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

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.