Odds Ratio vs. Risk Ratio

"The odds of winning are 1 to 4." "The probability of winning is 20%."

These sound similar. In science, they are very different.

Probability (Risk)

Probability is: Events / Total People. If 1 out of 5 people get sick, the risk is 1/5 = 0.2 (20%).

Odds

Odds are: Events / Non-Events. If 1 person gets sick and 4 do not, the odds are 1/4 = 0.25.

The Trap

When events are rare, Risk and Odds are almost the same. Risk: 1/100 = 0.01. Odds: 1/99 = 0.0101.

But when events are common, they diverge wildly.

Imagine a disease that affects 80 out of 100 people. Risk: 80/100 = 0.8 (80%). Odds: 80/20 = 4.0.

The Odds Ratio (OR)

Scientists often use the Odds Ratio because it is easier to calculate in some studies (like case-control studies).

But journalists interpret it as Risk.

If a study says "The Odds Ratio is 4," a journalist writes "The risk is 4 times higher!"

If the disease is common, this is a lie. The risk might only be 1.2 times higher.

The Diagnosis

If a paper reports an Odds Ratio, be careful.

If the outcome is rare (<10%), it's fine. If the outcome is common (>10%), the Odds Ratio exaggerates the effect. It makes the drug look better (or the danger look worse) than it really is.