Hazard ratio

The instantaneous hazard is the limit of the number of events per unit time divided by the number at risk as the time interval decreases.

<math> h(t) = </math> <math>observed \;events(t)/t \over N(t) </math><p>; where N(t) is the number at risk a the beginning of an interval.<p> The hazard ratio in survival analysisis a summary of the difference between two survival curves, representing the reduction in the risk of death on treatment compared to control, over the period of follow-up. It is a form of relative risk. Proportional hazards regressionmodels (also called Cox regression models after their inventor) assume that the relative risk of death between treatments and controls is constant at each interval of time. These models use a computable algorithm to summarise the relative risks of death across all time intervals into a single figure.
<p><math>O(treatment) /E(treatment) \over O(controls) /E(controls) </math> <p>where O is the observed number of deaths in the specified group, and E the expected number of deaths, based on their condition, but without taking into account any expectation about the treatment.

External link

• http://www.graphpad.com/www/book/compsurv.htm

Reference

• Altman, DG. Practical Statistics for Medical Research. Chapman & Hall. London, 1991. ISBN 0412276305. pp383-4.

Altman on Kaplan-Meier estimator:

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It uses material from the http://en.wikipedia.org/wiki/Hazard+ratio Wikipedia article Hazard ratio.