sksurv.linear_model.CoxnetSurvivalAnalysis

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

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, optional, default 0.0001) –

    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).

    The default value of alpha_min_ratio will depend on the sample size relative to the number of features in 0.13. If n_samples > n_features, the current default value 0.0001 will be used. If n_samples < n_features, 0.01 will be used instead.

  • 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,)
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='warn', l1_ratio=0.5, penalty_factor=None, normalize=False, copy_X=True, tol=1e-07, max_iter=100000, verbose=False, fit_baseline_model=False)

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)

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.
Returns:

Return type:

self

predict(X, alpha=None)

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.
Returns:

T – The predicted decision function

Return type:

array, shape = (n_samples,)

predict_cumulative_hazard_function(X, alpha=None)

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.
Returns:

cum_hazard – Predicted cumulative hazard functions.

Return type:

ndarray, shape = (n_samples,)

predict_survival_function(X, alpha=None)

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.
Returns:

survival – Predicted survival functions.

Return type:

ndarray, shape = (n_samples,)

score(X, y)

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