# Odds ratio

Reviewed and revised 26 August 2015

OVERVIEW

• An odds ratio (OR) is a measure of association between an exposure and an outcome.
• The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.
• odds are different to probability — odds is the ratio of the probability that the event of interest occurs to the probability that it does not
• don’t confuse odds with probability, and don’t confuse odds with odds ratio!
• odds ratio is not as intuitive as relative risk

USE OF ODDS RATIO

odds ratio gives an indication of the strength of association between groups

• commonly used in meta-analysis
• must be used in case-control studies rather than relative risk (RR) as there is no information on the numbers of all exposed and non-exposed
• used in logistic regression

CALCULATION

• the odds of the disease in exposed over the odds of the non-exposed

OR = odds of disease in exposed / odds of disease in the non-exposed

= (a/b) / (c/d)

INTERPRETATION

• OR is not equivalent to risk
• OR is approximately the same as the relative risk (RR) when the outcome is rare (approx <10%)
• OR <1 tends to underestimate RR, OR >1 tends to overestimate RR; degree of mis-estimation increases at higher base event rates
• OR of 1 means no association
• if OR is reported with a CI which includes 1 then the OR is not significant

Journal articles

• Bland JM, Altman DG. Statistics notes. The odds ratio. BMJ. 2000 May 27;320(7247):1468. PMC1127651.
• Pepe MS, Janes H, Longton G, Leisenring W, Newcomb P. Limitations of the odds ratio in gauging the performance of a diagnostic, prognostic, or screening marker. Am J Epidemiol. 2004 May 1;159(9):882-90. PMID: 15105181.
• Szumilas M. Explaining odds ratios. J Can Acad Child Adolesc Psychiatry. 2010 Aug;19(3):227-9. PMC2938757.
• CSM — BMJ Statistics Notes
• When can odds ratios mislead? BMJ 1998;316:989

## Critical Care

Compendium

##### Chris Nickson

Chris is an Intensivist and ECMO specialist at the Alfred ICU in Melbourne. He is also a 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 three amazing children.