Odds Ratio (OR)

Authors
Affiliations

Doctor of Physical Therapy

B.S. in Kinesiology

Doctor of Physical Therapy

B.A. in Neuroscience

Definition

  • Odds ratio (OR) is defined as “the ratio of the exposure odds among the case group to the exposure odds among the control group”
  • The odds ratio (OR) is a measure of how strongly an event is associated with exposure.
  • Odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure

I like to think of odds ratio as the reverse of an RCT

In an RCT, we compare the experimental and control group, which only differ by the independent variable. Then the results are measured using dependent variables

An odds ratio compares two groups of people who only differ based on exposure. You could think of exposure as the “independent variable.” When viewing the results, you could view the exposure rates as the “dependent variables.” Thus when comparing the two using an odds ratio, you are trying to ascertain whether the exposure was statistically significant in outcome rates.

Practical use:

  • Odds ratios commonly are used to report case-control studies

Calculation

  • The odds ratio (OR) is a measure of how strongly an event is associated with exposure.
  • OR = odds that a case was exposed / Odds that a control was exposed
  • The odds ratio is a ratio of two sets of odds: the odds of the event occurring in an exposed group versus the odds of the event occurring in a non-exposed group
Disease (Case) No Disease (Control)
Exposed A B
Unexposed C D

Interpretation

To interpret the OR, you need to first determine what part of the test is considered the “exposure” and what part of the test is the “outcome.”

OR Value Interpretation
<1 Odds of disease lower with exposed than non-exposed
1 No difference in odds of disease
>1 Odds of disease greater in exposed than non-exposed
Example
  • An odds ratio of 0.98 indicates that the group who were exposed to the variable were 2% less likely to have the outcome.
  • An odds ratio of 1.02 indicates that the group who was exposed to the variable were 2% more likely to have the outcome.

Example

2x2 Contingency Table
Exposure Present Absent Total
Present A
(90)
B
(210)
A + B
(300)
Absent C
(350)
D
(350)
C + D
(700)
Total A + C
(440)
B + D
(760)
A + B + C + D
(1000)

How to calculate the Odds Ratio for the contingency table: Relative Risk=A(C)B(D)=90350/210350=0.260.6=0.43

Based on the results of the odds ratio calculation (0.43) we can conclude:

  • The exposed group has 0.43 times the odds of of exposure to the outcome compared to the control group.
  • The case group is 57% less likely to have the exposure compared to the control group

Videos

References

1.
Roberts MR, Ashrafzadeh S, Asgari MM. Research Techniques Made Simple: Interpreting Measures of Association in Clinical Research. The Journal of Investigative Dermatology. 2019;139(3):502-511.e1. doi:10.1016/j.jid.2018.12.023

Citation

For attribution, please cite this work as: