Statistics - explanations and formulas

Hazard Ratio

The hazard ratio is an expression of the hazard or chance of events occurring in the treatment arm as a ratio of the hazard of the events occurring in the control arm. The term hazard ratio is often used interchangeably with the term relative risk ratio to describe results in clinical trials. This is not strictly correct as there are subtle and important differences. It is useful to understand the meaning of the term and also be able to identify when it is used appropriately. Hazard ratios are increasingly used to express effects in studies comparing treatments when statistics which describe time-to-event or survival analyses are used. Hazard ratios define instantaneous risk over the study time period and indicate the relative likelihood of the measured event in treated versus control subjects at any given point in time but over a period of time (whereas Relative Risks are cumulative over an entire study, using a defined endpoint.

  • HR equal to 1 implies that the event (harm) is equally probable in both groups (experimental and control group). A HR >1 implies that the event is more likely in the first group (experimental). A HR <1 implies that the event (Harm) is less likely in the first group (experimental)

Reference: Duerden M,  What are hazard ratios? Accessed 1/14/14 at