Genomics Inform.  2022 Mar;20(1):e9. 10.5808/gi.21060.

Exploration of errors in variance caused by using the first-order approximation in Mendelian randomization

  • 1Interdisciplinary Program of Bioengineering, Seoul National University College of Engineering, Seoul, Korea
  • 2Department of Biomedical Sciences, Seoul National University College of Medicine, Seoul, Korea
  • 3Department of Bioinformatics and Computational Biology, The University of Texas MD Anderson Cancer Center, Houston, TX, USA
  • 4UTHealth Graduate School of Biomedical Sciences, The University of Texas MD Anderson Cancer Center, Houston, TX, USA


Mendelian randomization (MR) uses genetic variation as a natural experiment to investigate the causal effects of modifiable risk factors (exposures) on outcomes. Two-sample Mendelian randomization (2SMR) is widely used to measure causal effects between exposures and outcomes via genome-wide association studies. 2SMR can increase statistical power by utilizing summary statistics from large consortia such as the UK Biobank. However, the first-order term approximation of standard error is commonly used when applying 2SMR. This approximation can underestimate the variance of causal effects in MR, which can lead to an increased false-positive rate. An alternative is to use the second-order approximation of the standard error, which can considerably correct for the deviation of the first-order approximation. In this study, we simulated MR to show the degree to which the first-order approximation underestimates the variance. We show that depending on the specific situation, the first-order approximation can underestimate the variance almost by half when compared to the true variance, whereas the second-order approximation is robust and accurate.


computer simulation; delta method; Mendelian randomization analysis
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