Comparing relative risks in two risk groups
| COBRA trial | CSA+MTX trial | |||
|---|---|---|---|---|
| Low baseline risk | High baseline risk | Low baseline risk | High baseline risk | |
| *Values obtained by taking the natural logarithm; †the SE (log (RR)) can be calculated as follows: SE (log (RR)) = √(1/A − 1/(A+C) + 1/B − 1/(B+D)), in which A, B, C and D refer to the raw numbers in the 2×2 tables (tables 2.1 and 2.2); ‡CI, confidence interval. | ||||
| 1. RR | 0.46 | 0.70 | 0.50 | 0.63 |
| 2. log (RR)* | −0.7765 (E1) | −0.3567 (E2) | −0.6931 (E1) | −0.4620 (E2) |
| 3. SE (log (RR))† | 0.4081 | 0.1692 | 0.3598 | 0.2178 |
| Difference between the logarithms of relative risks: | ||||
| 4. d ( = E1– E2) | −0.4198 | −0.2311 | ||
| 5. SE (d) | = √(0.40812+0.16922) = 0.4419 | 0.4206 | ||
| 6. CI (d)‡ | = −0.4198±1.96×0.4419, or: | −1.0555 to 0.5933 | ||
| −1.2859 to 0.4463 | ||||
| 7. Test of interaction | z = −0.4198/0.4419 = 0.95 (p = 0.17) | z = −0.55 (p = 0.29) | ||
| Ratio of relative risks (ratio): | ||||
| 8. Ratio = exp(d) | = exp (−0.4198) = 0.66 | 0.79 | ||
| 9. CI (ratio) | = exp (−1.2859) to exp(0.4463), or: | 0.35 to 1.81 | ||
| 0.28 to 1.56 | ||||