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Mendelian randomization mixed‐scale treatment effect robust identification and estimation for causal inference

Author

Listed:
  • Zhonghua Liu
  • Ting Ye
  • Baoluo Sun
  • Mary Schooling
  • Eric Tchetgen Tchetgen

Abstract

Standard Mendelian randomization (MR) analysis can produce biased results if the genetic variant defining an instrumental variable (IV) is confounded and/or has a horizontal pleiotropic effect on the outcome of interest not mediated by the treatment variable. We provide novel identification conditions for the causal effect of a treatment in the presence of unmeasured confounding by leveraging a possibly invalid IV for which both the IV independence and exclusion restriction assumptions may be violated. The proposed Mendelian randomization mixed‐scale treatment effect robust identification (MR MiSTERI) approach relies on (i) an assumption that the treatment effect does not vary with the possibly invalid IV on the additive scale; (ii) that the confounding bias does not vary with the possibly invalid IV on the odds ratio scale; and (iii) that the residual variance for the outcome is heteroskedastic with respect to the possibly invalid IV. Although assumptions (i) and (ii) have, respectively, appeared in the IV literature, assumption (iii) has not; we formally establish that their conjunction can identify a causal effect even with an invalid IV. MR MiSTERI is shown to be particularly advantageous in the presence of pervasive heterogeneity of pleiotropic effects on the additive scale. We propose a simple and consistent three‐stage estimator that can be used as a preliminary estimator to a carefully constructed efficient one‐step‐update estimator. In order to incorporate multiple, possibly correlated, and weak invalid IVs, a common challenge in MR studies, we develop a MAny Weak Invalid Instruments (MR MaWII MiSTERI) approach for strengthened identification and improved estimation accuracy. Both simulation studies and UK Biobank data analysis results demonstrate the robustness of the proposed methods.

Suggested Citation

  • Zhonghua Liu & Ting Ye & Baoluo Sun & Mary Schooling & Eric Tchetgen Tchetgen, 2023. "Mendelian randomization mixed‐scale treatment effect robust identification and estimation for causal inference," Biometrics, The International Biometric Society, vol. 79(3), pages 2208-2219, September.
  • Handle: RePEc:bla:biomet:v:79:y:2023:i:3:p:2208-2219
    DOI: 10.1111/biom.13735
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    References listed on IDEAS

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    1. Arthur Lewbel, 2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80.
    2. Sonja A. Swanson & Miguel A. Hernán & Matthew Miller & James M. Robins & Thomas S. Richardson, 2018. "Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 933-947, April.
    3. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    4. Hua Yun Chen, 2007. "A Semiparametric Odds Ratio Model for Measuring Association," Biometrics, The International Biometric Society, vol. 63(2), pages 413-421, June.
    5. Whitney K. Newey & Frank Windmeijer, 2009. "Generalized Method of Moments With Many Weak Moment Conditions," Econometrica, Econometric Society, vol. 77(3), pages 687-719, May.
    6. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    7. Guillaume Paré & Nancy R Cook & Paul M Ridker & Daniel I Chasman, 2010. "On the Use of Variance per Genotype as a Tool to Identify Quantitative Trait Interaction Effects: A Report from the Women's Genome Health Study," PLOS Genetics, Public Library of Science, vol. 6(6), pages 1-10, June.
    8. 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.
    9. Adam E. Locke & Bratati Kahali & Sonja I. Berndt & Anne E. Justice & Tune H. Pers & Felix R. Day & Corey Powell & Sailaja Vedantam & Martin L. Buchkovich & Jian Yang & Damien C. Croteau-Chonka & Tonu , 2015. "Genetic studies of body mass index yield new insights for obesity biology," Nature, Nature, vol. 518(7538), pages 197-206, February.
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