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class surpyval.univariate.nonparametric.nelson_aalen.NelsonAalen_

Bases: NonParametricFitter

Nelson-Aalen estimator class. Returns a NonParametric object from method fit() Calculates the Non-Parametric estimate of the survival function using:

\[R(x) = e^{-\sum_{i:x_{i} \leq x}^{} \frac{d_{i} }{r_{i}}}\]

The variance of the cumulative hazard used for confidence bounds is estimated with Aalen’s (Poisson) estimator, as recommended by Klein (1991):

\[\widehat{Var}(H(x)) = \sum_{i:x_{i} \leq x} \frac{d_{i}}{r_{i}^{2}}\]

Examples

>>> import numpy as np
>>> from surpyval import NelsonAalen
>>> x = np.array([1, 2, 3, 4, 5])
>>> model = NelsonAalen.fit(x)
>>> model.R
array([0.81873075, 0.63762815, 0.45688054, 0.27711205, 0.10194383])

The central feature to SurPyval’s capability. This function aimed to have an API to mimic the simplicity of the scipy API. That is, to use a simple fit() call, with as many or as few parameters as are needed.

Parameters

x (array like, optional) – Array of observations of the random variables. If x is None, xl and xr must be provided.
c (array like, optional) – Array of censoring flag. -1 is left censored, 0 is observed, 1 is right censored, and 2 is intervally censored. If not provided will assume all values are observed.
n (array like, optional) – Array of counts for each x. If data is proivded as counts, then this can be provided. If None will assume each observation is 1.
t (2D-array like, optional) – 2D array like of the left and right values at which the respective observation was truncated. If not provided it assumes that no truncation occurs.
tl (array like or scalar, optional) – Values of left truncation for observations. If it is a scalar value assumes each observation is left truncated at the value. If an array, it is the respective ‘late entry’ of the observation.
tr (array like or scalar, optional) – Values of right truncation for observations. If it is a scalar value assumes each observation is right truncated at the value. If an array, it is the respective right truncation value for each observation.
xl (array like, optional) – Array like of the left array for 2-dimensional input of x. This is useful for data that is all intervally censored. Must be used with the xr input.
xr (array like, optional) – Array like of the right array for 2-dimensional input of x. This is useful for data that is all intervally censored. Must be used with the xl input.
turnbull_estimator (('Nelson-Aalen', 'Kaplan-Meier', or) –
'Fleming-Harrington') – If using the Turnbull heuristic, you can elect to use either the KM, NA, or FH estimator with the Turnbull estimates of r, and d. Defaults to FH.
str – If using the Turnbull heuristic, you can elect to use either the KM, NA, or FH estimator with the Turnbull estimates of r, and d. Defaults to FH.
optional – If using the Turnbull heuristic, you can elect to use either the KM, NA, or FH estimator with the Turnbull estimates of r, and d. Defaults to FH.

Returns

model – A parametric model with the fitted parameters and methods for all functions of the distribution using the fitted parameters.

Return type

NonParametric

Examples

>>> from surpyval import NelsonAalen, Weibull, Turnbull
>>> import numpy as np
>>> x = Weibull.random(100, 10, 4)
>>> model = NelsonAalen.fit(x)
>>> print(model)
Non-Parametric SurPyval Model
=============================
Model            : Nelson-Aalen
>>> Turnbull.fit(x, turnbull_estimator='Kaplan-Meier')
Non-Parametric SurPyval Model
=============================
Model            : Turnbull
Estimator        : Kaplan-Meier

from_xrd(x: ArrayLike, r: ArrayLike, d: ArrayLike) → NonParametric

The central feature to SurPyval’s capability. This function aimed to have an API to mimic the simplicity of the scipy API. That is, to use a simple fit() call, with as many or as few parameters as are needed.

Parameters

x (array like, optional) – Array of observations of the random variables. If x is None, xl and xr must be provided.
r (array like, optional) – Array of at risk items. For each value of x the r array is the number of at risk items immediately prior to the failures at x.
d (array like, optional) – Array of counts of deaths/failures at each x. For each value of x the d array is the number of deaths at x (can be zero).

Returns

model – A non-parametric model with the survival curved estimated using the selected method.

Return type

NonParametric

Examples

>>> from surpyval import NelsonAalen, Weibull, Turnbull
>>> import numpy as np
>>> x = [1, 2, 3, 4, 5, 6]
>>> r = [10, 8, 6, 4, 3, 2]
>>> d = [2, 1, 1, 1, 1, 1]
>>> model = NelsonAalen.from_xrd(x, r, d)
>>> print(model)
Non-Parametric SurPyval Model
=============================
Model            : Nelson-Aalen