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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 that treat the logarithm of the HR as a function of a baseline hazard () and a linear combination of explanatory variables:
In epidemiology, a rate ratio, sometimes called an incidence density ratio or incidence rate ratio, is a relative difference measure used to compare the incidence rates of events occurring at any given point in time.
A concept closely-related but different [2] to instantaneous failure rate () is the hazard rate (or hazard function), (). In the many-system case, this is defined as the proportional failure rate of the systems still functioning at time t {\displaystyle t} (as opposed to f ( t ) {\displaystyle f(t)} , which is the expressed as a proportion of ...
The hazard rate at time is the probability per short time dt that an event will occur between and + given that up to time no event has occurred yet. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed, may double its hazard rate for failure.
In fact, the hazard rate is usually more informative about the underlying mechanism of failure than the other representations of a lifetime distribution. The hazard function must be non-negative, λ ( t ) ≥ 0 {\displaystyle \lambda (t)\geq 0} , and its integral over [ 0 , ∞ ] {\displaystyle [0,\infty ]} must be infinite, but is not ...
In practice the odds ratio is commonly used for case-control studies, as the relative risk cannot be estimated. [1] In fact, the odds ratio has much more common use in statistics, since logistic regression, often associated with clinical trials, works with the log of the odds ratio, not relative risk. Because the (natural log of the) odds of a ...
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.
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.)