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 following formulas:

Where:

• \( a \) — Exposed with outcome
• \( b \) — Exposed without outcome
• \( c \) — Unexposed with outcome
• \( d \) — Unexposed without outcome
• \( t \) — t-statistic (log(OR)/SE)
• \( df \) — Degrees of freedom (a+b+c+d-4)

Explanation: The odds ratio compares the odds of the outcome in two different groups, while the p-value assesses the statistical significance of this association.

3. Interpretation of Results

Details: An OR of 1 means no association. OR > 1 suggests increased odds of outcome with exposure. OR < 1 suggests reduced odds. The p-value indicates whether this association is statistically significant (typically p < 0.05).

4. Using the Calculator

Tips: Enter the counts in each of the four categories (a, b, c, d). All values must be non-negative integers, and at least one of b or d must be positive.

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. They're similar when outcomes are rare but diverge for common outcomes.

Q2: When should I use odds ratio?
A: OR is commonly used in case-control studies where relative risk can't be calculated directly.

Q3: What does a p-value < 0.05 mean?
A: It suggests the observed association is unlikely to be due to chance alone (less than 5% probability if no true association exists).

Q4: How do I interpret confidence intervals for OR?
A: If the 95% CI doesn't include 1, the association is statistically significant at p < 0.05 level.

Q5: What are limitations of odds ratio?
A: OR can overestimate risk for common outcomes, and doesn't provide information about absolute risk.