The results of this simulation study are shown in Table 1 (no causal effect of P on O) and Table 2 (causal effect of P on O). Where there is no causal effect of P on O, the effects of selection bias are strongest for stronger independent selection effects, and also where the allele score is more strongly associated with the phenotype (Table 1). However, even for moderate associations between missingness and both phenotype and outcome (OR = 1.5 for both phenotype and outcome) and between allele score and phenotype (r = 0.1, 1% variance explained by allele score) the confidence intervals contain zero only 89% of the time, and this continues to decrease with both greater strength of association between phenotype, outcome and missingness, and stronger association between allele score and phenotype. Table 1Results of simulation study showing the 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
