# 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

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.

## Critical Care

Compendium

##### Chris Nickson

Chris is an Intensivist and ECMO specialist at the Alfred ICU in Melbourne. He is also the Innovation Lead for the Australian Centre for Health Innovation at Alfred Health and Clinical Adjunct Associate Professor at Monash University. He is a co-founder of the Australia and New Zealand Clinician Educator Network (ANZCEN) and is the Lead for the ANZCEN Clinician Educator Incubator programme. He is on the Board of Directors for the Intensive Care Foundation and is a First Part Examiner for the College of Intensive Care Medicine. He is an internationally recognised Clinician Educator with a passion for helping clinicians learn and for improving the clinical performance of individuals and collectives.

After finishing his medical degree at the University of Auckland, he continued post-graduate training in New Zealand as well as Australia’s Northern Territory, Perth and Melbourne. He has completed fellowship training in both intensive care medicine and emergency medicine, as well as post-graduate training in biochemistry, clinical toxicology, clinical epidemiology, and health professional education.

He is actively involved in in using translational simulation to improve patient care and the design of processes and systems at Alfred Health. He coordinates the Alfred ICU’s education and simulation programmes and runs the unit’s education website, INTENSIVE.  He created the ‘Critically Ill Airway’ course and teaches on numerous courses around the world. He is one of the founders of the FOAM movement (Free Open-Access Medical education) and is co-creator of litfl.com, the RAGE podcast, the Resuscitology course, and the SMACC conference.

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