KaplanMeier#
- final class relife.lifetime_models.KaplanMeier[source]#
Kaplan-Meier estimator.
Compute the non-parametric Kaplan-Meier estimator (also known as the product limit estimator) of the survival function from lifetime data.
Notes
For a given time instant \(t\) and \(n\) total observations, this estimator is defined as:
\[\hat{S}(t) = \prod_{i: t_i \leq t} \left( 1 - \frac{d_i}{n_i}\right)\]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:
\[\widehat{Var}[\hat{S}(t)] = \hat{S}(t)^2 \sum_{i: t_i \leq t} \frac{d_i}{n_i(n_i - d_i)}\]which is often referred to as Greenwood’s formula.
References
[1]Lawless, J. F. (2011). Statistical models and methods for lifetime data. John Wiley & Sons.
[2]Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American statistical association, 53(282), 457-481.
Methods
Compute the non-parametric estimations with respect to lifetime data.
plotThe estimation of the survival function.
- fit(time, event=None, entry=None)[source]#
Compute the non-parametric estimations with respect to lifetime data.
- Parameters:
- timendarray
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.