A population was sub-typed into 4 groups and Kaplan-Meier curves were plotted. If there were only two survival curves then the hazard ratio would be the hazard of one group divided by the hazard of the other. How do we find the hazard ratio when there are more than two groups? Does it even make sense to do so?
This depends on what the multiple groups are.
For example, they might be a placebo group and 3 different drugs. Then one might compare each drug with the placebo, and perhaps also each drug versus the other ones.
Alternatively, the groups could be for drug A with history of some disease, without history, placebo with history and without history. In that case, you might be interested in the hazard ratio of drug versus placebo within subgroup, or an overall drug versus placebo one adjusted or stratified for disease history.
It does not make sense to do so. A hazard ratio is, by definition, a measure that compares exactly two groups. If you have K-M survivor curves four groups, say, A, B, C, and D, then you have exactly six possible comparisons which you could make:
- A vs B
- A vs C
- A vs D
- B vs C
- B vs D
- C vs D
For example, you could calculate six different hazard ratios, one for each of these comparisons.