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Variable elimination, graph reduction and the efficient g-formula

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  • F Richard Guo
  • Emilija Perković
  • Andrea Rotnitzky

Abstract

SummaryWe study efficient estimation of an interventional mean associated with a point exposure treatment under a causal graphical model represented by a directed acyclic graph without hidden variables. Under such a model, a subset of the variables may be uninformative, in that failure to measure them neither precludes identification of the interventional mean nor changes the semiparametric variance bound for regular estimators of it. We develop a set of graphical criteria that are sound and complete for eliminating all the uninformative variables, so that the cost of measuring them can be saved without sacrificing estimation efficiency, which could be useful when designing a planned observational or randomized study. Further, we construct a reduced directed acyclic graph on the set of informative variables only. We show that the interventional mean is identified from the marginal law by the g-formula (Robins, 1986) associated with the reduced graph, and the semiparametric variance bounds for estimating the interventional mean under the original and the reduced graphical model agree. The g-formula is an irreducible, efficient identifying formula in the sense that the nonparametric estimator of the formula, under regularity conditions, is asymptotically efficient under the original causal graphical model, and no formula with this property exists that depends only on a strict subset of the variables.

Suggested Citation

  • F Richard Guo & Emilija Perković & Andrea Rotnitzky, 2023. "Variable elimination, graph reduction and the efficient g-formula," Biometrika, Biometrika Trust, vol. 110(3), pages 739-761.
  • Handle: RePEc:oup:biomet:v:110:y:2023:i:3:p:739-761.
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    References listed on IDEAS

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    1. Manabu Kuroki & Masami Miyakawa, 2003. "Covariate selection for estimating the causal effect of control plans by using causal diagrams," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 209-222, February.
    2. Leonard Henckel & Emilija Perković & Marloes H. Maathuis, 2022. "Graphical criteria for efficient total effect estimation via adjustment in causal linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 579-599, April.
    3. Jinyong Hahn, 2004. "Functional Restriction and Efficiency in Causal Inference," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 73-76, February.
    4. Robin J. Evans, 2016. "Graphs for Margins of Bayesian Networks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 625-648, September.
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