A hazard ratio is the ratio of two hazard functions where a hazard function describes the chances of an event occurring within a group at a particular time. It’s commonly used to evaluate the effect of a particular drug on a disease. The hazard ratio may also be used to measure the effect of making a mechanical component out of a given material. You can calculate the hazard ratio by plotting the two hazard functions.
Establish the study groups. For example, you might want to test a drug’s effect on a specific disease. In this case, you would typically divide patients with the disease into two groups. The test group will receive the drug and the control group will receive a placebo (sugar pill).
Create the chart for the hazard function on graph paper. The horizontal line will represent time and the vertical line will represent the number of events that occur during each time period. This event should be something that occurs once to each member of the group, such as a fatality.
Plot the hazard function. For each time interval during the test period on the horizontal axis, mark the total number of deaths on the vertical axis. Perform this procedure for both study groups.
Divide the value of the hazard function for the test group by the value of control group to get the hazard ratio. Values less than 1 indicate the drug improved patient longevity and values greater than 1 mean that the drug impaired patient longevity.
Graph the hazard ratio over the test period. Typically, you will then estimate the hazard ratio function with a mathematical function.