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:
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
fit(NelsonAalen, ...) to compute the estimates and construct this type.
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.
Compute the pointwise confidence intervals for the cumulative hazard function as a vector of tuples.
- Nelson, W. (1969). Hazard plotting for incomplete failure data. Journal of Quality Technology 1, 27–52.