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

By Hyunseung Kang, Anru R. Zhang, Tommaso Cai, Dylan S. Small. 2014

328 citations recorded by the source corpus.

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 ℓ1 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.

Subfields: Genetics, Rheumatology, Statistics and Probability

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Citations in the corpus

Confidence intervals for causal effects with invalid instruments by using two‐stage hard thresholding with voting (2016, methodology): “guarantees under a general condition established in theorem 1 of Kang et al. (2016b), including”
Interpreting findings from Mendelian randomization using the MR-Egger method (2017, background): “bYj 1⁄4 aj þ hbXj ð1Þ where aj is the effect of the genetic variant on the outcome that is not mediated via the risk factor of interest, and h is the causal effect of the risk factor on the outcome [15]; see Fig.”
A Survey of Learning Causality with Data (2018, neutral): “In the second stage, we see how the changes in 𝑡 ,𝑗 caused by 𝑖 ,𝑗 would influence 𝑦 .”
Consistent Estimation in Mendelian Randomization with Some Invalid Instruments Using a Weighted Median Estimator (2016, methodology): “Figure 2 (left) shows a scatter plot of 10 geneexposure (γ̂ j ) and gene-outcome (̂j ) association estimates for an Mendelian randomization study with a finite sample size (Kang et al., 2015).”
Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression (2015, background): “However, in contrast with the method proposed in this paper, which allows all the genetic variants to be invalid IVs, Kang et al. require at least half of the genetic variants to be valid IVs.”
The confidence interval method for selecting valid instrumental variables (2019, methodology): “Di ] −E [ Z0,i.Di ]� E [ Z0,i.Z � 0,i. ]−1 E [ Z0,i.Di ])−1 , (6)Di=Z�i. + di, This is the same assumption as in Kang et al. (2016) and Windmeijer et al. (2019).”
Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score (2018, background): “In fact, the unique problem structure has sparked many recent methodological advancements [8, 9, 24, 32, 34, 50, 51].”
An examination of multivariable Mendelian randomization in the single-sample and two-sample summary data settings (2018, methodology): “However, alternative methods of estimation can be used to estimate the causal effects as long as at least 50% of the SNPs do not have a pleiotropic effect on the outcome.(36,37)”
Assessing the suitability of summary data for two-sample Mendelian randomization analyses using MR-Egger regression: the role of the I2 statistic (2016, methodology): “Model selection techniques have recently been proposed for MR analysis with the purpose of detecting and adjusting for invalid instruments, using methods that assume at least half of the genetic variants are valid instruments.(21,26,27) MR-Egger regression can work even if all variants are invalid (”
Evaluating the potential role of pleiotropy in Mendelian randomization studies (2018, positive): “While IVW and MR-Egger use a mean-based approach to obtain an overall estimate, one way to avoid the contribution of some invalid instruments is to instead base the overall estimate on the median of the instruments (63,64).”
A review of instrumental variable estimators for Mendelian randomization (2015, background): “Alternatively, a consistent causal estimate can be obtained by allowing the ‘instruments’ to have direct effects on the outcome, but limiting the total magnitude of these direct effects, for example using L1-penalization.(138) Confidence intervals under the assumption that over 50% of the ‘instrumen”