TABLE 4.

Simulation study results for collider bias on two phenotypes Y and Z across POP1 + POP2.

Selection scenarios with collider bias in POP1 + POP2	Type I error rate	Estimated genetic correlations of the phenotype Y between POP1 and POP2		Estimated genetic correlations between Y and Z on selected POP1 + POP2
		Mean	SE	Mean	SE
ORPOP1,Y = 2, ORPOP1,Z = 2, ORPOP2,Y = 3, ORPOP2,Z = 2	1%	1.0141	0.0189	−0.2516	0.0032
ORPOP1,Y = 2, ORPOP1,Z = 2, ORPOP2,Y = 3, ORPOP2,Z = 3	2%	1.0220	0.0165	−0.2942	0.0031
ORPOP1,Y = 2, ORPOP1,Z = 3, ORPOP2,Y = 3, ORPOP2,Z = 3	2%	1.0091	0.0187	−0.3415	0.0036

Different odds ratio combinations (OR_POP1,Y, OR_POP2,Y, OR_POP1,Z, and OR_POP2,Z) generated phenotypes in POP1 + POP2 with different selection bias levels. Type I error rates based on 100 simulation replicates were examined through estimated genetic correlations of the phenotype Y between POP1 and POP2 by bivariate GREML. Type I error rates under the null hypothesis that genetic correlation of 1 implies no interaction were controlled for these combinations (<5%), and meanwhile, significant negative genetic correlations between the two simulated phenotypes Y and Z demonstrated strong collider bias signal in selected POP1 + POP2. Here, we assume that the phenotype Z involves a sum of collider bias effects across all other traits on the main response Y. Here, we consider 0.05 as a significance level for controlling type I error rate. SE denotes standard error.