Table 4.
Coverage probability of the 95% confidence interval for the revised product-based estimator (ESRR) using a binomial variance
| Low exposure probability (.05)/Low disease probability in unexposed (.02) | |||||||
|---|---|---|---|---|---|---|---|
| RR/ESR | |||||||
| Sample Size (N1/N2) |
1.0/.02 | 1.5/.03 | 2.0/.04 | 2.5/.05 | 3.0/.06 | 4.0/.08 | 5.0/.10 |
| 1,000/1,000 | 66.1 | 78.1 | 83.2 | 87.1 | 89.6 | 88.9 | 90.0 |
| 1,000/5,000 | 98.9 | 99.3 | 99.6 | 99.7 | 99.9 | 99.5 | 99.5 |
| 5,000/1,000 | 54.4 | 60.6 | 61.2 | 62.3 | 63.5 | 64.9 | 65.0 |
| 5,000/5,000 | 90.0 | 92.8 | 92.8 | 93.7 | 92.4 | 94.4 | 94.8 |
| Low exposure probability (.05)/Moderate disease probability in unexposed (.09) | |||||||
| RR/ESR | |||||||
| Sample Size (N1/N2) |
1.0/.09 | 1.5/.14 | 2.0/.18 | 2.5/.23 | 3.0/.27 | 4.0/.36 | 5.0/.45 |
| 1,000/1,000 | 90.4 | 91.6 | 93.2 | 92.4 | 92.2 | 92.0 | 91.5 |
| 1,000/5,000 | 99.9 | 100 | 100 | 100 | 99.9 | 99.7 | 99.3 |
| 5,000/1,000 | 62.8 | 63.8 | 63.9 | 63.7 | 62.1 | 61.6 | 62.7 |
| 5,000/5,000 | 93.8 | 93.4 | 94.2 | 93.5 | 93.7 | 93.6 | 91.6 |
| High exposure probability (.20)/Low disease probability in unexposed (.02) | |||||||
| RR/ESR | |||||||
| Sample Size (N1/N2) |
1.0/.02 | 1.5/.03 | 2.0/.04 | 2.5/.05 | 3.0/.06 | 4.0/.08 | 5.0/.10 |
| 1,000/1,000 | 89.1 | 91.2 | 91.8 | 92.6 | 91.5 | 92.5 | 93.8 |
| 1,000/5,000 | 99.7 | 99.1 | 99.4 | 99.0 | 98.0 | 98.8 | 98.1 |
| 5,000/1,000 | 63.9 | 68.0 | 64.7 | 69.3 | 70.7 | 70.5 | 71.9 |
| 5,000/5,000 | 92.1 | 94.0 | 95.1 | 94.8 | 94.3 | 94.5 | 93.5 |
| High exposure probability (.20)/Moderate disease probability in unexposed (.09) | |||||||
| RR/ESR | |||||||
| Sample Size (N1/N2) |
1.0/.09 | 1.5/.14 | 2.0/.18 | 2.5/.23 | 3.0/.27 | 4.0/.36 | 5.0/.45 |
| 1,000/1,000 | 92.5 | 93.2 | 95.1 | 94.5 | 92.6 | 90.7 | 86.7 |
| 1,000/5,000 | 99.9 | 99.7 | 98.9 | 98.8 | 98.2 | 97.3 | 95.5 |
| 5,000/1,000 | 66.0 | 68.3 | 69.7 | 69.0 | 64.4 | 66.6 | 66.0 |
| 5,000/5,000 | 94.0 | 94.0 | 93.2 | 94.0 | 91.9 | 92.0 | 88.9 |
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%