Odds vs Risk: Mastering the Odds Ratio for Clinical and Epidemiological Insights

🎯 What Are Odds?

The Core Idea

Odds are the ratio of the chance something happens to the chance it doesn’t happen.It’s not the same as probability or risk.

จริง ๆ คนไทยใช้คำนี้บ่อย คือ "หมอคิดว่า 50 50"

aka. "หมอคิดว่า odd = 1" ทั้ง 2 แบบความหมายเดียวกัน

📌 Odds are less intuitive than risk, but they’re crucial in case-control studies and logistic regression.

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⚖️ Odds vs. Risk: Know the Distinction

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🔢 Odds Ratio (OR): Relative Odds Between Two Groups

If you want to compare odds between two groups (e.g., exposed vs. unexposed), you use:

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🧠 Derivation From 2x2 Table

	Disease +	Disease –
Exposed	A	B
Unexposed	C	D

So:

🔍 This is often how OR is calculated in case-control studies — because risk is not computable (no denominator for total exposed/unexposed).

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🔄 OR in Logistic Regression

If you model an outcome using logistic regression, the exponentiated coefficient is the Odds Ratio:

This is why logistic regression is used in cross-sectional and case-control studies: it estimates relative odds, not absolute risks.

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🔬 Clinical Interpretation

• OR = 1 → no association

• OR > 1 → exposure increases odds of disease

• OR < 1 → exposure decreases odds of disease

⚠️ When outcome is rare (e.g., <10%), OR ≈ Risk Ratio (RR). But when common, OR overstates the association.

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🏁 Key Takeaways

Odds = P / (1 – P)

Odds Ratio = relative odds of event between groups

• Odds ≠ Risk, especially when the outcome is common.

• Use Odds Ratio when working with case-control data or logistic models.

• For rare outcomes, OR ≈ RR — but don’t confuse them.

• OR answers: “How much more likely (in odds) is the outcome in the exposed vs unexposed?”