You may want to read this article first: What is an Odds Ratio?
What is an Adjusted Odds Ratio?
An adjusted odds ratio (AOR) is an odds ratio that controls for other predictor variables in a model. It gives you an idea of the dynamics between the predictors. Multiple regression, which works with several independent variables, produces AORs.
AOR is sometimes called a conditional odds ratio. In epidemiology, it’s sometimes called an Adjusted Disease Odds Ratio (ADOR).
Un-adjusted vs. Adjusted Odds Ratios
Odds ratios can be adjusted, or un-adjusted (also called crude).
In epidemiology, an un-adjusted OR will estimate the relative risk between a certain event in an exposed group with a certain event in an unexposed group.
Adjusted ORs are used to control for confounding bias. The AOR measures the association between a confounding variable and the outcome, and controls for that value.
Adjusted Odds Ratio Example
In real life, it’s rare to have a very clear relationship between a variable and an outcome. As an example, let’s say you were running an experiment on how sex is related to high school exam performance. Although sex may have an effect, it’s likely that many other factors might come into play.
As well as sex (male/female), you might want to control for “family encouragement” or “family income” as those would certainly have a strong effect. You can adjust the crude OR by controlling for family encouragement, or for family income, resulting for an adjusted odds ratio for each variable. You might report them as sex-adjusted odds ratios or family-encouragement-adjusted odds ratios.
Adjusting for multiple variable can be complex, so it’s best to try and control for variables before the experiment starts. In the above example, you might want to select participants from a similar family background, therefore making the “adjustment” before any data collection begins. This is of particular importance in clinical trials, where groups are often chosen for similar ages or health status.
References
Andresen, E. & Bouldin, E. (2010). Public Health Foundations: Concepts and Practices. John Wiley & Sons.
Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.
Meyers, L. et al. (2013). Performing Data Analysis Using IBM SPSS. John Wiley & Sons.
Szumilas, M. Explaining Odds Ratios. J Can Acad Child Adolesc Psychiatry. 2010 Aug; 19(3): 227–229.