Bayesian mendelian randomization with study heterogeneity and data partitioning for large studies

Table 2 Causal effects estimated from 200 simulated datasets for each configuration from two MR methods (Bayesian, IVW) when β₁=β₂=0, using four metrics: mean, standard deviation (sd), coverage and power. The six configurations were generated from three missing rates of the exposures (80%, 50%, 20%) and two levels of IV strength (α=0.3 and 0.1). \(\hat {\beta }_{1}\): estimated causal effect of X₁ on \(Y_{1}, \hat {\beta }_{2}\): estimated causal effect of X₂ on Y₂

Missing rate	α	\(\widehat {\beta _{1}}\)						\(\widehat {\beta _{2}}\)
		Bayesian			IVW			Bayesian			IVW
		mean	sd	coverage	mean	sd	coverage	mean	sd	coverage	mean	sd	coverage
80%	0.3	-0.001	0.005	0.960	0.007	0.061	0.955	-0.001	0.005	0.955	-0.005	0.062	0.960
	0.1	0.004	0.016	0.960	-0.010	0.112	0.965	0.004	0.015	0.960	-0.001	0.130	0.960
50%	0.3	0.000	0.005	0.975	-0.014	0.087	0.935	0.000	0.005	0.955	-0.002	0.090	0.955
	0.1	0.004	0.013	0.970	0.005	0.188	0.960	0.004	0.013	0.955	-0.011	0.202	0.950
20%	0.3	0.000	0.004	0.950	0.010	0.148	0.930	0.000	0.004	0.965	-0.003	0.152	0.935
	0.1	0.003	0.012	0.965	0.012	0.394	0.920	0.003	0.012	0.965	0.020	0.361	0.945

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