Risk ratio

Definition

A comparison of the risk between a treatment group and a placebo group. Also known as relative risk.

“How many times higher is the risk of the outcome among people who are exposed to the risk factor?”

The risk for the exposed group would be $\frac{B}{A+B}$
The risk for the unexposed group would be $\frac{D}{C+D}$

Then the risk ratio would be: $\frac{\frac{B}{A+B}}{\frac{D}{C+D}}$

Interpretation

If the relative risk (RR):

• …is equal to 1 then the risk are the same
• … is greater than 1, the treatment group has more risk
• … is less than 1, the treatment group has less risk

Transformed

Seems that most of the time, the risk ratio is often logged as it takes a normal distribution. Here, no change in the relative ratio when logged should be 0.

Confidence interval

Calculated through the Delta method:

Example

General Notes

• Don't confuse it with Odds ratio

Usage

Vaccine efficacy

One way to calculate Vaccine efficacy is:

where RR is relative risk.

Reference