NelsonAalen#

class relife.NelsonAalen[source]#

Nelson-Aalen estimator.

Compute the non-parametric Nelson-Aalen estimator of the cumulative hazard function from lifetime data.

Notes

For a given time instant \(t\) and \(n\) total observations, this estimator is defined as:

\[\hat{H}(t) = \sum_{i: t_i \leq t} \frac{d_i}{n_i}\]

where \(d_i\) is the number of failures until \(t_i\) and \(n_i\) is the number of assets at risk just prior to \(t_i\).

The variance estimation is obtained by:

\[\widehat{Var}[\hat{H}(t)] = \sum_{i: t_i \leq t} \frac{d_i}{n_i^2}\]

Note that the alternative survivor function estimate:

\[\tilde{S}(t) = \exp{(-\hat{H}(t))}\]

is sometimes suggested for the continuous-time case.

References

[1]

Lawless, J. F. (2011). Statistical models and methods for lifetime data. John Wiley & Sons.

Methods

`chf`	Cumulative hazard function.
`fit`	Compute the non-parametric estimations with respect to lifetime data.

Attributes

`plot`
`estimates`

chf(time)[source]#

Cumulative hazard function.

Parameters:

timenp.ndarray of shape (n, ): The times at which to estimate the cumulative hazard function.

Returns:

np.ndarray of shape (n, ): The estimated cumulative hazard values at each time.

fit(time, event=None, entry=None, departure=None, inplace=False)[source]#

Compute the non-parametric estimations with respect to lifetime data.

Parameters:

timendarray (1d or 2d): Observed lifetime values.
eventndarray of boolean values (1d), default is None: Boolean indicators tagging lifetime values as right censored or complete.
entryndarray of float (1d), default is None: Left truncations applied to lifetime values.
departurendarray of float (1d), default is None: Right truncations applied to lifetime values.
inplaceboolean, default is True: If true, estimations are stored in the object