Odd's Ratio

  • ODDS:The probability that an event will occur divided by the probability that the event will not occur
  • Odds = Probability/(1-probability)
  • RATIO:Is the number (a) of observations in a given group with a given characteristic ( such as having an MI) divided by the number (b) of observations without the given characteristic (such as not having MI). v ODDS RATIO: Is the ODDS that a patient is exposed to the risk factor divided by the ODDS that a control is exposed
Odd ratio in case control study:
    Case control
    Exposed a b
    unexposed c d
  • Odd of exposure among the cases : a/c
  • Odd of exposure among the control: b/d
  • Therefore Exposure odd ratio is: a/c ⁄b/d
a/c = ad
b/d bc

  • In a case control study, the most characteristic feature is odd's ratio 
Odds ratio in cohort study:
Outcome YES Outcome No
Exposed a b
unexposed c d
  • Odd of outcome among exposed=a/b
  • Odd of outcome among unexposed=c/d
Odd ratio= a/b = ad/bc

  • Odds ratio can be calculated in a cohort study and in a case-control study.
  • The exposure odds ratio is equal to the disease odds ratio.
  • Relative risk can only be calculated in a cohort study.
  • Odds ratio can be a measure of relative risk in case control study.
Odds ratio is a measure of true relative risk when:
  • The outcome is relatively rare. ( prevalence is 10% or less in general population)
  • The cases must be representative of the cases in the population.
  • The controls must be representative of the controls in the population
Interpretation of odds ratio (OR) :
  • OR of >1 indicates that the exposure is associated with an increased risk of developing the disease.
  • OR of Closer the value of OR to 0 greater the protection.
  • The OR will rarely equal to 1 in absence of true risk or protection
Uses of OR
  • OR are appropriate measure of RR in case control studies.
  • OR are commonly used in meta analysis.
  • Odds ratio is the measure of the strength of the association between risk factor and outcome.
  • OR are the output of logistic regression analysis.
  • OR exaggerate RR in common outcomes(prevalence>10). 
  • In those cases if OR >1 it is larger than the true RR and conversely if OR
Exam Question
  • In a study done to establish Smoking as a risk factor for a disease, 30 out of 50 smokers developed the disease while 10 out of 50 non-smokers developed the disease. Odd's ratio is 6
  • Odds ratio is related to Relative risk
  • Odds = Probability/(1-probability)
  • Using case control study only odds ratio can be calculated.
  • Association can be measured by odds ratio
  • In a case control study, the most characteristic feature is odd's ratio
  • Odds ration is designated as ad/bc

Don't Forget to Solve all the previous Year Question asked on Odd's Ratio