Statistical measure · BEGINNER LESSON
Odds ratio
An odds ratio is a number that compares the odds of an event in one group with the odds of the same event in another group. It is often used to describe how strongly an exposure is associated with an outcome, especially in logistic regression and case-control studies.
What it is and what is measured
Odds are not the same as probability. If an event has probability p, its odds are p divided by (1 - p). An odds ratio (OR) compares the odds in an exposed group with the odds in an unexposed group. Values above 1 mean higher odds with exposure, values below 1 mean lower odds, and 1 means no difference in odds. In a 2 by 2 table, the OR can be written as (a/b)/(c/d), which is also ad/bc. These sources describe the OR as a measure of association between a binary exposure and a binary outcome, and note that it is commonly reported in logistic regression and case-control studies. [1,2]
[2] Odds Ratio - StatPearls - NCBI Bookshelf [3] Overestimation of Relative Risk and Prevalence Ratio - PMC - NIH
How it works and why it is used
The OR summarizes the relation between two groups by comparing odds rather than raw probabilities. This can be useful when the outcome is rare, because the OR then closely approximates the relative risk, also called the risk ratio or prevalence ratio in these sources. Logistic regression often produces ORs because it can adjust for other variables, called covariates, while estimating association between exposure and outcome. [0,1,2]
[1] At Odds: Concerns Raised by Using Odds Ratios for Continuous or ... [2] Odds Ratio - StatPearls - NCBI Bookshelf [3] Overestimation of Relative Risk and Prevalence Ratio - PMC - NIH
When interpretation becomes difficult
For common outcomes, ORs move farther from 1 than the corresponding prevalence ratios or relative risks, so they can make an association look larger than the underlying probability difference. One source explains that for common outcomes such as obesity, the OR may be much more extreme than the prevalence ratio, and another notes that adjusted ORs from logistic regression can overestimate relative risk, sometimes dramatically. Because of that, the OR can be harder to communicate clearly when the event is not rare. [0,2]
[1] At Odds: Concerns Raised by Using Odds Ratios for Continuous or ... [3] Overestimation of Relative Risk and Prevalence Ratio - PMC - NIH
Limitations and practical cautions
These sources warn that dichotomizing a continuous measure, such as turning body mass index into only 'obese' versus 'not obese', loses information and can reduce statistical power. They also note that ORs can be misleading in interaction testing if one subgroup has a more common outcome than another. A confidence interval helps show uncertainty around an estimated OR; if the interval includes 1, the data do not clearly show a positive or negative association at the stated confidence level. [0,1,2]
[1] At Odds: Concerns Raised by Using Odds Ratios for Continuous or ... [2] Odds Ratio - StatPearls - NCBI Bookshelf [3] Overestimation of Relative Risk and Prevalence Ratio - PMC - NIH
SEE THE IDEA
How an odds ratio is used
People or samples with the factor being studied, such as a treatment or environmental condition.
People or samples without that factor.
For each group, event odds are event count divided by non-event count.
The exposed odds divided by the unexposed odds.
Compare the odds in two groups to summarize how strongly the exposure and outcome are associated.
The OR compares odds, not direct probabilities; it is easiest to interpret when the outcome is rare.
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.