Table 1.
Summary statistics of the exposure–response parameter estimates for each scenario with exposure intensity distribution 1
| True hazard ratio |
Match | ~30 cases per cohort |
~100 cases per cohort |
||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Na | Meanb | Empirical standard errorc |
Estimated standard errord |
Relative efficiencye (%) |
Na | Meanb | Empirical standard errorc |
Estimated standard errord |
Relative efficiencye (%) |
||
| 1 | 1:01 | 10,000 | 1.0000 | 2.16E–03 | 2.02E–03 | 38.7 | 3,000 | 1.0000 | 1.13E–03 | 1.11E–03 | 48.1 |
| 1:05 | 10,000 | 1.0000 | 1.52E–03 | 1.48E–03 | 78.3 | 3,000 | 1.0000 | 8.52E–04 | 8.45E–04 | 84.5 | |
| 1:10 | 10,000 | 1.0000 | 1.43E–03 | 1.41E–03 | 88.7 | 3,000 | 1.0000 | 8.20E–04 | 8.07E–04 | 91.4 | |
| 1:15 | 10,000 | 1.0000 | 1.40E–03 | 1.39E–03 | 92.6 | 3,000 | 1.0000 | 8.10E–04 | 7.95E–04 | 93.5 | |
| 1:20 | 10,000 | 1.0000 | 1.38E–03 | 1.38E–03 | 94.0 | 3,000 | 1.0000 | 8.08E–04 | 7.88E–04 | 94.0 | |
| Full | 10,000 | 1.0000 | 1.34E–03 | 1.34E–03 | 3,000 | 1.0000 | 7.84E–04 | 7.69E–04 | |||
| 1.005 | 1:01 | 10,000 | 1.0056 | 5.80E–03 | 2.63E–03 | 5.9 | 3,000 | 1.0052 | 1.41E–03 | 1.37E–03 | 33.4 |
| 1:05 | 10,000 | 1.0051 | 1.71E–03 | 1.66E–03 | 68.4 | 3,000 | 1.0050 | 9.59E–04 | 9.43E–04 | 72.1 | |
| 1:10 | 10,000 | 1.0051 | 1.57E–03 | 1.54E–03 | 81.4 | 3,000 | 1.0050 | 8.84E–04 | 8.78E–04 | 84.9 | |
| 1:15 | 10,000 | 1.0051 | 1.52E–03 | 1.49E–03 | 86.7 | 3,000 | 1.0050 | 8.52E–04 | 8.54E–04 | 91.3 | |
| 1:20 | 10,000 | 1.0050 | 1.49E–03 | 1.47E–03 | 90.2 | 3,000 | 1.0050 | 8.58E–04 | 8.42E–04 | 89.9 | |
| Full | 10,000 | 1.0050 | 1.41E–03 | 1.40E–03 | 3,000 | 1.0050 | 8.14E–04 | 8.05E–04 | |||
| 1.015 | 1:01 | 9,782 | 1.0189 | 1.50E–02 | 8.47E–03 | 1.2 | 3,000 | 1.0160 | 4.15E–03 | 3.34E–03 | 5.2 |
| 1:05 | 9,999 | 1.0158 | 3.56E–03 | 3.11E–03 | 21.6 | 3,000 | 1.0152 | 1.81E–03 | 1.72E–03 | 27.3 | |
| 1:10 | 10,000 | 1.0154 | 2.68E–03 | 2.49E–03 | 38.0 | 3,000 | 1.0152 | 1.46E–03 | 1.43E–03 | 42.0 | |
| 1:15 | 10,000 | 1.0153 | 2.40E–03 | 2.26E–03 | 47.6 | 3,000 | 1.0151 | 1.31E–03 | 1.31E–03 | 51.8 | |
| 1:20 | 10,000 | 1.0153 | 2.25E–03 | 2.13E–03 | 54.1 | 3,000 | 1.0151 | 1.25E–03 | 1.24E–03 | 57.8 | |
| Full | 10,000 | 1.0151 | 1.65E–03 | 1.62E–03 | 3,000 | 1.0150 | 9.46E–04 | 9.70E–04 | |||
Notes:
a
N is the number of parameter estimates with corresponding standard error less than 1 as calculated by the PHREG procedure.
b
Mean is the exponential of the mean of the estimated log hazard ratios.
c
Empirical standard error is the sample standard deviation of the estimated log hazard ratios.
d
Estimated standard error is the mean of the estimated standard errors.
e
Relative efficiency of 1:m sampling was estimated by dividing the empirical variance obtained from the full risk-set analyses by the empirical variance obtained from the m-sampled risk-set analyses.