Understanding Odds Ratios

Introduction to Odds Ratios

• Frequently used in research, especially medical and health fields.
• Can be confusing without proper explanation.
• Aim: Explain what they mean and how to communicate them effectively.

Probability vs. Odds

• Example using dice:
  • Probability of rolling a six = 1/6 ≈ 17%.
  • Odds of rolling a six = 1/(6-1) = 1/5 = 20%.

Calculating Odds Ratios

• Odds Ratio Basics: Odds in one group divided by odds in another group.
• Example Study (2020): Link between depression and cannabis use.
  • Data approximation:
    • Depressed & cannabis users: 34
    • Depressed & non-users: 187
    • Non-depressed & cannabis users: 132
    • Non-depressed & non-users: 2366

Calculation Steps

1. Odds in Depressed Group: 34/187 ≈ 0.182
2. Odds in Non-Depressed Group: 132/2366 ≈ 0.056
3. Odds Ratio: 0.182 / 0.056 ≈ 3.3

• Published odds ratio adjusted for other factors: 3.16

Interpretation of Odds Ratio

• OR > 1 indicates positive association.
• Cannot establish causation (e.g., depression causing cannabis use).
• Association doesn’t imply causation.

Why Use Odds Ratios?

• Versatile across different study designs (randomized experiments, case-control studies).
• Good mathematical properties.
• Logistic regression allows for adjustment of other influencing factors.

Effective Communication of Odds Ratios

• Translate odds ratios to more understandable formats.
• Example Data Translation: Basic Percentages
  • Depressed group: 34/221 ≈ 15% are daily cannabis users.
  • Non-depressed group: 132/2498 ≈ 5% are daily cannabis users.
  • Relative risk: 15% / 5% = 3 (similar to OR in rare events).

Moving Beyond Percentages

• Use