What is the difference between a hazard ratio and a relative risk?

Both a hazard ratio (HR) and a relative risk (RR) are measures used to compare the likelihood of an event occurring between two groups. While they are related, they serve different purposes based on how you are measuring time and risk.

Relative Risk (RR)

• The Focus: It compares the probability of an event happening over a fixed period of time.
• How it works: It is calculated as the ratio of the risk in the treatment group to the risk in the control group.
• Best Use: It is most useful for studies where everyone is followed for the exact same amount of time, such as in a trial where you check for a specific outcome (like an infection or a birth defect) at a set endpoint.
• Limitation: It ignores when the event happens. It treats an event happening on day one the same as an event happening on day 100.

Hazard Ratio (HR)

• The Focus: It compares the probability of an event happening at any specific moment in time.
• How it works: It uses "time-to-event" data (survival analysis). It looks at the rate of events occurring over the entire duration of a study, accounting for the fact that participants may enter or leave the study at different times.
• Best Use: It is essential for long-term studies where people drop out or where the event could happen at any time, such as cancer survival trials or heart attack incidence studies.
• The "Hazard": A hazard is not a probability; it is the instantaneous rate at which events occur. If an HR is 0.5, it means that at any given moment, a person in the treatment group is half as likely to experience the event as someone in the control group.

The Key Difference

The easiest way to think about the distinction is time:

• Relative Risk asks: "What is the chance this happens by the end of the study?"
• Hazard Ratio asks: "At any point during the study, how much faster or slower are these events happening?"

In short, RR is static (a snapshot at the end), while HR is dynamic (captures the "velocity" of events throughout the study).