Hi! Odds Ratio or Adjusted Odds Ratio? Adjusted Odds Ratio is super-complicated, since it adjusts the OR for any number of confounding factors (like when you read in an article, "after adjusting for lifestyle, age, and previous history of cancer..."). Honestly, it is calculated by plugging the numbers into a computer program like SPSS! The important things to know about adjusted odds ratio are:
what it means in general (i.e., the OR adjusted for confounding factors),
that it is the closest thing to Relative Risk that can be calculated from some studies (case control, meta-analysis), and
that, like the unadjusted OR, it only approximates RR when the incidence of the outcome (or prevalence of the disease) is low.
You can see in this figure from a JAMA article that the greater the incidence, the more different the RR is from the OR:
Interpreting adjusted OR is just like interpreting OR: if it's greater than one, the event is more likely to happen than not; if it's less than one, then the event is less likely to happen than not. Remember that the OR for the other outcome is the inverse, so if the OR is 4.0 for outcome X over not-X, then the OR is 0.25 for outcome not-X over X.
Odds Ratio and Relative Risk are on p. 52 in FA 2011 (p. 54 in 2010). Hope that helps!
If you are analyzing risk data where exposed/unexposed is on the x-axis and cases/non-cases are on the Y-axis (such that A=Exposed Cases, B=Unexposed Cases,C=Exposed Non-Cases, and D=Unexposed Non-Cases)