Table 4 Bisection procedure to determine conditional log-hazard ratio for treatment in a Cox proportional hazards model to produce a time-to-event outcome with a given marginal hazard ratio for treatment (target marginal hazard ratio for treatment: 0.80)
Iteration | Target marginal hazard ratio | \(\gamma_{{}}^{{{\text{midpoint}}}} \,\) | Empirical marginal hazard ratio \({\text{(HR}}_{{{\text{marginal}}}}^{{\gamma_{{}}^{{{\text{midpoint}}}} }} )\) |
|---|---|---|---|
1 | 0.8 | 0 | 0.000354 |
2 | 0.8 | 5 | 2.203321 |
3 | 0.8 | 2.5 | 1.561186 |
4 | 0.8 | 1.25 | 1.114086 |
5 | 0.8 | 0.625 | 0.796174 |
6 | 0.8 | 0.9375 | 0.969266 |
7 | 0.8 | 0.78125 | 0.887425 |
8 | 0.8 | 0.703125 | 0.843299 |
9 | 0.8 | 0.664063 | 0.820148 |
10 | 0.8 | 0.644531 | 0.808168 |
11 | 0.8 | 0.634766 | 0.802396 |
12 | 0.8 | 0.629883 | 0.799151 |