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The hazard ratio in survival analysis is the effect of an explanatory variable on the hazard or risk of an event. In this context, the hazard is the instantaneous probability of the event (such as death) within the next small interval of time, assuming that one has survived to the start of that interval. The hazard ratio then compares the hazard of the event under one condition (e.g., treatment for a disease) with the hazard of the same event under a second (baseline) condition (e.g., placebo) by taking the ratio of one hazard over the other. A hazard ratio greater than 1 indicates an increase in the hazard of the event under the first condition over the hazard of the event under the second condition.

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