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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

From: Evaluation of exposure-specific risks from two independent samples: A simulation study

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
  1. N1 is the sample the overall risk is derived from
  2. N2 is the sample the relative risk is derived from
  3. Relative Risk/Exposure-Specific Risk (RR/ESR) values are the hypothesized values
  4. Italics denote coverage probabilities that did not attain 95%