selection bias in estimating an association that is null in the intended study populationSimulation settingsResults—association between allele score and outcomeAssociation between missingness and both phenotype and outcome (OR)Association between allele score and phenotype (r)Mean regression coefficient (SD)Mean z-score (SD)Number of 95% CIs containing zeroOR = 1.80.05−0.001 (0.001)−1.04 (1.00)83(0.25% variance)0.10−0.003 (0.001)−2.06 (0.98)45(1.00% variance)0.15−0.004 (0.001)−3.07 (0.98)9(2.25% variance)0.20−0.006 (0.001)−4.10 (0.98)0(4.00% variance)0.30−0.008 (0.001)−6.18 (1.06)0(9.00% variance)OR = 1.50.05−0.001 (0.001)−0.42 (0.95)94(0.25% variance)0.10−0.001 (0.001)−0.80 (0.96)89(1.00% variance)0.15−0.001 (0.001)−1.22 (0.96)77(2.25% variance)0.20−0.002 (0.001)−1.64 (0.97)61(4.00% variance)0.30−0.003 (0.001)−2.44 (0.94)35(9.00% variance)OR = 1.20.05−0.0002 (0.001)−0.16 (0.92)97(0.25% variance)0.10−0.0003 (0.001)−0.25 (0.94)97(1.00% variance)0.15−0.0005 (0.001)−0.38 (0.95)93(2.25% variance)0.20−0.0006 (0.001)−0.47 (0.95)91(4.00% variance)0.30−0.0009 (0.001)−0.66 (0.96)89(9.00% variance)Each scenario was simulated 100 times.Table 2Results of simulation study showing the selection bias in estimating an association that is not null in the intended study population (regression coefficient for outcome on phenotype is 0.1)Simulation settingsResults—association between allele score and outcomeAssociation between missingness and both phenotype and outcome (OR)Association between allele score and phenotype (r)Mean regression coefficient (SD)True regression coefficientNumber of 95% CIs containing true valueOR = 1.80.050.003 (0.001)0.00578(0.25% variance)0.100.006 (0.001)0.0123(1.00% variance)0.150.010 (0.001)0.0152(2.25% variance)0.200.013 (0.001)0.020(4.00% variance)0.300.020 (0.001)0.030(9.00% variance)OR = 1.50.050.004 (0.001)0.00594(0.25% variance)0.100.009 (0.001)0.0186(1.00% variance)0.150.013 (0.001)0.01569(2.25% variance)0.200.017 (0.001)0.0253(4.00% variance)0.300.026 (0.001)0.0319(9.00% variance)OR = 1.20.050.005 (0.001)0.00598(0.25% variance)0.100.01 (0.001)0.0196(1.00% variance)0.150.014 (0.001)0.01594(2.25% variance)0.200.019 (0.001)0.0292(4.00% variance)0.300.029 (0.001)0.0395(9.00% variance)Each scenario was simulated 100
