Hazard Rate

Hazard function(instantaneous failure rate, conditional failure, intensity, or force of mortality function):

The function that describes the probability of failure during a very small time increment (assuming that no failures have occurred prior to that time). Hazard is the slope of the survival curve – a measure of how rapidly subjects are having the event (dying, developing an outcome etc).

Hazard Rate:

It is a time-to-failure function used in survival analysis. It is defined as the probability per time unit that a case that has survived to the beginning of the respective interval will fail in that interval. Specifically, it is computed as the number of failures per time units in the respective interval, divided by the average number of surviving cases at the mid-point of the interval.

Hazard Ratio (Relative Hazard):

Hazard ratio compares two groups differing in treatments or prognostic variables etc. If the hazard ratio is 2.0, then the rate of failure in one group is twice the rate in the other group. The computation of the hazard ratio assumes that the ratio is consistent over time, and that any differences are due to random sampling. Before performing any tests of hypotheses to compare survival curves, the proportionality of hazards assumption should be checked (and should hold for the validity of Cox's proportional hazard models). (See also Log-rank test).