Intended for healthcare professionals

CCBYNC Open access
Research Methods & Reporting

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

BMJ 2017; 357 doi: https://doi.org/10.1136/bmj.j2250 (Published 25 May 2017) Cite this as: BMJ 2017;357:j2250
  1. Hakim-Moulay Dehbi, medical statistician1,
  2. Patrick Royston, medical statistician2,
  3. Allan Hackshaw, medical statistician1
  1. 1Cancer Research UK and UCL Cancer Trials Centre, 90 Tottenham Court Road, London, W1T 4TJ, UK
  2. 2MRC Clinical Trials Unit at UCL, Aviation House, 125 Kingsway Road, London, WC2B 6NH, UK
  1. Correspondence to: H-M Dehbi h.dehbi.11{at}ucl.ac.uk

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.

Summary

  • When survival curves cross over or separate only after considerable time in a trial, the hazard ratio (HR) is not an appropriate summary measure of treatment effect, because the proportional hazards assumption of the Cox model is violated and the HR changes with time

  • Life expectancy difference (LED) and life expectancy ratio (LER) are complementary absolute and relative measures that can be calculated for any shape of survival curves

  • LED is obtained by taking the difference between the mean survival times in the intervention and control arms restricted between two time points, usually the beginning of the trial and the end of follow-up; the LER is the ratio of these two quantities

  • LED and LER have intuitive interpretations as absolute and relative gains or losses in life expectancy due to an intervention

In randomised controlled trials (RCTs), time-to-event endpoints, such as overall survival or time to disease occurrence, are shown as Kaplan-Meier curves. The effect of an intervention compared with a control is …

View Full Text