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Sensitivity analysis and power for instrumental variable studies

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  • Xuran Wang
  • Yang Jiang
  • Nancy R. Zhang
  • Dylan S. Small

Abstract

In observational studies to estimate treatment effects, unmeasured confounding is often a concern. The instrumental variable (IV) method can control for unmeasured confounding when there is a valid IV. To be a valid IV, a variable needs to be independent of unmeasured confounders and only affect the outcome through affecting the treatment. When applying the IV method, there is often concern that a putative IV is invalid to some degree. We present an approach to sensitivity analysis for the IV method which examines the sensitivity of inferences to violations of IV validity. Specifically, we consider sensitivity when the magnitude of association between the putative IV and the unmeasured confounders and the direct effect of the IV on the outcome are limited in magnitude by a sensitivity parameter. Our approach is based on extending the Anderson–Rubin test and is valid regardless of the strength of the instrument. A power formula for this sensitivity analysis is presented. We illustrate its usage via examples about Mendelian randomization studies and its implications via a comparison of using rare versus common genetic variants as instruments.

Suggested Citation

  • Xuran Wang & Yang Jiang & Nancy R. Zhang & Dylan S. Small, 2018. "Sensitivity analysis and power for instrumental variable studies," Biometrics, The International Biometric Society, vol. 74(4), pages 1150-1160, December.
    • Handle: RePEc:bla:biomet:v:74:y:2018:i:4:p:1150-1160
    DOI: 10.1111/biom.12873
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    References listed on IDEAS

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    Cited by:

    1. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: Evidence from an instrumental variable analysis of China's One-Child Policy," Papers 2005.09130, arXiv.org, revised Jun 2020.
    2. Weiming Zhang & Debashis Ghosh, 2021. "A General Approach to Sensitivity Analysis for Mendelian Randomization," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(1), pages 34-55, April.
    3. Byeong Yeob Choi, 2021. "Instrumental variable estimation of truncated local average treatment effects," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-12, April.
    4. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: evidence from an instrumental variable analysis of China's one‐child policy," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1615-1635, October.

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