Question 1

What is the difference between odds ratio and relative risk?

Accepted Answer

Relative risk (RR) = P(outcome|exposed) / P(outcome|unexposed) — the ratio of probabilities. Odds ratio = [P/(1−P) for exposed] / [P/(1−P) for unexposed] — the ratio of odds. When outcomes are rare (<10%), OR ≈ RR. For common outcomes, OR overestimates RR. Use RR for cohort studies; OR for case-control studies and logistic regression.

Question 2

What does an OR of 1 mean?

Accepted Answer

OR = 1 means the exposure has no association with the outcome — the odds are equal in both groups. OR > 1 suggests positive association (exposure increases odds of outcome); OR < 1 suggests negative association (exposure decreases odds). Whether the association is statistically significant depends on the confidence interval.

Question 3

How do I interpret the confidence interval for OR?

Accepted Answer

A 95% CI that does not include 1 indicates statistical significance at the 5% level. For example, OR = 2.5 (95% CI: 1.3–4.8) is statistically significant; OR = 2.5 (95% CI: 0.8–7.2) is not, because the CI includes 1. Wider CIs indicate more uncertainty, often due to small sample sizes.

Question 4

Why is OR preferred in case-control studies?

Accepted Answer

In case-control studies, investigators select participants based on outcome (cases and controls), so disease prevalence in the sample does not reflect true population prevalence. This makes relative risk calculation misleading. Odds ratio is valid regardless of sampling strategy and is equivalent to the OR from a cohort study when outcomes are rare.

Question 5

What is a log-odds and why is it used in logistic regression?

Accepted Answer

Log-odds = ln(OR). Logistic regression models the log-odds as a linear function of predictors. Taking the exponent of a logistic regression coefficient gives the odds ratio for a one-unit increase in that predictor. Log-odds are unbounded (−∞ to +∞), making them mathematically convenient compared to probabilities (0 to 1) or odds (0 to +∞).

Question 6

Can OR be used for any type of study?

Accepted Answer

OR is primarily used in case-control studies and logistic regression. It can be computed for cohort studies, but relative risk is preferred there. OR cannot be computed if any cell in the 2×2 table is zero (add 0.5 to each cell — Haldane-Anscombe correction — as an approximation). It is not appropriate for matched studies without special handling.

	Outcome (+)	No Outcome (−)
Exposed (+)
Unexposed (−)

Odds Ratio Calculator

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2×2 Contingency Table

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