Table 5. Simulation results for estimating K_YX.

The means, standard deviations (sd) and SEs (se) from each method are shown for each set-up based on 500 simulated datasets. μ_α represents the mean of the pleiotropic/direct effects (with standard deviation σ_α = 0.1).

No pleiotropy
μα	KYX	CD-Ratio			CD-Egger			CD-GLS
		Mean($\widehat{K}$)	sd($\widehat{K}$)	Mean $\left(se\right(\widehat{K}\left)\right)$	Mean($\widehat{K}$)	sd($\widehat{K}$)	Mean $\left(se\right(\widehat{K}\left)\right)$	Mean($\widehat{K}$)	sd($\widehat{K}$)	Mean $\left(se\right(\widehat{K}\left)\right)$
0	0	0.0001	0.0034	0.0035	0.0001	0.0034	0.0036	0.0001	0.0034	0.0036
0	0.2257	0.2256	0.0033	0.0036	0.2256	0.0033	0.0036	0.2256	0.0033	0.0036
0	-0.2344	-0.2341	0.0032	0.0036	-0.2341	0.0032	0.0036	-0.2341	0.0032	0.0036
Balanced pleiotropy
μα	KYX	CD-Ratio			CD-Egger			CD-GLS
		Mean($\widehat{K}$)	sd($\widehat{K}$)	Mean $\left(se\right(\widehat{K}\left)\right)$	Mean($\widehat{K}$)	sd($\widehat{K}$)	Mean $\left(se\right(\widehat{K}\left)\right)$	Mean($\widehat{K}$)	sd($\widehat{K}$)	Mean $\left(se\right(\widehat{K}\left)\right)$
0	0	0.0013	0.0563	0.0037	-0.0007	0.0431	0.0410	-0.0005	0.0436	0.0419
0	0.2257	0.2181	0.0531	0.0037	0.2201	0.0397	0.0393	0.2203	0.0402	0.0401
0	-0.2344	-0.2233	0.0545	0.0037	-0.2296	0.0409	0.0408	-0.2295	0.0414	0.0416
Directional pleiotropy
μα	KYX	CD-Ratio			CD-Egger			CD-GLS
		Mean($\widehat{K}$)	sd($\widehat{K}$)	Mean $\left(se\right(\widehat{K}\left)\right)$	Mean($\widehat{K}$)	sd($\widehat{K}$)	Mean $\left(se\right(\widehat{K}\left)\right)$	Mean($\widehat{K}$)	sd($\widehat{K}$)	Mean $\left(se\right(\widehat{K}\left)\right)$
0.2	0	-0.0112	0.0538	0.0039	-0.0005	0.0386	0.0368	-0.0004	0.0392	0.0375
0.4	0	-0.0183	0.0448	0.0041	-0.0004	0.0306	0.0291	-0.0003	0.0311	0.0297
0.6	0	-0.0317	0.0357	0.0042	-0.0003	0.0240	0.0228	-0.0002	0.0244	0.0233
1	0	-0.0506	0.0241	0.0043	-0.0002	0.0161	0.0153	-0.0002	0.0164	0.0156
0.2	0.2027	0.1898	0.0514	0.0039	0.1987	0.0369	0.0355	0.1989	0.0375	0.0362
0.4	0.1614	0.1438	0.0448	0.0041	0.1593	0.0301	0.0285	0.1595	0.0307	0.0290
0.6	0.1272	0.0944	0.0362	0.0042	0.1261	0.024	0.0225	0.1263	0.0244	0.0230
1	0.0856	0.0313	0.0244	0.0043	0.0851	0.0162	0.0152	0.0852	0.0165	0.0155
0.2	-0.2093	-0.2172	0.0517	0.0039	-0.2061	0.037	0.0366	-0.206	0.0373	0.0373
0.4	-0.1649	-0.1796	0.0435	0.0041	-0.1636	0.0298	0.0290	-0.1635	0.0300	0.0296
0.6	-0.1290	-0.1552	0.0351	0.0042	-0.1285	0.0236	0.0228	-0.1285	0.0238	0.0233
1	-0.0862	-0.1301	0.0238	0.0043	-0.0862	0.0159	0.0153	-0.0862	0.0161	0.0156