Table 3. Simulation results with a relevant liability period excluded.

			MR	MVMR
Correlated genetic effects
β 1	Liability effect		0.363	0.191
	Effect estimate		0.326	0.186
	Est. Std. Error		0.031	0.020
	Simulation Std. Error		0.015	0.013
	Absolute bias		0.037	0.011
	Coverage		95%	100%
	F-statistic		88.50
	Conditional F-statistic			54.82
	No. SNPs		59	93
β 2	Liability effect		0.428	0.353
	Effect estimate		0.418	0.351
	Est. Std. Error		0.024	0.020
	Simulation Std. Error		0.012	0.013
	Absolute bias		0.013	0.010
	Coverage		100%	100%
	F-statistic		102.40
	Conditional F-statistic			63.66
	No. SNPs		60	93
Independent genetic effects
β 1	Liability effect		0.378	0.220
	Effect Estimate		0.321	0.211
	Est. Std. Error		0.037	0.024
	Simulation Std. Error		0.015	0.014
	Absolute bias		0.057	0.013
	Coverage		80%	100%
	F-statistic		80.20
	Conditional F-statistic			48.00
	No. SNPs		53	92
β 2	Liability effect		0.395	0.328
	Effect estimate		0.386	0.322
	Est. Std. Error		0.027	0.022
	Simulation Std. Error		0.013	0.013
	Absolute bias		0.013	0.011
	Coverage		100%	100%
	F-statistic		98.63
	Conditional F-statistic			66.32
	No. SNPs		62	92

N = 150,000 reps = 2000, β₁ = 0.2, β₂ = 0.3. Total effect of the exposures; X₁ on Y = 0.232, X₂ on Y = 0.320. Effect of the liability for each exposure are given in the table. Absolute bias is the mean value of the absolute bias of the effect estimate across the simulations. For each of Effect estimate, Est. Std Error, F-statistic and Conditional F-statistic mean values across each iteration of the simulation are reported. Simulation Std. Error is the estimated standard error in the effect estimate across the repetitions in the simulation. Coverage gives the proportion of times the true effect estimate falls within the 95%CI, No. SNPs is the mean number of SNPS selected for estimation.