TABLE 3.

Simulation study results for selection bias on the phenotype Y across POP1 + POP2.

Selection scenarios in POP1 + POP2	Type I error rate by G × P RNM with PC1	Type I error rate by bivariate GREML	100 estimated genetic correlations
			Mean	SE
ORPOP1,Y = 1, ORPOP2,Y = 1	5%	0%	0.9722	0.0145
ORPOP1,Y = 1, ORPOP2,Y = 2	55%	2%	0.9876	0.0166
ORPOP1,Y = 2, ORPOP2,Y = 2	1%	0%	1.0245	0.0160
ORPOP1,Y = 2, ORPOP2,Y = 3	64%	6%	0.9882	0.0202

Different odds ratio combinations (OR_POP1,Y andOR_POP2,Y) generated phenotypic values in POP1 + POP2 with different selection bias levels. Type I error rates based on 100 simulation replicates were examined by G × P RNM and bivariate GREML respectively. The genetic correlations of the phenotype between POP1 and POP2 were estimated by bivariate GREML. The results by G × P RNM indicated high type I error rates for selection scenarios of OR_POP1,Y = 1, OR_POP2,Y = 2 and OR_POP1,Y = 2, OR_POP2,Y = 3. But for same selection pressures (OR_POP1,Y = 1, OR_POP2,Y = 1 and OR_POP1,Y = 2, OR_POP2,Y = 2), G × P RNM can effectively control false positive rate. Type I error rates assessed by bivariate GREML were controlled for all scenarios and the estimated genetic correlations were not significantly different from one for all selection scenarios. Here, we consider 0.05 as a significance level for controlling type I error rate. SE denotes standard error.