# sksurv.linear_model.CoxnetSurvivalAnalysis¶

class sksurv.linear_model.CoxnetSurvivalAnalysis(n_alphas=100, alphas=None, alpha_min_ratio='auto', l1_ratio=0.5, penalty_factor=None, normalize=False, copy_X=True, tol=1e-07, max_iter=100000, verbose=False, fit_baseline_model=False)[source]

Cox’s proportional hazard’s model with elastic net penalty.

See [1] for further description.

Parameters: n_alphas (int, optional, default: 100) – Number of alphas along the regularization path. alphas (array-like or None, optional) – List of alphas where to compute the models. If None alphas are set automatically. alpha_min_ratio (float or { "auto" }, optional, default: "auto") – Determines minimum alpha of the regularization path if alphas is None. The smallest value for alpha is computed as the fraction of the data derived maximum alpha (i.e. the smallest value for which all coefficients are zero). If set to “auto”, the value will depend on the sample size relative to the number of features. If n_samples > n_features, the default value is 0.0001 If n_samples <= n_features, 0.01 is the default value. l1_ratio (float, optional, default: 0.5) – The ElasticNet mixing parameter, with 0 < l1_ratio <= 1. For l1_ratio = 0 the penalty is an L2 penalty. For l1_ratio = 1 it is an L1 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2. penalty_factor (array-like or None, optional) – Separate penalty factors can be applied to each coefficient. This is a number that multiplies alpha to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables. Note: the penalty factors are internally rescaled to sum to n_features, and the alphas sequence will reflect this change. normalize (boolean, optional, default: False) – If True, the features X will be normalized before optimization by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False. copy_X (boolean, optional, default: True) – If True, X will be copied; else, it may be overwritten. tol (float, optional, default: 1e-7) – The tolerance for the optimization: optimization continues until all updates are smaller than tol. max_iter (int, optional, default: 100000) – The maximum number of iterations. verbose (bool, optional, default: False) – Whether to print additional information during optimization. fit_baseline_model (bool, optional, default: False) – Whether to estimate baseline survival function and baseline cumulative hazard function for each alpha. If enabled, predict_cumulative_hazard_function() and predict_survival_function() can be used to obtain predicted cumulative hazard function and survival function.
alphas_

The actual sequence of alpha values used.

Type: ndarray, shape=(n_alphas,)
alpha_min_ratio_

The inferred value of alpha_min_ratio.

Type: float
penalty_factor_

The actual penalty factors used.

Type: ndarray, shape=(n_features,)
coef_

Matrix of coefficients.

Type: ndarray, shape=(n_features, n_alphas)
deviance_ratio_

The fraction of (null) deviance explained.

Type: ndarray, shape=(n_alphas,)

References

 [1] Simon N, Friedman J, Hastie T, Tibshirani R. Regularization paths for Cox’s proportional hazards model via coordinate descent. Journal of statistical software. 2011 Mar;39(5):1.
__init__(n_alphas=100, alphas=None, alpha_min_ratio='auto', l1_ratio=0.5, penalty_factor=None, normalize=False, copy_X=True, tol=1e-07, max_iter=100000, verbose=False, fit_baseline_model=False)[source]

Initialize self. See help(type(self)) for accurate signature.

Methods

 __init__([n_alphas, alphas, …]) Initialize self. fit(X, y) Fit estimator. predict(X[, alpha]) The linear predictor of the model. predict_cumulative_hazard_function(X[, alpha]) Predict cumulative hazard function. predict_survival_function(X[, alpha]) Predict survival function. score(X, y) Returns the concordance index of the prediction.
fit(X, y)[source]

Fit estimator.

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. self
predict(X, alpha=None)[source]

The linear predictor of the model.

Parameters: X (array-like, shape = (n_samples, n_features)) – Test data of which to calculate log-likelihood from alpha (float, optional) – Constant that multiplies the penalty terms. If the same alpha was used during training, exact coefficients are used, otherwise coefficients are interpolated from the closest alpha values that were used during training. If set to None, the last alpha in the solution path is used. T – The predicted decision function array, shape = (n_samples,)
predict_cumulative_hazard_function(X, alpha=None)[source]

Predict cumulative hazard function.

Only available if fit() has been called with fit_baseline_model = True.

The cumulative hazard function for an individual with feature vector $$x_\alpha$$ is defined as

$H(t \mid x_\alpha) = \exp(x_\alpha^\top \beta) H_0(t) ,$

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. alpha (float, optional) – Constant that multiplies the penalty terms. The same alpha as used during training must be specified. If set to None, the last alpha in the solution path is used. cum_hazard – Predicted cumulative hazard functions. ndarray of sksurv.functions.StepFunction, shape = (n_samples,)

Examples

>>> import matplotlib.pyplot as plt
>>> from sksurv.preprocessing import OneHotEncoder
>>> from sksurv.linear_model import CoxnetSurvivalAnalysis


>>> X, y = load_breast_cancer()
>>> X = OneHotEncoder().fit_transform(X)


Fit the model.

>>> estimator = CoxnetSurvivalAnalysis(l1_ratio=0.99, fit_baseline_model=True)
>>> estimator.fit(X, y)


Estimate the cumulative hazard function for one sample and the five highest alpha.

>>> chf_funcs = {}
>>> for alpha in estimator.alphas_[:5]:
...     chf_funcs[alpha] = estimator.predict_cumulative_hazard_function(
...         X.iloc[:1], alpha=alpha)
...


Plot the estimated cumulative hazard functions.

>>> for alpha, chf_alpha in chf_funcs.items():
...     for fn in chf_alpha:
...         plt.step(fn.x, fn(fn.x), where="post",
...                  label="alpha = {:.3f}".format(alpha))
...
>>> plt.ylim(0, 1)
>>> plt.legend()
>>> plt.show()

predict_survival_function(X, alpha=None)[source]

Predict survival function.

Only available if fit() has been called with fit_baseline_model = True.

The survival function for an individual with feature vector $$x_\alpha$$ is defined as

$S(t \mid x_\alpha) = S_0(t)^{\exp(x_\alpha^\top \beta)} ,$

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. alpha (float, optional) – Constant that multiplies the penalty terms. The same alpha as used during training must be specified. If set to None, the last alpha in the solution path is used. survival – Predicted survival functions. ndarray of sksurv.functions.StepFunction, shape = (n_samples,)

Examples

>>> import matplotlib.pyplot as plt
>>> from sksurv.preprocessing import OneHotEncoder
>>> from sksurv.linear_model import CoxnetSurvivalAnalysis


>>> X, y = load_breast_cancer()
>>> X = OneHotEncoder().fit_transform(X)


Fit the model.

>>> estimator = CoxnetSurvivalAnalysis(l1_ratio=0.99, fit_baseline_model=True)
>>> estimator.fit(X, y)


Estimate the survival function for one sample and the five highest alpha.

>>> surv_funcs = {}
>>> for alpha in estimator.alphas_[:5]:
...     surv_funcs[alpha] = estimator.predict_survival_function(
...         X.iloc[:1], alpha=alpha)
...


Plot the estimated survival functions.

>>> for alpha, surv_alpha in surv_funcs.items():
...     for fn in surv_alpha:
...         plt.step(fn.x, fn(fn.x), where="post",
...                  label="alpha = {:.3f}".format(alpha))
...
>>> plt.ylim(0, 1)
>>> plt.legend()
>>> 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. cindex – Estimated concordance index. float