_def-hazard.qmd

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:::{#def-hazard}

##### Hazard function, hazard rate, hazard rate function

::: notes
The **hazard function**, **hazard rate**,  **hazard rate function**, 
for a random variable $T$ at value $t$,
typically denoted as 
$\text{h}(t)$
^[for example in 
@dobson4e, 
@vittinghoff2e, 
@klein2003survival, and 
@kleinbaum2012survival]
or $\lambda(t)$,
^[for example, in @me4 and @kalbfleisch2011statistical]
is the conditional [density](probability.qmd#def-pdf) of $T$ at $t$, 
given $T \ge t$.
That is:
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::: notes
If $T$ represents the time at which an event occurs, 
then $\haz(t)$ is the probability that the event occurs at time $t$, 
given that it has not occurred prior to time $t$.
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