Overlevingscurven

Consider a graph of the cumulative probability of death plotted as age on the X axis versus the proportion dead on the Y axis for a specific year.

This can be expressed as an equation, where the cumulative distribution function F(t) is the ratio of the number of people dead by time t to the total number observed.

As all population members are not observed until death, this curve cannot estimate survival.

So, the survivorship function or survival curve — S(t) — is the proportion or percent of people living till time t or beyond. It is expressed as follows.

The survival curve is then plotted using age and the percentage of people surviving.

There are various types of survival models. The exponential survival model characterizes a constant hazard over time, meaning the risk of the event occurring is independent of time.

The Weibull survival model can be used in various situations where the hazard rate monotonically increases or decreases over time.

The Log-normal and log-logistic models can be used in scenarios when the hazard rate is not monotonic.