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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 of the control population.
Survival analysis attempts to answer certain questions, such as what is the proportion of a population which will survive past a certain time? ... The hazard ratio HR ...
If the hazard ratio is , there are total subjects, is the probability a subject in either group will eventually have an event (so that is the expected number of events at the time of the analysis), and the proportion of subjects randomized to each group is 50%, then the logrank statistic is approximately normal with mean () and variance 1. [4]
a 8.3x higher risk of death does not mean that 8.3x more patients will die in hospital A: survival analysis examines how quickly events occur, not simply whether they occur. More specifically, "risk of death" is a measure of a rate. A rate has units, like meters per second.
In full generality, the accelerated failure time model can be specified as [2] (|) = ()where denotes the joint effect of covariates, typically = ([+ +]). (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)
In survival analysis, hazard rate models are widely used to model duration data in a wide range of disciplines, from bio-statistics to economics. [ 1 ] Grouped duration data are widespread in many applications.
The relative survival form of analysis is more complex than "competing risks" but is considered the gold-standard for performing a cause-specific survival analysis. It is based on two rates: the overall hazard rate observed in a diseased population and the background or expected hazard rate in the general or background population.
The Nelson–Aalen estimator is a non-parametric estimator of the cumulative hazard rate function in case of censored data or incomplete data. [1] It is used in survival theory, reliability engineering and life insurance to estimate the cumulative number of expected events. An "event" can be the failure of a non-repairable component, the death ...