Hazard Ratio, Median Ratio and Kaplan-Meier Curves

Reviewed and revised 26 August 2015

OVERVIEW

  • Time-to-event curves analyzed by Cox proportional hazards regression are useful for analysing events occurring over time
  • uses all available information, including patients who fail to follow up or reach the endpoint (censored data)
  • These data are commonly depicted with a Kaplan-Meier curve
  • if viewed as a race, the hazard ratio quantifies ‘the odds of winning the race’ whereas the median ratio quantifies the ‘margin of victory’ of the treatment

COX PROPORTIONAL REGRESSION MODEL

  • used for time-to-event analysis (alternatives include log-rank and Wilcoxon two-sample test)
  • provides an estimate of the hazard ratio and its confidence interval
  • avoids bias from loss to follow up
  • can incorporate information about subjects that may change over time (time-dependent covariates)
  • avoids loss of clinically important information by only analysing data at one point in time (e.g. the end of a trial)

HAZARD RATIO

  • a hazard rate is the rate at which a particular event happens
  • the hazard ratio = treatment hazard rate/placebo hazard rate
  • i.e. the ratio of the particular event taking place in treatment group compared to control group
  • need to interpret hazard ratio alongside a measure of time
  • used to reflect time survived to an event
  • does not indicate how fast something occurs
  • commonly used when presenting data from a clinical trial (not the same as a relative risk ratio)

Interpretation

  • quantifies ‘the odds of winning the race’ not the margin of victory (see median ratio)
  • hazard ratio of 1 = equal event rate between groups
  • hazard ratio of 2 = twice as many patients in the active group will have the event compared to the control in the next unit of time
  • hazard ratio of 0.5 = half as many patients in the active group are having the event compared to the control in the next unit of time

MEDIAN RATIO

  • time-to-event curves can be constructed which allows the ratio of median times between treatment and placebo to be used to measure the magnitude of benefit to patients
  • median ratio = placebo median time/treatment median time
  • quantifies the ‘margin of victory’ of the treatment (see hazard ratio)

KAPLAN-MEIER CURVE

  • length of time from study entry to disease end-point for a treatment and control group
  • from this curve, we can derive:

-> median time (time at which 50% of cases resolve)
-> mean time (average resolution time)

  • allows comparisons of patients throughout study and provides information on patients who may be lost to follow up

References and Links

Journal articles

  • Spruance SL, Reid JE, Grace M, Samore M. Hazard ratio in clinical trials. Antimicrob Agents Chemother. 2004 Aug;48(8):2787-92. PMC478551.

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Critical Care

Compendium

Chris is an Intensivist and ECMO specialist at The Alfred ICU, where he is Deputy Director (Education). He is a Clinical Adjunct Associate Professor at Monash University, the Lead for the  Clinician Educator Incubator programme, and a CICM First Part Examiner.

He is an internationally recognised Clinician Educator with a passion for helping clinicians learn and for improving the clinical performance of individuals and collectives. He was one of the founders of the FOAM movement (Free Open-Access Medical education) has been recognised for his contributions to education with awards from ANZICS, ANZAHPE, and ACEM.

His one great achievement is being the father of three amazing children.

On Bluesky, he is @precordialthump.bsky.social and on the site that Elon has screwed up, he is @precordialthump.

| INTENSIVE | RAGE | Resuscitology | SMACC

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