Cumulative Hazard

Definition

Cumulative Hazard $H(t)$: $H(t)=\int \_0^{t}h(u)du=-\ln S(t)$

Total hazard accumulated up to time $t$.

About Cumulative Hazard

Accumulated risk over time.

Driving a car: every hour you drive, you face some hazard of an accident. $H(t)$ is the total risk you’ve accumulated after $t$ hours of driving. Even if the hourly risk is small, $H(t)$ keeps growing the longer you drive.

Example

With Weibull hazard $\alpha =2,\lambda =0.001$, so $H(t)=0.001t^2$:

$t$ (days)	$H(t)$
10	0.1
30	0.9
60	3.6

By day 60, survival probability is $e^{-3.6}\approx 0.027$, meaning only 2.7% of people have avoided getting sick by day 60.

Related

• Hazard Function
• Survival Function