Table 1.
Simulation results for WMR and comparison with semi-parametric method. We assumed (log(T),M)∼N2(0,0,1,1, − 0.7). An independent censoring time was generated such that either 20% or 40% subjects were censored. The results are based on 1000 such simulations. The MLE and semi-parametric estimates are cited from Heagerty and Zheng (2005). MCSD denotes the Monte-Carlo SD. The nominal coverage is 95.0. Estimate of integrated AUC (iAUC) and its variance is based on 10 equi-spaced quantiles of time. The variance of integrated AUC is estimated assuming a constant weight
MLE |
Semi-parametric |
WMR (n = 200) |
|||||||
---|---|---|---|---|---|---|---|---|---|
Log time | AUC(t) | Mean | SD | Mean | SD | Mean | MCSD | EstSD | Coverage |
20% censoring | |||||||||
− 2.0 | 0.884 | 0.884 | 0.018 | 0.881 | 0.044 | 0.876 | 0.055 | 0.050 | 90.2 |
− 1.5 | 0.833 | 0.834 | 0.019 | 0.829 | 0.035 | 0.828 | 0.040 | 0.041 | 93.4 |
− 1.0 | 0.782 | 0.782 | 0.019 | 0.771 | 0.033 | 0.780 | 0.037 | 0.036 | 93.2 |
− 0.5 | 0.734 | 0.734 | 0.019 | 0.720 | 0.033 | 0.734 | 0.035 | 0.034 | 94.1 |
0.0 | 0.693 | 0.693 | 0.018 | 0.686 | 0.034 | 0.695 | 0.037 | 0.037 | 94.0 |
0.5 | 0.660 | 0.660 | 0.016 | 0.657 | 0.040 | 0.664 | 0.047 | 0.045 | 94.9 |
1.0 | 0.634 | 0.634 | 0.015 | 0.637 | 0.041 | 0.638 | 0.066 | 0.064 | 93.0 |
iAUC | 0.741 | 0.741 | 0.016 | 0.740 | 0.018 | 0.738 | 0.020 | 0.017 | 89.6 |
40% censoring | |||||||||
− 2.0 | 0.884 | 0.884 | 0.019 | 0.875 | 0.048 | 0.876 | 0.056 | 0.050 | 89.9 |
− 1.5 | 0.833 | 0.834 | 0.021 | 0.827 | 0.037 | 0.828 | 0.041 | 0.042 | 92.9 |
− 1.0 | 0.782 | 0.782 | 0.021 | 0.772 | 0.035 | 0.781 | 0.038 | 0.037 | 92.7 |
− 0.5 | 0.734 | 0.734 | 0.020 | 0.722 | 0.039 | 0.735 | 0.039 | 0.038 | 94.3 |
0.0 | 0.693 | 0.693 | 0.019 | 0.687 | 0.041 | 0.696 | 0.044 | 0.043 | 93.5 |
0.5 | 0.660 | 0.660 | 0.018 | 0.655 | 0.043 | 0.666 | 0.061 | 0.059 | 92.6 |
1.0 | 0.634 | 0.635 | 0.016 | 0.637 | 0.048 | 0.640 | 0.108 | 0.100 | 91.8 |
iAUC | 0.741 | 0.741 | 0.017 | 0.742 | 0.021 | 0.739 | 0.023 | 0.019 | 88.3 |