sksurv.linear_model.CoxPHSurvivalAnalysis#

class sksurv.linear_model.CoxPHSurvivalAnalysis(alpha=0, *, ties='breslow', n_iter=100, tol=1e-09, verbose=0)[source]#

Cox proportional hazards model.

There are two possible choices for handling tied event times. The default is Breslow’s method, which considers each of the events at a given time as distinct. Efron’s method is more accurate if there are a large number of ties. When the number of ties is small, the estimated coefficients by Breslow’s and Efron’s method are quite close. Uses Newton-Raphson optimization.

See [1], [2], [3] for further description.

Parameters:

alpha (float, ndarray of shape (n_features,), optional, default: 0) – Regularization parameter for ridge regression penalty. If a single float, the same penalty is used for all features. If an array, there must be one penalty for each feature. If you want to include a subset of features without penalization, set the corresponding entries to 0.
ties ({'breslow', 'efron'}, optional, default: 'breslow') – The method to handle tied event times. If there are no tied event times all the methods are equivalent.
n_iter (int, optional, default: 100) – Maximum number of iterations.
tol (float, optional, default: 1e-9) –
Convergence criteria. Convergence is based on the negative log-likelihood:
```
|1 - (new neg. log-likelihood / old neg. log-likelihood) | < tol
```
verbose (int, optional, default: 0) – Specifies the amount of additional debug information during optimization.

coef_#

Coefficients of the model

Type:: ndarray, shape = (n_features,)

cum_baseline_hazard_#

Estimated baseline cumulative hazard function.

Type:: sksurv.functions.StepFunction

baseline_survival_#

Estimated baseline survival function.

Type:: sksurv.functions.StepFunction

n_features_in_#

Number of features seen during fit.

Type:: int

feature_names_in_#

Names of features seen during fit. Defined only when X has feature names that are all strings.

Type:: ndarray of shape (n_features_in_,)

unique_times_#

Unique time points.

Type:: array of shape = (n_unique_times,)

See also

sksurv.linear_model.CoxnetSurvivalAnalysis: Cox proportional hazards model with l1 (LASSO) and l2 (ridge) penalty.

References

__init__(alpha=0, *, ties='breslow', n_iter=100, tol=1e-09, verbose=0)[source]#

Methods

`__init__`([alpha, ties, n_iter, tol, verbose])
`fit`(X, y)	Minimize negative partial log-likelihood for provided data.
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`predict`(X)	Predict risk scores.
`predict_cumulative_hazard_function`(X[, ...])	Predict cumulative hazard function.
`predict_survival_function`(X[, return_array])	Predict survival function.
`score`(X, y)	Returns the concordance index of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

Attributes

`baseline_survival_`
`cum_baseline_hazard_`
`unique_times_`

fit(X, y)[source]#

Minimize negative partial log-likelihood for provided data.

Parameters:

X (array-like, shape = (n_samples, n_features)) – Data matrix
y (structured array, shape = (n_samples,)) – A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.

Return type:

self

get_metadata_routing()#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:: routing – A MetadataRequest encapsulating routing information.
Return type:: MetadataRequest

get_params(deep=True)#

Get parameters for this estimator.

Parameters:: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:: params – Parameter names mapped to their values.
Return type:: dict

predict(X)[source]#

Predict risk scores.

Parameters:: X (array-like, shape = (n_samples, n_features)) – Data matrix.
Returns:: risk_score – Predicted risk scores.
Return type:: array, shape = (n_samples,)

predict_cumulative_hazard_function(X, return_array=False)[source]#

Predict cumulative hazard function.

The cumulative hazard function for an individual with feature vector \(x\) is defined as

\[H(t \mid x) = \exp(x^\top \beta) H_0(t) ,\]

where \(H_0(t)\) is the baseline hazard function, estimated by Breslow’s estimator.

Parameters:

X (array-like, shape = (n_samples, n_features)) – Data matrix.
return_array (boolean) – If set, return an array with the cumulative hazard rate for each self.unique_times_, otherwise an array of sksurv.functions.StepFunction.

Returns:

cum_hazard – If return_array is set, an array with the cumulative hazard rate for each self.unique_times_, otherwise an array of length n_samples of sksurv.functions.StepFunction instances will be returned.

Return type:

ndarray

Examples

>>> import matplotlib.pyplot as plt
>>> from sksurv.datasets import load_whas500
>>> from sksurv.linear_model import CoxPHSurvivalAnalysis

Load the data.

>>> X, y = load_whas500()
>>> X = X.astype(float)

Fit the model.

>>> estimator = CoxPHSurvivalAnalysis().fit(X, y)

Estimate the cumulative hazard function for the first 10 samples.

>>> chf_funcs = estimator.predict_cumulative_hazard_function(X.iloc[:10])

Plot the estimated cumulative hazard functions.

>>> for fn in chf_funcs:
...     plt.step(fn.x, fn(fn.x), where="post")
...
>>> plt.ylim(0, 1)
>>> plt.show()

predict_survival_function(X, return_array=False)[source]#

Predict survival function.

The survival function for an individual with feature vector \(x\) is defined as

\[S(t \mid x) = S_0(t)^{\exp(x^\top \beta)} ,\]

where \(S_0(t)\) is the baseline survival function, estimated by Breslow’s estimator.

Parameters:

X (array-like, shape = (n_samples, n_features)) – Data matrix.
return_array (boolean, default: False) – If set, return an array with the probability of survival for each self.unique_times_, otherwise an array of sksurv.functions.StepFunction.

Returns:

survival – If return_array is set, an array with the probability of survival for each self.unique_times_, otherwise an array of length n_samples of sksurv.functions.StepFunction instances will be returned.

Return type:

ndarray

Examples

>>> import matplotlib.pyplot as plt
>>> from sksurv.datasets import load_whas500
>>> from sksurv.linear_model import CoxPHSurvivalAnalysis

Load the data.

>>> X, y = load_whas500()
>>> X = X.astype(float)

Fit the model.

>>> estimator = CoxPHSurvivalAnalysis().fit(X, y)

Estimate the survival function for the first 10 samples.

>>> surv_funcs = estimator.predict_survival_function(X.iloc[:10])

Plot the estimated survival functions.

>>> for fn in surv_funcs:
...     plt.step(fn.x, fn(fn.x), where="post")
...
>>> plt.ylim(0, 1)
>>> plt.show()

score(X, y)[source]#

Returns the concordance index of the prediction.

Parameters:

X (array-like, shape = (n_samples, n_features)) – Test samples.
y (structured array, shape = (n_samples,)) – A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.

Returns:

cindex – Estimated concordance index.

Return type:

float

set_params(**params)#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: estimator instance