IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v81y2019i4p735-761.html
   My bibliography  Save this article

Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap

Author

Listed:
  • Qingyuan Zhao
  • Dylan S. Small
  • Bhaswar B. Bhattacharya

Abstract

To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the ‘missingness at random’ and ‘no unmeasured confounder’ assumptions. However, these assumptions are unverifiable by using empirical data and pose serious threats to the validity of the qualitative conclusions of statistical inference. A sensitivity analysis asks how the conclusions may change if the unverifiable assumptions are violated to a certain degree. We consider a marginal sensitivity model which is a natural extension of Rosenbaum's sensitivity model that is widely used for matched observational studies. We aim to construct confidence intervals based on inverse probability weighting estimators, such that asymptotically the intervals have at least nominal coverage of the estimand whenever the data‐generating distribution is in the collection of marginal sensitivity models. We use a percentile bootstrap and a generalized minimax–maximin inequality to transform this intractable problem into a linear fractional programming problem, which can be solved very efficiently. We illustrate our method by using a real data set to estimate the causal effect of fish consumption on blood mercury level.

Suggested Citation

  • Qingyuan Zhao & Dylan S. Small & Bhaswar B. Bhattacharya, 2019. "Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(4), pages 735-761, September.
  • Handle: RePEc:bla:jorssb:v:81:y:2019:i:4:p:735-761
    DOI: 10.1111/rssb.12327
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssb.12327
    Download Restriction: no

    File URL: https://libkey.io/10.1111/rssb.12327?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Evan T.R. Rosenman & Guillaume Basse & Art B. Owen & Mike Baiocchi, 2023. "Combining observational and experimental datasets using shrinkage estimators," Biometrics, The International Biometric Society, vol. 79(4), pages 2961-2973, December.
    2. Bo Zhang & Eric J. Tchetgen Tchetgen, 2022. "A semi‐parametric approach to model‐based sensitivity analysis in observational studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 668-691, December.
    3. Jacob Dorn & Kevin Guo & Nathan Kallus, 2021. "Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding," Papers 2112.11449, arXiv.org, revised Jul 2022.
    4. Ashesh Rambachan & Amanda Coston & Edward Kennedy, 2022. "Robust Design and Evaluation of Predictive Algorithms under Unobserved Confounding," Papers 2212.09844, arXiv.org, revised May 2024.
    5. Nathan Kallus & Angela Zhou, 2021. "Minimax-Optimal Policy Learning Under Unobserved Confounding," Management Science, INFORMS, vol. 67(5), pages 2870-2890, May.
    6. Zelin Zhang & Kejia Yang & Jonathan Z. Zhang & Robert W. Palmatier, 2023. "Uncovering Synergy and Dysergy in Consumer Reviews: A Machine Learning Approach," Management Science, INFORMS, vol. 69(4), pages 2339-2360, April.
    7. Colin B. Fogarty, 2023. "Testing weak nulls in matched observational studies," Biometrics, The International Biometric Society, vol. 79(3), pages 2196-2207, September.
    8. Matthew J Tudball & Rachael A Hughes & Kate Tilling & Jack Bowden & Qingyuan Zhao, 2023. "Sample-constrained partial identification with application to selection bias," Biometrika, Biometrika Trust, vol. 110(2), pages 485-498.
    9. Xinkun Nie & Guido Imbens & Stefan Wager, 2021. "Covariate Balancing Sensitivity Analysis for Extrapolating Randomized Trials across Locations," Papers 2112.04723, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jorssb:v:81:y:2019:i:4:p:735-761. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.