IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i18p2801-d1475374.html
   My bibliography  Save this article

Identifiability and Estimation for Potential-Outcome Means with Misclassified Outcomes

Author

Listed:
  • Shaojie Wei

    (School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China)

  • Chao Zhang

    (School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China)

  • Zhi Geng

    (School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China)

  • Shanshan Luo

    (School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China)

Abstract

Potential outcomes play a fundamental and important role in many causal inference problems. If the potential-outcome means are identifiable, a series of causal effect measures, including the risk difference, the risk ratio, and the treatment benefit rate, among others, can also be identified. However, current identification and estimation methods for these means often implicitly assume that the collected data for analysis are measured precisely. In many fields such as medicine and economics, the collected variables may be subject to measurement errors, such as medical diagnostic results and individual wage data. Misclassification, as a non-classic measurement error, can lead to severely biased estimates in causal inference. In this paper, we leverage a combined sample to study the identifiability of potential-outcome means corresponding to different treatment levers under a plausible misclassification assumption for the outcome, allowing the misclassification probability to depend on not only the true outcome but also the covariates. Furthermore, we propose the multiply-robust and semiparametric efficient estimators for the means, consistent even under partial misspecification of the observed data law, based on the semiparametric theory framework. The simulation studies and real data analysis demonstrate the satisfactory performance of the proposed method.

Suggested Citation

  • Shaojie Wei & Chao Zhang & Zhi Geng & Shanshan Luo, 2024. "Identifiability and Estimation for Potential-Outcome Means with Misclassified Outcomes," Mathematics, MDPI, vol. 12(18), pages 1-19, September.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2801-:d:1475374
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/18/2801/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/18/2801/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alberto Abadie & Jann Spiess, 2022. "Robust Post-Matching Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 983-995, April.
    2. Linbo Wang & Eric Tchetgen Tchetgen, 2018. "Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 531-550, June.
    3. Xinwei Ma & Jingshen Wang, 2020. "Robust Inference Using Inverse Probability Weighting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1851-1860, December.
    4. Zhichao Jiang & Peng Ding, 2020. "Measurement errors in the binary instrumental variable model," Biometrika, Biometrika Trust, vol. 107(1), pages 238-245.
    5. Donald B. Rubin, 2005. "Causal Inference Using Potential Outcomes: Design, Modeling, Decisions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 322-331, March.
    6. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    7. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
    8. Xu Shi & Wang Miao & Jennifer C. Nelson & Eric J. Tchetgen Tchetgen, 2020. "Multiply robust causal inference with double‐negative control adjustment for categorical unmeasured confounding," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(2), pages 521-540, April.
    9. Jake Olivier & Warren L. May & Melanie L. Bell, 2017. "Relative effect sizes for measures of risk," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 6774-6781, July.
    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. Ting Ye & Ashkan Ertefaie & James Flory & Sean Hennessy & Dylan S. Small, 2023. "Instrumented difference‐in‐differences," Biometrics, The International Biometric Society, vol. 79(2), pages 569-581, June.
    2. Ashesh Rambachan & Jonathan Roth, 2020. "Design-Based Uncertainty for Quasi-Experiments," Papers 2008.00602, arXiv.org, revised Oct 2024.
    3. Horvath, Akos & Lang, Peter, 2021. "Do loan subsidies boost the real activity of small firms?," Journal of Banking & Finance, Elsevier, vol. 122(C).
    4. Donald, Stephen G. & Hsu, Yu-Chin, 2014. "Estimation and inference for distribution functions and quantile functions in treatment effect models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 383-397.
    5. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    6. Gregory N, Price & Bussey, Tiffany, 2024. "Can business clinics induce minority entrepreneurship? Treatment effect estimates from Atlanta and New Orleans," Journal of Business Venturing Insights, Elsevier, vol. 21(C).
    7. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    8. Carlos A. Flores & Alfonso Flores-Lagunes, 2007. "Identification and Estimation of Casual Mechanisms and Net Effects of a Treatment," Working Papers 0706, University of Miami, Department of Economics.
    9. Michael Lechner & Ruth Miquel, 2010. "Identification of the effects of dynamic treatments by sequential conditional independence assumptions," Empirical Economics, Springer, vol. 39(1), pages 111-137, August.
    10. Tenglong Li & Kenneth A. Frank & Mingming Chen, 2024. "A Conceptual Framework for Quantifying the Robustness of a Regression-Based Causal Inference in Observational Study," Mathematics, MDPI, vol. 12(3), pages 1-14, January.
    11. Christoph Wunder & Johannes Schwarze, 2014. "Is Posner Right? An Empirical Test of the Posner Argument for Transferring Health Spending from Old Women to Old Men," Journal of Happiness Studies, Springer, vol. 15(6), pages 1239-1257, December.
    12. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    13. Hongming Pu & Bo Zhang, 2021. "Estimating optimal treatment rules with an instrumental variable: A partial identification learning approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 318-345, April.
    14. Gregory N. Price & Chris W. Surprenant, 2022. "The Treatment Effect of Business Education on the Supply of High School Entrepreneurs in Atlanta and New Orleans," The American Economist, Sage Publications, vol. 67(1), pages 85-98, March.
    15. Harsh Parikh & Cynthia Rudin & Alexander Volfovsky, 2018. "MALTS: Matching After Learning to Stretch," Papers 1811.07415, arXiv.org, revised Jun 2023.
    16. Arun Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2012. "Inference for best linear approximations to set identified functions," CeMMAP working papers 43/12, Institute for Fiscal Studies.
    17. Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2016. "Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies," Journal of Educational and Behavioral Statistics, , vol. 41(2), pages 146-179, April.
    18. Ruonan Xu, 2023. "Difference-in-Differences with Interference," Papers 2306.12003, arXiv.org, revised Jan 2025.
    19. Matt Taddy & Matt Gardner & Liyun Chen & David Draper, 2016. "A Nonparametric Bayesian Analysis of Heterogenous Treatment Effects in Digital Experimentation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 661-672, October.
    20. Shu Yang & Yunshu Zhang, 2023. "Multiply robust matching estimators of average and quantile treatment effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 235-265, March.

    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:gam:jmathe:v:12:y:2024:i:18:p:2801-:d:1475374. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.