Table 2.
Examples of differences among population rate ratios and the odds-ratio estimands in case-control studies*
| Hazard ratio in each interval | Rate of new exposure in each interval | Outcome-rate ratio | Matched odds ratio estimand | Unmatched odds ratio estimand | Final proportion unexposed |
|---|---|---|---|---|---|
| 0.4, 0.4, 0.4 |
0, 0, 0 |
0.40 |
0.40 |
0.40 |
0.79 |
| 0.4, 0.4, 0.4 |
0.1, 0.5, 0.1 |
0.40 |
0.40 |
0.43 |
0.39 |
| 0.4, 0.4, 0.4 |
0.1, 0.1, 0.1 |
0.40 |
0.40 |
0.41 |
0.58 |
| 2.5, 2.5, 2.5 |
0, 0, 0 |
2.50 |
2.50 |
2.50 |
0.82 |
| 2.5, 2.5, 2.5 |
0.1, 0.5, 0.1 |
2.50 |
2.50 |
2.31 |
0.42 |
| 2.5, 2.5, 2.5 |
0.1, 0.1, 0.1 |
2.50 |
2.50 |
2.46 |
0.61 |
| 0.8. 0.4, 0.2 |
0, 0, 0 |
0.47 |
0.47 |
0.47 |
0.79 |
| 0.8. 0.4, 0.2 |
0.1, 0.5, 0.1 |
0.39 |
0.44 |
0.45 |
0.39 |
| 0.8. 0.4, 0.2 |
0.1, 0.1, 0.1 |
0.42 |
0.44 |
0.44 |
0.58 |
| 1.25, 2.5, 5.0 |
0, 0, 0 |
2.83 |
2.84 |
2.85 |
0.82 |
| 1.25, 2.5, 5.0 |
0.1, 0.5, 0.1 |
3.34 |
3.02 |
2.61 |
0.43 |
| 1.25, 2.5, 5.0 | 0.1, 0.1, 0.1 | 3.11 | 3.01 | 2.88 | 0.62 |
*In all examples, intervals are one week each and the rates are per person-week; the initial proportion unexposed is 0.8; the outcome-event rate in the unexposed is 0.025 cases per person-week; and individuals are removed from risk when the outcome occurs.