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Hazard ratio. In survival analysis, the hazard ratio (HR) is the ratio of the hazard rates corresponding to the conditions characterised by two distinct levels of a treatment variable of interest. For example, in a clinical study of a drug, the treated population may die at twice the rate per unit time [clarify] of the control population.
Survival analysis. Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory, reliability analysis or reliability engineering in engineering, duration analysis or duration ...
Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the ...
The Kaplan–Meier estimator is one of the most frequently used methods of survival analysis. The estimate may be useful to examine recovery rates, the probability of death, and the effectiveness of treatment. It is limited in its ability to estimate survival adjusted for covariates; parametric survival models and the Cox proportional hazards ...
Hazard rate and ROCOF (rate of occurrence of failures) are often incorrectly seen as the same and equal to the failure rate. [clarification needed] To clarify; the more promptly items are repaired, the sooner they will break again, so the higher the ROCOF. The hazard rate is however independent of the time to repair and of the logistic delay time.
The assumption of constant hazard may not be appropriate. For example, among most living organisms, the risk of death is greater in old age than in middle age – that is, the hazard rate increases with time. For some diseases, such as breast cancer, the risk of recurrence is lower after 5 years – that is, the hazard rate decreases with time.