Table 1.

The type I error rates of genetic association tests with phenotypes imputed with different methods. ($\alpha$=0.05, 95$\%$ confidence interval of $\alpha$: (0.0362, 0.0638); heritability $h^2=0;$ correlation of phenotypes $\rho$ =0.5; 1000 replicated samples; sample size $n=1000$)

Dist. $_{}^1$	Association tests	Unimputed	PHENIX	PIM	C-MSE	C-(0–1)	C-QL
MVN	TATES	0.055	0.057	0.045	0.040	0.052	0.043
	MANOVA	0.049	0.036	0.043	0.038	0.037	0.042
	M-Phen	0.051	0.044	0.059	0.060	0.057	0.062
	AFC	0.055	0.046	0.037	0.043	0.058	0.061
	Tippel	0.049	0.061	0.055	0.056	0.049	0.044
MG	TATES	0.051	$\mathbf{0.066}$	$\mathbf{0.071}$	0.039	0.053	0.060
	MANOVA	0.054	$\mathbf{0.065}$	$\mathbf{0.073}$	0.051	0.047	0.043
	M-Phen	0.045	$\mathbf{0.080}$	$\mathbf{0.075}$	0.044	0.050	0.053
	AFC	0.055	$\mathbf{0.065}$	$\mathbf{0.063}$	0.047	0.056	0.059
	Tippel	0.050	$\mathbf{0.074}$	$\mathbf{0.077}$	0.060	0.054	0.039
Mixed	TATES	0.055	$\mathbf{0.077}$	$\mathbf{0.085}$	0.037	0.042	0.045
	MANOVA	0.049	$\mathbf{0.079}$	$\mathbf{0.084}$	0.056	0.052	0.061
	M-Phen	0.049	$\mathbf{0.088}$	$\mathbf{0.079}$	0.057	0.061	0.060
	AFC	0.036	$\mathbf{0.068}$	$\mathbf{0.070}$	0.048	0.060	0.054
	Tippel	0.048	$\mathbf{0.090}$	$\mathbf{0.085}$	0.056	0.061	0.053

$_{}^1$Dist.: Phenotypes’ distributions; MVN: 7 phenotypes follow multivariate normal distribution (MVN); MG: 7 phenotypes follow multivariate gamma distribution; Mixed: 7 phenotypes follow a mixture of multivariate normal, beta, and gamma distributions

Bold values indicate inflated type I errors