# Nelson-Aalen Estimator

The Nelson-Aalen estimator is a nonparametric estimator of the cumulative hazard function.

The estimate is given by

where $d_i$ is the number of observed events at time $t_i$ and $n_i$ is the number of subjects at risk for the event just before time $t_i$.

The pointwise standard error of the log of the survivor function can be computed directly as the standard error or a Bernoulli random variable with $d_i$ successes from $n_i$ samples:

## API

`Survival.NelsonAalen`

— Type.`NelsonAalen`

An immutable type containing cumulative hazard function estimates computed using the Nelson-Aalen method. The type has the following fields:

`times`

: Distinct event times`nevents`

: Number of observed events at each time`ncensor`

: Number of right censored events at each time`natrisk`

: Size of the risk set at each time`chaz`

: Estimate of the cumulative hazard at each time`stderr`

: Standard error of the cumulative hazard

Use `fit(NelsonAalen, ...)`

to compute the estimates and construct this type.

`StatsBase.fit`

— Method.`fit(NelsonAalen, times, status) -> NelsonAalen`

Given a vector of times to events and a corresponding vector of indicators that dictate whether each time is an observed event or is right censored, compute the Nelson-Aalen estimate of the cumulative hazard rate function.

`StatsBase.confint`

— Method.`confint(na::NelsonAalen, α=0.05)`

Compute the pointwise confidence intervals for the cumulative hazard function as a vector of tuples.

## References

- Nelson, W. (1969).
*Hazard plotting for incomplete failure data*. Journal of Quality Technology 1, 27–52.