TABLE II.
Simulation results for studying the effect of an untyped SNP on a quantitative trait under the cross-sectional design
| β | MLE |
IMP-DOS |
IMP-MLG |
|||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bias | SE | SEE | CP | PW | Bias | SE | SEE | CP | PW | Bias | SE | SEE | CP | PW | ||
| S1 | 0.0 | 0.000 | 0.051 | 0.051 | 0.989 | 0.011 | 0.000 | 0.051 | 0.051 | 0.990 | 0.010 | 0.000 | 0.041 | 0.041 | 0.989 | 0.011 |
| 0.1 | 0.000 | 0.051 | 0.051 | 0.990 | 0.274 | −0.001 | 0.051 | 0.051 | 0.990 | 0.267 | −0.031 | 0.041 | 0.041 | 0.965 | 0.190 | |
| 0.2 | 0.000 | 0.052 | 0.051 | 0.990 | 0.905 | −0.002 | 0.051 | 0.051 | 0.990 | 0.903 | −0.062 | 0.042 | 0.041 | 0.857 | 0.781 | |
| 0.6 | 0.000 | 0.053 | 0.052 | 0.990 | 1.00 | −0.007 | 0.056 | 0.053 | 0.987 | 1.00 | −0.185 | 0.047 | 0.043 | 0.063 | 1.00 | |
| 0.9 | −0.002 | 0.054 | 0.052 | 0.988 | 1.00 | −0.010 | 0.061 | 0.056 | 0.982 | 1.00 | −0.277 | 0.053 | 0.046 | 0.001 | 1.00 | |
| S2 | 0.0 | 0.000 | 0.046 | 0.046 | 0.991 | 0.009 | 0.000 | 0.046 | 0.046 | 0.990 | 0.010 | 0.000 | 0.036 | 0.036 | 0.991 | 0.009 |
| 0.1 | 0.000 | 0.046 | 0.047 | 0.991 | 0.325 | 0.000 | 0.046 | 0.046 | 0.990 | 0.336 | −0.026 | 0.036 | 0.036 | 0.965 | 0.309 | |
| 0.2 | 0.000 | 0.048 | 0.048 | 0.992 | 0.960 | 0.000 | 0.048 | 0.046 | 0.988 | 0.963 | −0.051 | 0.038 | 0.036 | 0.843 | 0.937 | |
| 0.6 | 0.001 | 0.057 | 0.057 | 0.988 | 1.00 | −0.001 | 0.061 | 0.047 | 0.954 | 1.00 | −0.154 | 0.048 | 0.037 | 0.151 | 1.00 | |
| 0.9 | 0.000 | 0.060 | 0.060 | 0.985 | 1.00 | −0.001 | 0.077 | 0.049 | 0.903 | 1.00 | −0.231 | 0.060 | 0.038 | 0.059 | 1.00 | |
| S3 | 0.0 | 0.000 | 0.055 | 0.054 | 0.992 | 0.008 | 0.000 | 0.055 | 0.054 | 0.991 | 0.009 | 0.000 | 0.041 | 0.041 | 0.990 | 0.010 |
| 0.1 | 0.000 | 0.055 | 0.055 | 0.992 | 0.217 | 0.001 | 0.055 | 0.054 | 0.989 | 0.237 | −0.025 | 0.041 | 0.041 | 0.977 | 0.233 | |
| 0.2 | 0.001 | 0.057 | 0.057 | 0.991 | 0.856 | 0.001 | 0.058 | 0.054 | 0.986 | 0.871 | −0.050 | 0.042 | 0.041 | 0.907 | 0.863 | |
| 0.6 | 0.001 | 0.070 | 0.070 | 0.987 | 1.00 | 0.004 | 0.078 | 0.055 | 0.936 | 1.00 | −0.149 | 0.046 | 0.041 | 0.172 | 1.00 | |
