator–outcome confounders affected by exposure. In particular, identification of direct effects is guaranteed in experiments that randomize the exposure and the mediator.We propose various estimators of the direct and indirect effects, including substitution, reweighted and efficient estimators based on flexible regression techniques, allowing for multivariate mediators. Our efficient estimator is asymptotically linear under a condition requiring n 1/4-consistency of certain regression functions. We perform a simulation study in which we assess the finite sample properties of our proposed estimators.We present the results of an illustrative study where we assess the effect of participation in a sports team on the body mass index among children, using mediators such as exercise habits, daily consumption of snacks and overweight status.

Statistical aspects of causality are reviewed in simple form and the impact of recent work discussed. Three distinct notions of causality are set out and implications for densities and for linear dependencies explained. The importance of appreciating the possibility of effect modifiers is stressed, be they intermediate variables, background variables or unobserved confounders. In many contexts the issue of unobserved confounders is salient. The difficulties of interpretation when there are joint effects are discussed and possible modifications of analysis explained. The dangers of uncritical conditioning and marginalization over intermediate response variables are set out and some of the problems of generalizing conclusions to populations and individuals explained. In general terms the importance of search for possibly causal variables is stressed but the need for caution is emphasized. /// On fait une revue critique de la causalité statistique. On presente trois definitions de la causalité et on discute les consequences pour l'analyse statistique et l'interpretation.