Table 2.
Results for case 2 in which a chi-squared distribution with two degrees of freedom was created for the outcome data with three repeated measures.
α = 0.3 |
α = 0.7 |
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n | % Censor | LOD/2 | MLE | Quantile | LOD/2 | MLE | Quantile | |
100 | 10 | Bias | 0.0197 | 0.0210 | −0.0008 | 0.0073 | 0.0138 | 0.0006 |
MSE | 0.0006 | 0.0006 | 0.0005 | 0.0003 | 0.0004 | 0.0007 | ||
RE | 1.000 | 0.921 | 1.279 | 1.000 | 0.741 | 0.413 | ||
20 | Bias | 0.0186 | 0.0221 | −0.0001 | −0.0032 | 0.0166 | 0.0003 | |
MSE | 0.0006 | 0.0007 | 0.0005 | 0.0003 | 0.0005 | 0.0007 | ||
RE | 1.000 | 0.823 | 1.194 | 1.000 | 0.588 | 0.424 | ||
30 | Bias | 0.0192 | 0.0231 | −0.0020 | −0.0155 | 0.0195 | −0.0022 | |
MSE | 0.0006 | 0.0007 | 0.0005 | 0.0007 | 0.0006 | 0.0008 | ||
RE | 1.000 | 0.884 | 1.324 | 1.000 | 1.087 | 0.873 | ||
40 | Bias | 0.0169 | 0.0236 | −0.0057 | −0.0477 | 0.0216 | −0.0036 | |
MSE | 0.0010 | 0.0008 | 0.0006 | 0.0044 | 0.0007 | 0.0008 | ||
RE | 1.000 | 1.261 | 1.679 | 1.000 | 6.211 | 5.668 | ||
500 | 10 | Bias | 0.0194 | 0.0207 | −0.0010 | 0.0062 | 0.0127 | −0.0007 |
MSE | 0.0004 | 0.0005 | 0.0001 | 0.0001 | 0.0002 | 0.0001 | ||
RE | 1.000 | 0.891 | 4.172 | 1.000 | 0.425 | 0.670 | ||
20 | Bias | 0.0185 | 0.0219 | −0.0017 | −0.0045 | 0.0156 | −0.0014 | |
MSE | 0.0004 | 0.0005 | 0.0001 | 0.0001 | 0.0003 | 0.0001 | ||
RE | 1.000 | 0.742 | 3.859 | 1.000 | 0.274 | 0.609 | ||
30 | Bias | 0.0192 | 0.0229 | −0.0033 | −0.0164 | 0.0185 | −0.0031 | |
MSE | 0.0004 | 0.0006 | 0.0001 | 0.0004 | 0.0004 | 0.0002 | ||
RE | 1.000 | 0.748 | 3.843 | 1.000 | 0.913 | 2.380 | ||
40 | Bias | 0.0188 | 0.0234 | −0.0068 | −0.0415 | 0.0205 | −0.0064 | |
MSE | 0.0004 | 0.0006 | 0.0002 | 0.0021 | 0.0005 | 0.0002 | ||
RE | 1.000 | 0.762 | 2.801 | 1.000 | 4.373 | 10.85 |
Bias - empirical bias.
MSE - empirical mean squared error.
RE - relative efficiency. These are the italicized ratios that, for each setting (n), compare the empirical MSE from the LOD/2 substitution method to the MSE from the use of MLE method or quantile regression model.