Fig. 4: Simulation results of the type I error rate for spurious exposures and statistical power for causal exposures when there is correlated and uncorrelated pleiotropy (MVMR).

The number of IVs is 100, and the proportion of invalid IVs is 30%. The number of populations is \(E=3\). Among total of eight exposures, two (\({X}_{1}\) and \({X}_{2}\)) are causal exposures (with a causal effect of 0.2), and the other six (\({X}_{3},{\mathrm{}}...,{X}_{8}\)) are spurious exposures (with a causal effect of 0). This figure displays the type I error rates for \({X}_{1}\) and \({X}_{2}\), the statistical power for \({X}_{3},{\mathrm{}}...,{X}_{8}\).