1. What is Odds Ratio?

The odds ratio (OR) is a measure of association between an exposure and an outcome. It 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.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \beta \) — Coefficient from logistic regression
• \( e \) — Euler's number (~2.71828)

Explanation: The odds ratio is calculated by exponentiating the logistic regression coefficient. This converts the log-odds from the regression output to a more interpretable odds ratio.

3. Interpretation of Odds Ratio

Details:

• OR = 1: No association
• OR > 1: Positive association (increased odds)
• OR < 1: Negative association (decreased odds)

The further from 1, the stronger the association.

4. Using the Calculator

Tips: Enter the coefficient (β) from your logistic regression model. The coefficient can be positive or negative, representing the direction of the relationship.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between odds ratio and relative risk?
A: Odds ratio compares odds, while relative risk compares probabilities. OR is used in case-control studies, while RR is used in cohort studies.

Q2: When should I use odds ratio?
A: OR is commonly used in logistic regression, case-control studies, and when outcome is rare (<10%).

Q3: How do I get the coefficient for this calculation?
A: The coefficient comes from logistic regression output in R (glm function) or other statistical software.

Q4: What does an OR of 2.5 mean?
A: The odds of the outcome are 2.5 times higher in the exposed group compared to unexposed.

Q5: Can odds ratio be less than 1?
A: Yes, an OR < 1 indicates a protective effect (reduced odds of outcome with exposure).