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The relationship between treatment effect and the hazard ratio is given as . A statistically important, but practically insignificant effect can produce a large hazard ratio, e.g. a treatment increasing the number of one-year survivors in a population from one in 10,000 to one in 1,000 has a hazard ratio of 10.
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 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.)
The hazard function is defined as the event rate at time , conditional on survival at time . Synonyms for hazard function in different fields include hazard rate, force of mortality ( demography and actuarial science , denoted by μ {\displaystyle \mu } ), force of failure, or failure rate ( engineering , denoted λ {\displaystyle \lambda } ).
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The Failures In Time (FIT) rate of a device is the number of failures that can be expected in one billion (10 9) device-hours of operation [17] (e.g. 1,000 devices for 1,000,000 hours, or 1,000,000 devices for 1,000 hours each, or some other combination).