IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v110y2023i3p739-761..html
   My bibliography  Save this article

Variable elimination, graph reduction and the efficient g-formula

Author

Listed:
  • 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.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asac062
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    3. Manabu Kuroki & Hisayoshi Nanmo, 2020. "Variance formulas for estimated mean response and predicted response with external intervention based on the back-door criterion in linear structural equation models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 667-685, December.
    4. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    5. Xun Lu, 2015. "A Covariate Selection Criterion for Estimation of Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 506-522, October.
    6. David Cheng & Abhishek Chakrabortty & Ashwin N. Ananthakrishnan & Tianxi Cai, 2020. "Estimating average treatment effects with a double‐index propensity score," Biometrics, The International Biometric Society, vol. 76(3), pages 767-777, September.
    7. Toru Kitagawa & Chris Muris, 2013. "Covariate selection and model averaging in semiparametric estimation of treatment effects," CeMMAP working papers 61/13, Institute for Fiscal Studies.
    8. Lorenza Rossi & Emilio Zanetti Chini, 2016. "Firms’ Dynamics and Business Cycle: New Disaggregated Data," DEM Working Papers Series 123, University of Pavia, Department of Economics and Management.
    9. Dingke Tang & Dehan Kong & Wenliang Pan & Linbo Wang, 2023. "Ultra‐high dimensional variable selection for doubly robust causal inference," Biometrics, The International Biometric Society, vol. 79(2), pages 903-914, June.
    10. White, Halbert & Chalak, Karim, 2010. "Testing a conditional form of exogeneity," Economics Letters, Elsevier, vol. 109(2), pages 88-90, November.
    11. Fan, Yanqin & Guerre, Emmanuel & Zhu, Dongming, 2017. "Partial identification of functionals of the joint distribution of “potential outcomes”," Journal of Econometrics, Elsevier, vol. 197(1), pages 42-59.
    12. Chi Wang & Giovanni Parmigiani & Francesca Dominici, 2012. "Rejoinder: Bayesian Effect Estimation Accounting for Adjustment Uncertainty," Biometrics, The International Biometric Society, vol. 68(3), pages 680-686, September.
    13. Boitani, Andrea & Punzo, Chiara, 2019. "Banks’ leverage behaviour in a two-agent new Keynesian model," Journal of Economic Behavior & Organization, Elsevier, vol. 162(C), pages 347-359.
    14. Edward H. Kennedy & Sivaraman Balakrishnan, 2018. "Discussion of “Data†driven confounder selection via Markov and Bayesian networks†by Jenny Häggström," Biometrics, The International Biometric Society, vol. 74(2), pages 399-402, June.
    15. Häggström, Jenny & Persson, Emma & Waernbaum, Ingeborg & de Luna, Xavier, 2015. "CovSel: An R Package for Covariate Selection When Estimating Average Causal Effects," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i01).
    16. Lu, Xun & White, Halbert, 2014. "Robustness checks and robustness tests in applied economics," Journal of Econometrics, Elsevier, vol. 178(P1), pages 194-206.
    17. Tyler J. VanderWeele & James M. Robins, 2010. "Signed directed acyclic graphs for causal inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 111-127, January.
    18. Bryan Keller, 2020. "Variable Selection for Causal Effect Estimation: Nonparametric Conditional Independence Testing With Random Forests," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 119-142, April.
    19. Navascués Miguel & Wolfe Elie, 2020. "The Inflation Technique Completely Solves the Causal Compatibility Problem," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 70-91, January.
    20. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:biomet:v:110:y:2023:i:3:p:739-761.. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.