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Unbiased estimation and asymptotically valid inference in multivariable Mendelian randomization with many weak instrumental variables

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  • Yihe Yang
  • Noah Lorincz-Comi
  • Xiaofeng Zhu

Abstract

Mendelian randomization (MR) is an instrumental variable (IV) approach to infer causal relationships between exposures and outcomes with genome-wide association studies (GWAS) summary data. However, the multivariable inverse-variance weighting (IVW) approach, which serves as the foundation for most MR approaches, cannot yield unbiased causal effect estimates in the presence of many weak IVs. To address this problem, we proposed the MR using Bias-corrected Estimating Equation (MRBEE) that can infer unbiased causal relationships with many weak IVs and account for horizontal pleiotropy simultaneously. While the practical significance of MRBEE was demonstrated in our parallel work (Lorincz-Comi (2023)), this paper established the statistical theories of multivariable IVW and MRBEE with many weak IVs. First, we showed that the bias of the multivariable IVW estimate is caused by the error-in-variable bias, whose scale and direction are inflated and influenced by weak instrument bias and sample overlaps of exposures and outcome GWAS cohorts, respectively. Second, we investigated the asymptotic properties of multivariable IVW and MRBEE, showing that MRBEE outperforms multivariable IVW regarding unbiasedness of causal effect estimation and asymptotic validity of causal inference. Finally, we applied MRBEE to examine myopia and revealed that education and outdoor activity are causal to myopia whereas indoor activity is not.

Suggested Citation

  • Yihe Yang & Noah Lorincz-Comi & Xiaofeng Zhu, 2023. "Unbiased estimation and asymptotically valid inference in multivariable Mendelian randomization with many weak instrumental variables," Papers 2301.05130, arXiv.org, revised Feb 2024.
  • Handle: RePEc:arx:papers:2301.05130
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    References listed on IDEAS

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    1. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    2. Qing Cheng & Xiao Zhang & Lin S. Chen & Jin Liu, 2022. "Mendelian randomization accounting for complex correlated horizontal pleiotropy while elucidating shared genetic etiology," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    3. 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.
    4. Guanghao Qi & Nilanjan Chatterjee, 2019. "Mendelian randomization analysis using mixture models for robust and efficient estimation of causal effects," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    5. Stephen Burgess & Christopher N Foley & Elias Allara & James R Staley & Joanna M. M. Howson, 2020. "A robust and efficient method for Mendelian randomization with hundreds of genetic variants," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
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