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A General Approach to Sensitivity Analysis for Mendelian Randomization

Author

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  • Weiming Zhang

    (Colorado School of Public Health)

  • Debashis Ghosh

    (Colorado School of Public Health)

Abstract

Mendelian Randomization (MR) represents a class of instrumental variable methods using genetic variants. It has become popular in epidemiological studies to account for the unmeasured confounders when estimating the effect of exposure on outcome. The success of Mendelian Randomization depends on three critical assumptions, which are difficult to verify. Therefore, sensitivity analysis methods are needed for evaluating results and making plausible conclusions. We propose a general and easy to apply approach to conduct sensitivity analysis for Mendelian Randomization studies. Bound et al. (J Am Stat Assoc 90:443–450. 10.2307/2291055, 1995) derived a formula for the asymptotic bias of the instrumental variable estimator. Based on their work, we derive a new sensitivity analysis formula. The parameters in the formula include sensitivity parameters such as the correlation between instruments and unmeasured confounder, the direct effect of instruments on outcome and the strength of instruments. In our simulation studies, we examined our approach in various scenarios using either individual SNPs or unweighted allele score as instruments. By using a previously published dataset from researchers involving a bone mineral density study, we demonstrate that our proposed method is a useful tool for MR studies, and that investigators can combine their domain knowledge with our method to obtain bias-corrected results and make informed conclusions on the scientific plausibility of their findings.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stabio:v:13:y:2021:i:1:d:10.1007_s12561-020-09280-5
    DOI: 10.1007/s12561-020-09280-5
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    References listed on IDEAS

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    1. Chao, John & Swanson, Norman R., 2007. "Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction," Journal of Econometrics, Elsevier, vol. 137(2), pages 515-555, April.
    2. 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.
    3. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    4. 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.
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