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Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization

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  • Hyunseung Kang
  • Anru Zhang
  • T. Tony Cai
  • Dylan S. Small

Abstract

Instrumental variables have been widely used for estimating the causal effect between exposure and outcome. Conventional estimation methods require complete knowledge about all the instruments’ validity; a valid instrument must not have a direct effect on the outcome and not be related to unmeasured confounders. Often, this is impractical as highlighted by Mendelian randomization studies where genetic markers are used as instruments and complete knowledge about instruments’ validity is equivalent to complete knowledge about the involved genes’ functions. In this article, we propose a method for estimation of causal effects when this complete knowledge is absent. It is shown that causal effects are identified and can be estimated as long as less than 50% of instruments are invalid, without knowing which of the instruments are invalid. We also introduce conditions for identification when the 50% threshold is violated. A fast penalized ℓ 1 estimation method, called sisVIVE, is introduced for estimating the causal effect without knowing which instruments are valid, with theoretical guarantees on its performance. The proposed method is demonstrated on simulated data and a real Mendelian randomization study concerning the effect of body mass index(BMI) on health-related quality of life (HRQL) index. An R package sisVIVE is available on CRAN. Supplementary materials for this article are available online.

Suggested Citation

  • Hyunseung Kang & Anru Zhang & T. Tony Cai & Dylan S. Small, 2016. "Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 132-144, March.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:132-144
    DOI: 10.1080/01621459.2014.994705
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    References listed on IDEAS

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