Hazard ratio
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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. For a less technical definition than is provided here, consider hazard ratio to be an estimate of relative risk and see the explanation on that page.
The instantaneous hazard rate is the limit of the number of events per unit time divided by the number at risk as the time interval decreases.
where N(t) is the number at risk at the beginning of an interval.
The hazard ratio is the effect on this hazard rate of a difference, such as group membership (for example, treatment or control, male or female), as estimated by regression models which treat the log of the hazard rate as a function of a baseline hazard h0(t) and a linear combination of explanatory variables:
Such models are generally classed proportional hazards regression models (they differ in their treatment of h0(t), the underlying pattern the hazard rate over time), and include the Cox semi-parametric proportional hazards model, and the exponential, Gompertz and Weibull parametric models.
For two individuals who differ only in the relevant membership (e.g. treatment vs control) their predicted log-hazard will differ additively by the relevant parameter estimate, which is to say that their predicted hazard rate will differ by eβ, i.e. multiplicatively by the anti-log of the estimate. Thus the estimate can be considered a hazard ratio, that is, the ratio between the predicted hazard for a member of one group and that for a member of the other group, holding everything else constant.
For a continuous explanatory variable, the same interpretation applies to a unit difference.
Other hazard rate models have different formulations and the interpretation of the parameter estimates differs accordingly.
See also
- Survival analysis
- Failure rate and Hazard rate
- Proportional hazards models
- Odds ratio
- Relative risk ratio
External links
- http://www.graphpad.com/www/book/compsurv.htm
- Spruance et al.. Hazard Ratio in Clinical Trials <http://aac.asm.org/cgi/content/full/48/8/2787>
References
- Altman, DG. Practical Statistics for Medical Research. Chapman & Hall. London, 1991. ISBN 0-412-27630-5. pp383-4.
- Altman on Kaplan-Meier estimator
Acknowledgement and Attribution Regarding Sources of Content
Some of the initial content on this page may be incorporated in part from copyleft sources in the public domain including wikis such as Wikipedia and AskDrWiki. Drug information for patients came from the The National Library of Medicine. Infectious disease information may have come from the Centers for Disease Control (CDC). Differential Diagnoses are drawn from clinicians as well as an amalgamation of 3 sources: 1.The Disease Database; 2. Kahan, Scott, Smith, Ellen G. In A Page: Signs and Symptoms. Malden, Massachusetts: Blackwell Publishing, 2004:3; 3. Sailer, Christian, Wasner, Susanne. Differential Diagnosis Pocket. Hermosa Beach, CA: Borm Bruckmeir Publishing LLC, 2002:7 .
