Hazard function: The risk which an individual experiences an event in a small time interval, given that the individual has survived up to the starting of the interval.

It is the measure of how likely an individual is to experience the event as a function of time.

Generally denoted h(t), the function can be given in terms of the probability distribution of the survival times f (t) and the survival function S(t), as h(t)= f (t)/S(t). The hazard function might remain constant, increase, decrease or take on some much more complex shape. The function can be expected as the proportion of the individuals experiencing an event in the interval per unit time, provided that they have survived to the beginning of the interval,

 
Care is required in the interpretation of the hazard function because of both the selection effects due to dissimilarity between the individuals and variation within each individual over time. For instance, individuals with a high risk are more prone to experience an event soon, and those remaining at risk will tend to be the selected group with a lower risk. This will result in hazard rate being 'pulled down' to an increasing extent as the time passes.