Table 2.
Results of simulation study with alternative incidence rates
| a) Discrimination measures | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Incidence* 10 years (25 years) |
Sampling fraction |
% Cases (25 years) |
Harrell’s C |
Royston and saubrei’s D |
||||||||||||
| |
|
|
Full cohort |
Case-cohort |
Full cohort |
Case-cohort |
||||||||||
| |
|
|
|
UW (bias %) |
W |
SE |
ESE** |
RE‡ |
ERE‡‡ |
|
UW (bias %) |
W |
SE |
ESE** |
RE‡ |
ERE‡‡ |
| 0.073 (0.277) |
0.03 |
91 |
0.674 |
0.552 (18.1) |
0.675 |
0.018 |
0.018 |
0.135 |
0.126 |
1.060 |
0.336 (68.3) |
1.099 |
0.162 |
0.172 |
0.064 |
0.055 |
| 0.1 |
76 |
|
0.591 (12.4) |
0.675 |
0.011 |
0.011 |
0.354 |
0.349 |
|
0.568 (46.5) |
1.070 |
0.094 |
0.092 |
0.192 |
0.197 |
|
| 0.3 |
52 |
|
0.637 (5.5) |
0.674 |
0.008 |
0.008 |
0.678 |
0.672 |
|
0.832 (21.4) |
1.063 |
0.060 |
0.057 |
0.474 |
0.479 |
|
| 0.5 |
39 |
|
0.655 (2.7) |
0.674 |
0.007 |
0.007 |
0.831 |
0.817 |
|
0.942 (11.0) |
1.060 |
0.050 |
0.047 |
0.671 |
0.682 |
|
| 0.9 |
26 |
|
0.672 (0.3) |
0.675 |
0.007 |
0.006 |
0.978 |
0.981 |
|
1.046 (1.4) |
1.061 |
0.043 |
0.040 |
0.933 |
0.935 |
|
| 0.027 (0.112) |
0.03 |
76 |
0.679 |
0.576 (15.3) |
0.681 |
0.021 |
0.020 |
0.283 |
0.288 |
1.073 |
0.491 (54.4) |
1.087 |
0.173 |
0.167 |
0.147 |
0.157 |
| 0.1 |
49 |
|
0.627 (7.6) |
0.679 |
0.014 |
0.014 |
0.582 |
0.580 |
|
0.771 (28.1) |
1.072 |
0.109 |
0.102 |
0.368 |
0.4179 |
|
| 0.3 |
24 |
|
0.662 (2.5) |
0.679 |
0.012 |
0.011 |
0.843 |
0.862 |
|
0.970 (9.4) |
1.073 |
0.080 |
0.075 |
0.682 |
0.7407 |
|
| 0.5 |
16 |
|
0.671 (1.1) |
0.679 |
0.011 |
0.011 |
0.926 |
0.928 |
|
1.023 (4.3) |
1.069 |
0.073 |
0.07 |
0.823 |
0.8868 |
|
| |
0.9 |
10 |
|
0.679 (0.1) |
0.680 |
0.011 |
0.011 |
0.991 |
0.997 |
|
1.070 (0.5) |
1.076 |
0.068 |
0.066 |
0.956 |
0.9835 |
|
b) NRI |
|
|
||||||||||||||
|
Incidence* 10 years (25 years) |
Sampling fraction |
% Cases (25 years) |
Category-based NRI |
Continuous NRI |
|
|||||||||||
|
Full cohort |
Case-cohort |
Full cohort |
Case-cohort |
|||||||||||||
| |
|
|
|
NRI |
SE |
ESE** |
RE‡ |
ERE‡‡ |
|
NRI |
SE |
ESE** |
RE‡ |
ERE‡‡ |
|
|
| 0.073 (0.277) |
0.03 |
97 |
0.028 |
0.029 |
0.025 |
0.033 |
0.414 |
0.265 |
0.170 |
0.166 |
0.086 |
0.095 |
0.296 |
0.214 |
|
|
| 0.1 |
86 |
|
0.028 |
0.019 |
0.023 |
0.713 |
0.506 |
|
0.170 |
0.060 |
0.069 |
0.602 |
0.490 |
|
||
| 0.3 |
76 |
|
0.027 |
0.017 |
0.018 |
0.906 |
0.798 |
|
0.169 |
0.050 |
0.051 |
0.854 |
0.753 |
|
||
| 0.5 |
52 |
|
0.028 |
0.017 |
0.018 |
0.960 |
0.814 |
|
0.171 |
0.048 |
0.050 |
0.932 |
0.898 |
|
||
| 0.9 |
26 |
|
0.028 |
0.016 |
0.018 |
0.997 |
0.963 |
|
0.170 |
0.047 |
0.046 |
0.992 |
0.981 |
|||
| 0.027 (0.112) |
0.03 |
91 |
0.011 |
0.015 |
0.014 |
0.022 |
0.571 |
0.308 |
0.156 |
0.154 |
0.106 |
0.114 |
0.561 |
0.456 |
|
|
| 0.1 |
66 |
|
0.012 |
0.012 |
0.015 |
0.813 |
0.603 |
|
0.160 |
0.087 |
0.096 |
0.822 |
0.730 |
|
||
| 0.3 |
49 |
|
0.010 |
0.011 |
0.012 |
0.954 |
0.965 |
|
0.156 |
0.081 |
0.080 |
0.947 |
0.903 |
|
||
| 0.5 |
24 |
|
0.011 |
0.011 |
0.013 |
0.990 |
0.933 |
|
0.160 |
0.080 |
0.083 |
0.976 |
0.959 |
|
||
| 0.9 | 10 | 0.011 | 0.011 | 0.012 | 1.008 | 0.944 | 0.155 | 0.079 | 0.076 | 0.997 | 0.978 | |||||
Results are shown for the full cohort, the case-cohort subsample with Prentice weights using the standard unweighted measures of discrimination (UW) as well as the weighted versions (W). For the weighted estimates we also show the analytical and empirical SE and relative efficiency.
* Incidence from Kaplan-Meier.
** Empirical standard error.
‡ Relative efficiency calculated as the ratio of analytical variances (full cohort/case-cohort).
‡‡ Empirical relative efficiency calculated as the ratio of empirical variances (full cohort/case-cohort).