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Definition: Hazard Ratio
Hazard Ratio is a term that describes the probability or the chance of events of a hazard/accident/failure occurring at a group relative to the other. It compares two entities- an experiment group and a control/reference group that act as cause of the events.
Ex: Hazard ratio of machines A and B on two different assembly lines is 2.0. This means the rate of failure at machine A is twice the rate of failure at machine B.
Hazard Ratio= (Rate of failure of the experiment group/ Rate of failure of the control group)
Hazard ratios represent the instantaneous failure rate at a given period, making it starkly different from the relative risk ratios which give the values for a cumulative period. Also, hazard ratios do not give any idea with regard to the actual average failure/hazard rate of any of the groups.
The formula for translating a hazard ratio to a probability is:
Probability = (hazard ratio) / (1 + hazard ratio)
For the above example, the probability would be 1/ (1+2) = 0.33
The confidence interval of a hazard ratio is given by (1-Probability)