IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v12y2016i1p333-349n14.html
   My bibliography  Save this article

Second-Order Inference for the Mean of a Variable Missing at Random

Author

Listed:
  • Díaz Iván

    (Google Inc. New York, NY)

  • Carone Marco

    (Department of Biostatistics, University of Washington, Seattle, WA, USA)

  • van der Laan Mark J.

    (Division of Biostatistics, University of California, Berkeley, CA, USA)

Abstract

We present a second-order estimator of the mean of a variable subject to missingness, under the missing at random assumption. The estimator improves upon existing methods by using an approximate second-order expansion of the parameter functional, in addition to the first-order expansion employed by standard doubly robust methods. This results in weaker assumptions about the convergence rates necessary to establish consistency, local efficiency, and asymptotic linearity. The general estimation strategy is developed under the targeted minimum loss-based estimation (TMLE) framework. We present a simulation comparing the sensitivity of the first and second-order estimators to the convergence rate of the initial estimators of the outcome regression and missingness score. In our simulation, the second-order TMLE always had a coverage probability equal or closer to the nominal value 0.95, compared to its first-order counterpart. In the best-case scenario, the proposed second-order TMLE had a coverage probability of 0.86 when the first-order TMLE had a coverage probability of zero. We also present a novel first-order estimator inspired by a second-order expansion of the parameter functional. This estimator only requires one-dimensional smoothing, whereas implementation of the second-order TMLE generally requires kernel smoothing on the covariate space. The first-order estimator proposed is expected to have improved finite sample performance compared to existing first-order estimators. In the best-case scenario of our simulation study, the novel first-order TMLE improved the coverage probability from 0 to 0.90. We provide an illustration of our methods using a publicly available dataset to determine the effect of an anticoagulant on health outcomes of patients undergoing percutaneous coronary intervention. We provide R code implementing the proposed estimator.

Suggested Citation

  • Díaz Iván & Carone Marco & van der Laan Mark J., 2016. "Second-Order Inference for the Mean of a Variable Missing at Random," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 333-349, May.
    • Handle: RePEc:bpj:ijbist:v:12:y:2016:i:1:p:333-349:n:14
    DOI: 10.1515/ijb-2015-0031
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/ijb-2015-0031
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/ijb-2015-0031?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Porter Kristin E. & Gruber Susan & van der Laan Mark J. & Sekhon Jasjeet S., 2011. "The Relative Performance of Targeted Maximum Likelihood Estimators," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, August.
    2. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    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. Susan Gruber & Mark J. van der Laan, 2013. "An Application of Targeted Maximum Likelihood Estimation to the Meta-Analysis of Safety Data," Biometrics, The International Biometric Society, vol. 69(1), pages 254-262, March.
    2. Lars van der Laan & Wenbo Zhang & Peter B. Gilbert, 2023. "Nonparametric estimation of the causal effect of a stochastic threshold‐based intervention," Biometrics, The International Biometric Society, vol. 79(2), pages 1014-1028, June.
    3. Radice Rosalba & Ramsahai Roland & Grieve Richard & Kreif Noemi & Sadique Zia & Sekhon Jasjeet S., 2012. "Evaluating treatment effectiveness in patient subgroups: a comparison of propensity score methods with an automated matching approach," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-45, August.
    4. Díaz Iván & Rosenblum Michael, 2015. "Targeted Maximum Likelihood Estimation using Exponential Families," The International Journal of Biostatistics, De Gruyter, vol. 11(2), pages 233-251, November.
    5. Stitelman Ori M. & De Gruttola Victor & van der Laan Mark J., 2012. "A General Implementation of TMLE for Longitudinal Data Applied to Causal Inference in Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-39, September.
    6. Stitelman Ori M & Wester C. William & De Gruttola Victor & van der Laan Mark J., 2011. "Targeted Maximum Likelihood Estimation of Effect Modification Parameters in Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, March.
    7. van der Laan Mark J. & Gruber Susan, 2012. "Targeted Minimum Loss Based Estimation of Causal Effects of Multiple Time Point Interventions," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-41, May.
    8. Noémi Kreif & Richard Grieve & Iván Díaz & David Harrison, 2015. "Evaluation of the Effect of a Continuous Treatment: A Machine Learning Approach with an Application to Treatment for Traumatic Brain Injury," Health Economics, John Wiley & Sons, Ltd., vol. 24(9), pages 1213-1228, September.
    9. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    10. Ruoxuan Xiong & Allison Koenecke & Michael Powell & Zhu Shen & Joshua T. Vogelstein & Susan Athey, 2021. "Federated Causal Inference in Heterogeneous Observational Data," Papers 2107.11732, arXiv.org, revised Apr 2023.
    11. Jelena Bradic & Weijie Ji & Yuqian Zhang, 2021. "High-dimensional Inference for Dynamic Treatment Effects," Papers 2110.04924, arXiv.org, revised May 2023.
    12. Görg Holger & Marchal Léa, 2019. "Die Effekte deutscher Direktinvestitionen im Empfängerland vor dem Hintergrund des Leistungsbilanzüberschusses: Empirische Evidenz mit Mikrodaten für Frankreich," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 20(1), pages 53-69, June.
    13. Tran Linh & Petersen Maya & Schwab Joshua & van der Laan Mark J., 2023. "Robust variance estimation and inference for causal effect estimation," Journal of Causal Inference, De Gruyter, vol. 11(1), pages 1-27, January.
    14. Léa Marchal & Clément Nedoncelle, 2019. "Immigrants, occupations and firm export performance," Review of International Economics, Wiley Blackwell, vol. 27(5), pages 1480-1509, November.
    15. Hisaki Kono & Yasuyuki Sawada & Abu S. Shonchoy, 2016. "DVD-based Distance-learning Program for University Entrance Exams: Experimental Evidence from Rural Bangladesh," CIRJE F-Series CIRJE-F-1027, CIRJE, Faculty of Economics, University of Tokyo.
    16. Masahiro Kato & Masaaki Imaizumi & Takuya Ishihara & Toru Kitagawa, 2023. "Asymptotically Optimal Fixed-Budget Best Arm Identification with Variance-Dependent Bounds," Papers 2302.02988, arXiv.org, revised Jul 2023.
    17. Takahiro Hoshino & Yuya Shimizu, 2019. "Doubly Robust-type Estimation of Population Moments and Parameters in Biased Sampling," Keio-IES Discussion Paper Series 2019-006, Institute for Economics Studies, Keio University.
    18. Uysal, S. Derya, 2013. "Doubly Robust Estimation of Causal Effects with Multivalued Treatments," Economics Series 297, Institute for Advanced Studies.
    19. Paul Frédéric Blanche & Anders Holt & Thomas Scheike, 2023. "On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 441-482, April.
    20. Ignaciuk, Ada & Malevolti, Giulia & Scognamillo, Antonio & Sitko, Nicholas J., 2022. "Can food aid relax farmers’ constraints to adopting climate-adaptive agricultural practices? Evidence from Ethiopia, Malawi and the United Republic of Tanzania," ESA Working Papers 324073, Food and Agriculture Organization of the United Nations, Agricultural Development Economics Division (ESA).

    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:bpj:ijbist:v:12:y:2016:i:1:p:333-349:n:14. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.