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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:
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 ...
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.)
The 'bathtub curve' hazard function (blue, upper solid line) is a combination of a decreasing hazard of early failure (red dotted line) and an increasing hazard of wear-out failure (yellow dotted line), plus some constant hazard of random failure (green, lower solid line). The bathtub curve is a particular shape of a failure rate graph.
This approach performs well for certain measures and can approximate arbitrary hazard functions relatively well, while not imposing stringent computational requirements. [5] When the covariates are omitted from the analysis, the maximum likelihood boils down to the Kaplan-Meier estimator of the survivor function.
The Cox model may be specialized if a reason exists to assume that the baseline hazard follows a particular form. In this case, the baseline hazard () is replaced by a given function. For example, assuming the hazard function to be the Weibull hazard function gives the Weibull proportional hazards model.
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 ...
A hazard quotient is the ratio of the potential exposure to a substance and the level at which no adverse effects are expected. If the Hazard Quotient is calculated to be less than 1, then no adverse health effects are expected as a result of exposure. If the Hazard Quotient is greater than 1, then adverse health effects are possible.