Fig. 2
Simulation results when genetic correlation due to causal and pleiotropic effects are in the same direction. Mean and standard deviation of causal estimates are reported over 100 simulations. The true causal effect θ is 0.2. Estimates of association coefficient for SNPs across two traits are simulated assuming an underlying four-component model for effect-size distribution (Scenario A, see Methods), where SNPs could have direct effects on neither traits, only on X, only on Y, or on both with the effects being correlated. The proportion of valid instruments, i.e., the SNPs which have only direct effects on X, as a proportion of the total number of SNPs which are associated with X, are fixed at 50% or 25%. nx = N: sample size of the study associated with X; ny: sample size of the study associated with Y. Standard error bars higher than 60 are truncated and marked with *true-value. The average number of IVs, defined as the SNPs which reach genome-wide significance (z-test p < 5 × 10−8) in the study associated with X, is 14, 105, 399, 1135, and 1780 for N = 50 k, 100 k, 200 k, 500 k, and 1000 k, respectively. Source data are provided as a Source Data file
