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For example, a hazard ratio of 2 is thought to mean that a group has twice the chance of dying than a comparison group. In the Cox-model, this can be shown to translate to the following relationship between group survival functions : S 1 ( t ) = S 0 ( t ) r {\displaystyle S_{1}(t)=S_{0}(t)^{r}} (where r is the hazard ratio). [ 4 ]
For example, the hazard ratio of company 5 to company 2 is (()) =. This means that, within the interval of study, company 5's risk of "death" is 0.33 ≈ 1/3 as large as company 2's risk of death. There are important caveats to mention about the interpretation:
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 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.
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.)
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When used as part of an aviation hazard analysis, a "Likelihood" is a specific probability. It is the joint probability of a hazard occurring, that hazard causing or contributing to an aircraft accident or incident, and the resulting degree of loss or harm falling within one of the defined severity categories.