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Contrasting identifying assumptions of average causal effects: robustness and semiparametric efficiency
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. (Stat4Reg)ORCID iD: 0000-0003-2135-9963
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. (Stat4Reg)ORCID iD: 0000-0003-3187-1987
Department of Statistics, Uppsala University, Uppsala, Sweden.ORCID iD: 0000-0002-4457-5311
Department of Mathematics and Statistics, University of Jyvaskyla, Jyväskylä, Finland.
2023 (English)In: Journal of machine learning research, ISSN 1532-4435, E-ISSN 1533-7928, Vol. 24, no 197, p. 1-65Article in journal (Refereed) Published
Abstract [en]

Semiparametric inference on average causal effects from observational data is based on assumptions yielding identification of the effects. In practice, several distinct identifying assumptions may be plausible; an analyst has to make a delicate choice between these models. In this paper, we study three identifying assumptions based on the potential outcome framework:  the back-door assumption, which uses pre-treatment covariates, the front-door assumption, which uses mediators, and the two-door assumption using pre-treatment covariates and mediators simultaneously. We provide the efficient influence functions and the corresponding semiparametric efficiency bounds that hold under these assumptions, and their combinations. We demonstrate that neither of the identification models provides uniformly the most efficient estimation and give conditions under which some bounds are lower than others. We show when semiparametric estimating equation estimators based on influence functions  attain the bounds, and study the robustness of the estimators to misspecification of the nuisance models. The theory is complemented with simulation experiments on the finite sample behavior of the estimators. The results obtained are relevant for an analyst facing a choice between several plausible identifying assumptions and corresponding estimators. Our results show that this choice implies a trade-off between efficiency and robustness to misspecification of the nuisance models. 

Place, publisher, year, edition, pages
2023. Vol. 24, no 197, p. 1-65
Keywords [en]
causal inference, efficiency bound, robustness, back-door, front-door
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-190082OAI: oai:DiVA.org:umu-190082DiVA, id: diva2:1616773
Funder
Forte, Swedish Research Council for Health, Working Life and Welfare, 2018-00852Swedish Research Council, 2018-02670Swedish Research Council, 2016-00703Marianne and Marcus Wallenberg Foundation, 2015.0060Academy of Finland, 311877Available from: 2021-12-03 Created: 2021-12-03 Last updated: 2023-09-04Bibliographically approved

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Gorbach, Tetianade Luna, XavierWaernbaum, Ingeborg

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