Table 3.
Coverage probability for the 95% confidence interval of the simple product-based estimator (ESRS) and revised product-based estimator (ESRR) using a log-based variance
| Low exposure probability (.05)/Low disease probability in unexposed (.02) | ||||
|---|---|---|---|---|
| N1 = 1,000, N2 = 1,000 | N1 = 5,000, N2 = 5,000 | |||
| RR/ESR | ESRS | ESRR | ESRS | ESRR |
| 1.0/.02 | 96.8 | 97.3 | 97.5 | 97.5 |
| 2.0/.04 | 96.4 | 98.1 | 95.9 | 97.2 |
| 3.0/.06 | 95.7 | 98.3 | 92.7 | 96.6 |
| 4.0/.08 | 94.1 | 98.2 | 90.3 | 98.0 |
| 5.0/.10 | 93.9 | 98.4 | 87.1 | 97.7 |
| Low exposure probability (.05)/Moderate disease probability in unexposed (.09) | ||||
| N1 = 1,000, N2 = 1,000 | N1 = 5,000, N2 = 5,000 | |||
| RR/ESR | ESRS | ESRR | ESRS | ESRR |
| 1.0/.09 | 96.8 | 97.2 | 95.9 | 96.2 |
| 2.0/.18 | 95.8 | 96.8 | 93.4 | 96.3 |
| 3.0/.27 | 94.3 | 97.0 | 87.8 | 96.4 |
| 4.0/.36 | 89.3 | 96.1 | 70.8 | 97.0 |
| 5.0/.45 | 83.2 | 96.6 | 45.0 | 96.6 |
| High exposure probability (.20)/Low disease probability in unexposed (.02) | ||||
| N1 = 1,000, N2 = 1,000 | N1 = 5,000, N2 = 5,000 | |||
| RR/ESR | ESRS | ESRR | ESRS | ESRR |
| 1.0/.02 | 97.6 | 98.5 | 94.5 | 96.6 |
| 2.0/.04 | 94.2 | 98.9 | 85.6 | 98.0 |
| 3.0/.06 | 89.5 | 99.0 | 55.1 | 98.6 |
| 4.0/.08 | 76.8 | 99.2 | 22.3 | 99.4 |
| 5.0/.10 | 65.4 | 99.6 | 4.2 | 99.4 |
| High exposure probability (.20)/Moderate disease probability in unexposed (.09) | ||||
| N1 = 1,000, N2 = 1,000 | N1 = 5,000, N2 = 5,000 | |||
| RR/ESR | ESRS | ESRR | ESRS | ESRR |
| 1.0/.09 | 94.7 | 96.8 | 94.7 | 96.5 |
| 2.0/.18 | 85.4 | 98.5 | 51.1 | 98.0 |
| 3.0/.27 | 55.9 | 98.5 | 1.8 | 98.6 |
| 4.0/.36 | 17.6 | 99.4 | 0 | 99.4 |
| 5.0/.45 | 2.9 | 99.5 | 0 | 99.4 |
N1 is the sample the overall risk is derived from
N2 is the sample the relative risk is derived from
Relative Risk/Exposure-Specific Risk (RR/ESR) values are the hypothesized values
Italics denote coverage probabilities that did not attain 95%