| 0.9 | 0.000 | 0.074 | 0.073 | 0.987 | 1.00 | 0.006 | 0.100 | 0.056 | 0.863 | 1.00 | −0.224 | 0.051 | 0.042 | 0.033 | 1.00 | |
| S4 | 0.0 | 0.000 | 0.037 | 0.037 | 0.989 | 0.011 | 0.000 | 0.037 | 0.037 | 0.989 | 0.011 | 0.000 | 0.035 | 0.035 | 0.989 | 0.011 |
| 0.1 | 0.000 | 0.037 | 0.037 | 0.989 | 0.544 | 0.000 | 0.037 | 0.037 | 0.989 | 0.544 | −0.007 | 0.035 | 0.035 | 0.986 | 0.540 | |
| 0.2 | 0.000 | 0.038 | 0.037 | 0.989 | 0.998 | −0.001 | 0.037 | 0.037 | 0.988 | 0.998 | −0.013 | 0.035 | 0.035 | 0.983 | 0.997 | |
| 0.6 | 0.000 | 0.038 | 0.038 | 0.988 | 1.00 | −0.002 | 0.039 | 0.038 | 0.986 | 1.00 | −0.039 | 0.036 | 0.036 | 0.929 | 1.00 | |
| 0.9 | 0.000 | 0.039 | 0.038 | 0.989 | 1.00 | −0.003 | 0.041 | 0.038 | 0.984 | 1.00 | −0.059 | 0.036 | 0.036 | 0.829 | 1.00 | |
| S5 | 0.0 | 0.000 | 0.041 | 0.040 | 0.991 | 0.009 | 0.000 | 0.041 | 0.040 | 0.991 | 0.009 | 0.000 | 0.036 | 0.036 | 0.991 | 0.009 |
| 0.1 | 0.000 | 0.041 | 0.041 | 0.991 | 0.456 | 0.000 | 0.041 | 0.040 | 0.990 | 0.463 | −0.012 | 0.036 | 0.036 | 0.985 | 0.463 | |
| 0.2 | 0.001 | 0.042 | 0.042 | 0.991 | 0.991 | 0.001 | 0.042 | 0.040 | 0.988 | 0.991 | −0.023 | 0.036 | 0.036 | 0.971 | 0.991 | |
| 0.6 | 0.001 | 0.048 | 0.048 | 0.988 | 1.00 | 0.001 | 0.050 | 0.041 | 0.966 | 1.00 | −0.071 | 0.036 | 0.036 | 0.722 | 1.00 | |
| 0.9 | 0.001 | 0.052 | 0.051 | 0.987 | 1.00 | 0.002 | 0.060 | 0.041 | 0.929 | 1.00 | −0.106 | 0.037 | 0.036 | 0.365 | 1.00 | |
| S6 | 0.0 | 0.000 | 0.050 | 0.050 | 0.990 | 0.010 | 0.000 | 0.050 | 0.050 | 0.990 | 0.010 | 0.000 | 0.048 | 0.047 | 0.990 | 0.010 |
| 0.1 | 0.000 | 0.050 | 0.050 | 0.990 | 0.286 | 0.000 | 0.050 | 0.050 | 0.990 | 0.284 | −0.008 | 0.048 | 0.047 | 0.988 | 0.266 | |
| 0.2 | 0.000 | 0.050 | 0.050 | 0.990 | 0.919 | −0.001 | 0.050 | 0.050 | 0.990 | 0.918 | −0.015 | 0.048 | 0.047 | 0.985 | 0.904 | |
| 0.6 | 0.000 | 0.050 | 0.050 | 0.990 | 1.00 | −0.003 | 0.050 | 0.050 | 0.990 | 1.00 | −0.046 | 0.048 | 0.048 | 0.943 | 1.00 | |
| 0.9 | 0.000 | 0.050 | 0.049 | 0.989 | 1.00 | −0.004 | 0.051 | 0.051 | 0.991 | 1.00 | −0.069 | 0.049 | 0.049 | 0.876 | 1.00 | |
| S7 | 0.0 | 0.000 | 0.056 | 0.056 | 0.990 | 0.010 | 0.000 | 0.056 | 0.056 | 0.990 | 0.010 | 0.000 | 0.055 | 0.055 | 0.990 | 0.010 |
