Backtracking Direct, Indirect and Total Effects

Jose M. Peña · 2026 · arXiv

DOI: 10.48550/arXiv.2610.28910 · open-access PDF

Abstract

Natural direct and indirect effects are defined through cross-world interventional counterfactuals. We propose an alternative construction based on backtracking counterfactuals. Rather than intervening on the treatment or mediator, we use a backtracking conditional distribution to construct an alternative exogenous state satisfying a desired treatment-mediator constraint. This yields the backtracking direct and indirect effects, and also the backtracking total effect. Likewise, we adapt the population intervention effects.

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