In a second simulation we investigate the performance of the IVW method and MR-Egger regression under the causal null β = 0 in scenario (c), with a fixed sample size of N = 2000 but varying the number of genetic variants. The results are shown in Table 2. The bias of the IVW estimator reduces by just under 20% as the number of genetic variants J increases from 3 (very strong) instruments to 150 (weaker) instruments. However, this coincides with a reduction in the estimate’s standard error, so that its type I error rate rises sharply from 12% to 100%. MR-Egger regression returns approximately unbiased estimates for β for all values of J. As J increases the power of the MR-Egger test to detect directional pleiotropy increases from around 5% to 95%. The type I error rate of MR-Egger regression to detect a causal effect is well controlled for J ≤ 50 variants, but for over 100 variants some type I error inflation is apparent. In summary, MR-Egger regression works well with large numbers of genetic variants (in the sense