| 0.1 | 0.000 | 0.056 | 0.056 | 0.990 | 0.215 | 0.000 | 0.056 | 0.056 | 0.990 | 0.214 | 0.000 | 0.055 | 0.055 | 0.990 | 0.215 | |
| 0.2 | 0.000 | 0.056 | 0.056 | 0.990 | 0.844 | 0.000 | 0.056 | 0.056 | 0.990 | 0.844 | −0.001 | 0.055 | 0.055 | 0.990 | 0.845 | |
| 0.6 | 0.000 | 0.056 | 0.056 | 0.990 | 1.00 | 0.000 | 0.056 | 0.056 | 0.990 | 1.00 | −0.003 | 0.055 | 0.055 | 0.990 | 1.00 | |
| 0.9 | 0.000 | 0.056 | 0.056 | 0.990 | 1.00 | 0.000 | 0.056 | 0.056 | 0.990 | 1.00 | −0.004 | 0.056 | 0.056 | 0.990 | 1.00 | |
| S8 | 0.0 | 0.000 | 0.036 | 0.036 | 0.990 | 0.010 | 0.000 | 0.036 | 0.036 | 0.990 | 0.010 | 0.000 | 0.035 | 0.035 | 0.990 | 0.010 |
| 0.1 | 0.000 | 0.036 | 0.036 | 0.990 | 0.590 | 0.000 | 0.036 | 0.036 | 0.990 | 0.590 | −0.002 | 0.035 | 0.035 | 0.991 | 0.590 | |
| 0.2 | 0.000 | 0.036 | 0.036 | 0.991 | 0.999 | 0.000 | 0.036 | 0.036 | 0.990 | 0.999 | −0.003 | 0.035 | 0.035 | 0.991 | 0.999 | |
| 0.6 | 0.000 | 0.037 | 0.037 | 0.990 | 1.00 | 0.000 | 0.037 | 0.036 | 0.987 | 1.00 | −0.009 | 0.035 | 0.035 | 0.988 | 1.00 | |
| 0.9 | 0.000 | 0.038 | 0.038 | 0.989 | 1.00 | 0.000 | 0.038 | 0.036 | 0.982 | 1.00 | −0.014 | 0.035 | 0.035 | 0.984 | 1.00 | |
| S9 | 0.0 | 0.000 | 0.036 | 0.035 | 0.990 | 0.010 | 0.000 | 0.036 | 0.035 | 0.990 | 0.010 | 0.000 | 0.035 | 0.035 | 0.990 | 0.010 |
| 0.1 | 0.000 | 0.036 | 0.035 | 0.990 | 0.599 | 0.000 | 0.036 | 0.035 | 0.990 | 0.599 | −0.001 | 0.035 | 0.035 | 0.990 | 0.598 | |
| 0.2 | 0.000 | 0.036 | 0.035 | 0.990 | 0.999 | 0.000 | 0.036 | 0.035 | 0.990 | 0.999 | −0.001 | 0.035 | 0.035 | 0.990 | 0.999 | |
| 0.6 | 0.000 | 0.036 | 0.035 | 0.990 | 1.00 | 0.000 | 0.036 | 0.035 | 0.990 | 1.00 | −0.004 | 0.035 | 0.035 | 0.991 | 1.00 | |
| 0.9 | −0.001 | 0.036 | 0.035 | 0.990 | 1.00 | −0.001 | 0.036 | 0.035 | 0.989 | 1.00 | −0.005 | 0.035 | 0.035 | 0.990 | 1.00 | |
S1–S9 denote the nine scenarios listed in Table I. Bias and SE are the bias and standard error of the parameter estimator. SEE is the mean of the standard error estimator. CP is the coverage probability of the 99% confidence interval. PW is the type I error/power for testing zero parameter value at the 0.01 nominal significance level. Each entry is based on 10,000 replicates.