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Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap

Author

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  • 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
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    Citations

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    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 Aug 2023.
    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.

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