Table 2.
Summary statistics of the exposure–response parameter estimates for each scenario with exposure intensity distribution 2
| 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 | 2.84E–03 | 2.62E–03 | 36.9 | 3,000 | 1.0000 | 1.42E–03 | 1.40E–03 | 44.7 |
| 1:05 | 10,000 | 0.9999 | 1.95E–03 | 1.89E–03 | 78.5 | 3,000 | 1.0000 | 1.06E–03 | 1.00E–03 | 80.1 | |
| 1:10 | 10,000 | 0.9998 | 1.84E–03 | 1.80E–03 | 88.3 | 3,000 | 1.0000 | 1.01E–03 | 1.00E–03 | 89.4 | |
| 1:15 | 10,000 | 0.9998 | 1.80E–03 | 1.76E–03 | 92.1 | 3,000 | 1.0000 | 9.96E–04 | 9.96E–04 | 91.2 | |
| 1:20 | 10,000 | 0.9998 | 1.78E–03 | 1.75E–03 | 93.9 | 3,000 | 1.0000 | 9.80E–04 | 9.87E–04 | 94.2 | |
| Full | 10,000 | 0.9998 | 1.73E–03 | 1.70E–03 | 3,000 | 1.0000 | 9.51E–04 | 9.63E–04 | |||
| 1.005 | 1:01 | 9,999 | 1.0058 | 4.00E–03 | 3.09E–03 | 11.3 | 3,000 | 1.0052 | 1.50E–03 | 1.40E–03 | 20.8 |
| 1:05 | 10,000 | 1.0051 | 1.87E–03 | 1.79E–03 | 52.1 | 3,000 | 1.0050 | 9.12E–04 | 9.04E–04 | 56.4 | |
| 1:10 | 10,000 | 1.0051 | 1.64E–03 | 1.59E–03 | 67.4 | 3,000 | 1.0050 | 8.14E–04 | 8.06E–04 | 70.8 | |
| 1:15 | 10,000 | 1.0050 | 1.57E–03 | 1.50E–03 | 74.0 | 3,000 | 1.0050 | 7.74E–04 | 7.68E–04 | 78.4 | |
| 1:20 | 10,000 | 1.0050 | 1.51E–03 | 1.46E–03 | 80.1 | 3,000 | 1.0050 | 7.51E–04 | 7.47E–04 | 83.1 | |
| Full | 10,000 | 1.0049 | 1.35E–03 | 1.31E–03 | 3,000 | 1.0049 | 6.85E–04 | 6.79E–04 | |||
| 1.015 | 1:01 | 7,911 | 1.0206 | 2.20E–02 | 1.51E–02 | 0.3 | 2,992 | 1.017 | 6.62E–03 | 4.50E–03 | 1.0 |
| 1:05 | 9,897 | 1.0175 | 1.09E–02 | 5.51E–03 | 1.3 | 3,000 | 1.0154 | 2.07E–03 | 1.90E–03 | 10.4 | |
| 1:10 | 9,987 | 1.0164 | 7.74E–03 | 3.51E–03 | 2.5 | 3,000 | 1.0153 | 1.55E–03 | 1.40E–03 | 18.5 | |
| 1:15 | 9,996 | 1.0159 | 3.82E–03 | 2.79E–03 | 10.3 | 3,000 | 1.0152 | 1.37E–03 | 1.30E–03 | 23.7 | |
| 1:20 | 9,996 | 1.0157 | 3.24E–03 | 2.48E–03 | 14.3 | 3,000 | 1.0152 | 1.23E–03 | 1.20E–03 | 29.4 | |
| Full | 10,000 | 1.0152 | 1.22E–03 | 1.20E–03 | 3,000 | 1.0150 | 6.68E–04 | 6.92E–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.