Introduction to Survival Models

Survival analysis concerns statistical tools for data analysis where the time until a particular event occurs is of interest.

Censoring

Censoring may be because the event does not occur before the study ends, a subject is lost during the study period or a subject withdraws from the study.

1. Right censoring: the event does not occur before the study ends.
2. Left censoring: the event has already occurred before the study begins.
3. Interval censoring: the event occurred in some interval during the study.

Hazard rate function

aka failure rate function is given by \[\lambda(t)=\frac{f(t)}{S(t)}\] The cumulative hazard rate is given by \[\Lambda(t)=\int_0^t\lambda(u)\mathrm{d}u\]

Exponential function

The hazard rate function of an exponential distribution with mean \(\beta\) is a constant \(1/\beta\).