Generalized Linear Models (GLM)
What is an odds ratio?
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 ratios are most commonly used in casecontrol studies, however, they can also be used in crosssectional and cohort study designs as well (with some modifications and/or assumptions).
Odds ratios and logistic regression
When a logistic regression is calculated, the regression coefficient (b1) is the estimated increase in the log odds of the outcome per unit increase in the value of the exposure. In other words, the exponential function of the regression coefficient (e^{b1}) is the odds ratio associated with a oneunit increase in the exposure.
When is it used?
Odds ratios are used to compare the relative odds of the occurrence of the outcome of interest (e.g. disease or disorder), given exposure to the variable of interest (e.g. health characteristic, the aspect of medical history). The odds ratio can also be used to determine whether a particular exposure is a risk factor for a particular outcome and to compare the magnitude of various risk factors for that outcome.

OR =1 Exposure does not affect odds of the outcome

OR >1 Exposure associated with higher odds of the outcome

OR <1 Exposure associated with lower odds of the outcome
What about confidence intervals?
The 95% confidence interval (CI) is used to estimate the precision of the OR. A large CI indicates a low level of precision of the OR, whereas a small CI indicates a higher precision of the OR. It is important to note, however, that unlike the pvalue, the 95% CI does not report a measure’s statistical significance. In practice, the 95% CI is often used as a proxy for the presence of statistical significance if it does not overlap the null value (e.g. OR=1). Nevertheless, it would be inappropriate to interpret an OR with 95% CI that spans the null value as indicating evidence for lack of association between the exposure and outcome.
Confounding
When a noncasual association is observed between a given exposure and outcome is as a result of the influence of a third variable, it is termed confounding, with the third variable termed a confounding variable. A confounding variable is causally associated with the outcome of interest, and noncausally or causally associated with the exposure, but is not an intermediate variable in the causal pathway between exposure and outcome (Szklo & Nieto, 2007). Stratification and multiple regression techniques are two methods used to address confounding and produce “adjusted” ORs.
This example illustrates a few important points. First, the presence of a positive OR for an outcome given a particular exposure does not necessarily indicate that this association is statistically significant. One must consider the confidence intervals and pvalue (where provided) to determine significance. Second, while the psychiatric literature shows that overall, depression is strongly linked to suicide and suicide attempt (Kutcher & Szumilas, 2009), in a particular sample, with a particular size and composition, and in the presence of other variables, the association may not be significant.
Understanding odds ratios, how they are calculated, what they mean, and how to compare them is an important part of understanding scientific research.