There is a multi-arm study, which reported HR and its 95% CI for arm A, arm B, arm C vs. control, respectively.(Example data line 1-3, SFC/Salmeterol/Fluticasone vs. Placebo)
Question 1: how to calculate HR and its 95% for the rest pairwise comparisons? e.g. SFC vs. Salmeterol, SFC vs. Fluticasone, Salmeterol vs. Fluticasone.
I think that HR is a relative effect, therefore HR(SFC vs. Salmeterol) should be equal to HR(SFC vs. Placebo)/HR(Salmeterol vs. Placebo), which seems to be correct. But I don't how to calculate its 95%CI.
Question 2: Similar to the first question. If I reverse the comparison, e.g. Placebo vs. SFC. Is it simply calculated as 1/HR, 1/95%LL and 1/95%UL?
The questions are naive. But I cannot find a clear explanation on them. Could you please help me with it? Thank you!
Example data:
| comparison | base | HR | 95%LL | 95%UL | logHR | selogHR |
|---|---|---|---|---|---|---|
| SFC | Placebo | 0.811 | 0.670 | 0.982 | -0.209 | 0.098 |
| Salmeterol | Placebo | 0.857 | 0.710 | 1.035 | -0.154 | 0.096 |
| Fluticasone | Placebo | 1.056 | 0.883 | 1.264 | 0.055 | 0.092 |
| SFC | Salmeterol | 0.946 | 0.777 | 1.151 | -0.056 | 0.100 |
| SFC | Fluticasone | 0.768 | 0.636 | 0.927 | -0.264 | 0.096 |