Kaplan–Meier estimator

Kaplan- Meier estimates (also product -limit estimator ) is used to estimate the probability that a test subject in a particular event within a time interval does not occur. It is a non-parametric estimate of the survival function in the context of survival analysis. The underlying data can be right - censored. This method was developed in 1958 by Edward Kaplan and Paul Meier.

• 2.1 variance
• 2.2 Confidence interval

Computation rule

The Kaplan- Meier estimator is defined by:

With

Example

Underlying the following table should be:

N (t)

Sets the table shows the results of a clinical trial is, it represents the following events:

Initially, 15 patients are available. In the event this has not yet arrived, but they are " under risk ".

Day 1: A patient gets lost after a day in the study, that is, it has left the study without having with him until then, the event has occurred (eg last observation 1 day prior to the end of study ).

Such caused by censorship terms are always 1 and therefore are no longer co-written in the following calculations. He is censored, so now are only 14 patients at risk.

Day 12: In one patient, the event occurs.

Now even more There are 13 patients at risk.

Day 22: Another patient needs to be censored. does not change:

The number of patients at risk is reduced to 12

Day 29: In another patient the event occurs.

There are now 11 patients at risk.

Etc.

Therefore, the observed longest patients are at the end of the curve. Due to the reduced number of patients at risk and the uncertainty of the estimate of the risk for later increases ( wider confidence intervals ).

Advanced Topics

Variance

The variance of the estimator may be in the interval

By means of

Be estimated.

Confidence interval

The confidence interval can be calculated as usual from the variance or the standard error.

This formula is also known as Greenwood's formula.

The 95% confidence interval is therefore: