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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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    1. Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," The Journal of Business, University of Chicago Press, vol. 63(1), pages 125-140, January.
    2. Paul R. Rosenbaum, 2004. "Design sensitivity in observational studies," Biometrika, Biometrika Trust, vol. 91(1), pages 153-164, March.
    3. Jesse Y. Hsu & Dylan S. Small, 2013. "Calibrating Sensitivity Analyses to Observed Covariates in Observational Studies," Biometrics, The International Biometric Society, vol. 69(4), pages 803-811, December.
    4. Small, Dylan S & Rosenbaum, Paul R, 2008. "War and Wages," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 924-933.
    5. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    6. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935, Elsevier.
    7. Guido W. Imbens & Paul R. Rosenbaum, 2005. "Robust, accurate confidence intervals with a weak instrument: quarter of birth and education," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 109-126, January.
    8. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 66(6), pages 1389-1404, November.
    9. Timothy G. Conley & Christian B. Hansen & Peter E. Rossi, 2012. "Plausibly Exogenous," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 260-272, February.
    10. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    11. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
    12. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    13. Small, Dylan S., 2007. "Sensitivity Analysis for Instrumental Variables Regression With Overidentifying Restrictions," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1049-1058, September.
    14. Brookhart M. Alan & Schneeweiss Sebastian, 2007. "Preference-Based Instrumental Variable Methods for the Estimation of Treatment Effects: Assessing Validity and Interpreting Results," The International Journal of Biostatistics, De Gruyter, vol. 3(1), pages 1-25, December.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

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