Life expectancy difference and life expectancy ratio: two measures of treatment effects in randomised trials with non-proportional hazards.

The hazard ratio (HR) is the most common measure of treatment effect in clinical trials that use time-to-event outcomes such as survival. When survival curves cross over or separate only after a considerable time, the proportional hazards assumption of the Cox model is violated, and HR can be misleading. We present two measures of treatment effects for situations where the HR changes over time: the life expectancy difference (LED) and life expectancy ratio (LER). LED is the difference between mean survival times in the intervention and control arms. LER is the ratio of these two times. LED and LER can be calculated for at least two time intervals during the trial, allowing for curves where the treatment effect changes over time. The two measures are readily interpretable as absolute and relative gains or losses in life expectancy.