A bias correction method for hazard ratio estimation and its inference in a multiple-arm clinical trial

A randomized clinical trial with multiple experimental groups and one common control group is often used to speed up development to select the best experimental regimen or to increase the chance of success of clinical trials. Most of the time, multiple dose levels of an experimental drug or multiple combinations of one experimental drug with other drugs comprise multiple experimental groups. Because the experimental drug appears in multiple comparisons with a shared control group, multiple testing adjustments to control the family-wise type I error rate are needed. We extend the stepwise over-correction (SOC) method that is applied to a multi-arm trial with a response rate as its endpoint to a multi-arm trial where time to event is the primary endpoint and confidence interval of the hazard ratio determines the statistical significance. We provide the formula of the bias of the maximum treatment effect estimate toward the true treatment effect between the selected experimental group and the shared control group. We aim to use the bias-corrected estimate for the inference of treatment effects in multi-arm trials on the full alpha level and demonstrate a completely new type of reject region. This approach does not require us to split alpha level among the multiple comparisons or to specify the test order ahead of time. The type I error control and the power enhancement of the proposed approach are both held.