Ratio and difference of average hazard with survival weight: New measures to quantify survival benefit of new therapy

The hazard ratio (HR) has been the most popular measure to quantify the magnitude of treatment effect on time-to-event outcomes in clinical research. However, the traditional Cox's HR approach has several drawbacks. One major issue is that there is no clear interpretation when the proportional hazards (PH) assumption does not hold, because the estimated HR is affected by study-specific censoring time distribution in non-PH cases. Another major issue is that the lack of a group-specific absolute hazard value in each group obscures the clinical significance of the magnitude of the treatment effect. Given these, we propose average hazard with survival weight (AH-SW) as a summary metric of event time distribution and will use difference in AH-SW (DAH-SW) or ratio of AH-SW (RAH-SW) to quantify the treatment effect magnitude. The AH-SW is interpreted as a person-time incidence rate that does not depend on random censoring. It is defined as the ratio of cumulative incidence probability and restricted mean survival time (RMST), which can be estimated non-parametrically. Numerical studies demonstrate that DAH-SW and RAH-SW offer almost identical power to Cox's HR-based tests under PH scenarios and can be more powerful for delayed-difference patterns often seen in immunotherapy trials. Like median and RMST differences, the proposed approach is a good model-free alternative to the HR-based approach for evaluating the treatment effect magnitude. Such a model-free measure will increase the likelihood that results from clinical studies are correctly interpreted and generalized to future populations.