Odds Ratio

Definition

An odds ratio is the ratio of the odds of an outcome occurring in one group to the odds of it occurring in another group. An odds ratio of 1 indicates no association; values greater than 1 indicate higher odds in the exposure group, while values below 1 indicate lower odds. Odds ratios are the natural effect measure in logistic regression and case-control studies.

Why It Matters

Odds ratios provide a standardised way to compare risks across studies with different baseline rates. They are interpretable regardless of the outcome prevalence, making them the preferred metric in case-control research and meta-analysis. Understanding odds ratios is essential for reading clinical epidemiology, public-health research, and any study with binary outcomes.

Example

A case-control study examines whether smoking is associated with lung cancer. The odds of smoking among cancer patients are 3.5 times the odds of smoking among healthy controls. The odds ratio is 3.5 (95% CI [2.1, 5.8], p < 0.001). This means smokers in this study have 3.5 times the odds of lung cancer compared with non-smokers, after adjusting for age and sex.

Related Terms

• Logistic Regression
• Chi-Square Test
• Confidence Interval
• P-Value
• Effect Size

Software Notes

• SPSS: Analyze > Descriptive Statistics > Crosstabs. Select Risk under Statistics to obtain the odds ratio for 2×2 tables. In logistic regression: Analyze > Regression > Binary Logistic; request CI for exp(B) under Options.
• R: fisher.test(matrix(c(a, b, c, d), nrow = 2)) returns an odds ratio and confidence interval for 2×2 tables. exp(coef(glm(y ~ x, family = binomial, data = df))) extracts odds ratios from logistic regression.
• Stata: cc case exposure or cci 10 20 30 40 for case-control data. logit y x, or reports odds ratios directly from logistic regression.