# sksurv.ensemble.RandomSurvivalForest¶

class sksurv.ensemble.RandomSurvivalForest(n_estimators=100, max_depth=None, min_samples_split=6, min_samples_leaf=3, min_weight_fraction_leaf=0.0, max_features='auto', max_leaf_nodes=None, bootstrap=True, oob_score=False, n_jobs=None, random_state=None, verbose=0, warm_start=False, max_samples=None)[source]

A random survival forest.

A random survival forest is a meta estimator that fits a number of survival trees on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control over-fitting. The sub-sample size is always the same as the original input sample size but the samples are drawn with replacement if bootstrap=True (default).

In each survival tree, the quality of a split is measured by the log-rank splitting rule.

See the User Guide, 1 and 2 for further description.

Parameters
• n_estimators (integer, optional, default: 100) – The number of trees in the forest.

• max_depth (int or None, optional, default: None) – The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.

• min_samples_split (int, float, optional, default: 6) –

The minimum number of samples required to split an internal node:

• If int, then consider min_samples_split as the minimum number.

• If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

• min_samples_leaf (int, float, optional, default: 3) –

The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

• If int, then consider min_samples_leaf as the minimum number.

• If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.

• min_weight_fraction_leaf (float, optional, default: 0.) – The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.

• max_features (int, float, string or None, optional, default: None) –

The number of features to consider when looking for the best split:

• If int, then consider max_features features at each split.

• If float, then max_features is a fraction and int(max_features * n_features) features are considered at each split.

• If “auto”, then max_features=sqrt(n_features).

• If “sqrt”, then max_features=sqrt(n_features).

• If “log2”, then max_features=log2(n_features).

• If None, then max_features=n_features.

Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than max_features features.

• max_leaf_nodes (int or None, optional, default: None) – Grow a tree with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.

• bootstrap (boolean, optional, default: True) – Whether bootstrap samples are used when building trees. If False, the whole datset is used to build each tree.

• oob_score (bool, default: False) – Whether to use out-of-bag samples to estimate the generalization accuracy.

• n_jobs (int or None, optional (default=None)) – The number of jobs to run in parallel for both fit and predict. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors.

• random_state (int, RandomState instance or None, optional, default: None) – If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

• verbose (int, optional, default: 0) – Controls the verbosity when fitting and predicting.

• warm_start (bool, optional, default: False) – When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest.

• max_samples (int or float, optional, default: None) – If bootstrap is True, the number of samples to draw from X to train each base estimator. - If None (default), then draw X.shape[0] samples. - If int, then draw max_samples samples. - If float, then draw max_samples * X.shape[0] samples. Thus, max_samples should be in the interval (0.0, 1.0].

estimators_

The collection of fitted sub-estimators.

Type

list of SurvivalTree instances

event_times_

Unique time points where events occurred.

Type

array of shape = (n_event_times,)

n_features_

The number of features when fit is performed.

Type

int

oob_score_

Concordance index of the training dataset obtained using an out-of-bag estimate.

Type

float

sksurv.tree.SurvivalTree

A single survival tree.

Notes

The default values for the parameters controlling the size of the trees (e.g. max_depth, min_samples_leaf, etc.) lead to fully grown and unpruned trees which can potentially be very large on some data sets. To reduce memory consumption, the complexity and size of the trees should be controlled by setting those parameter values.

Compared to scikit-learn’s random forest models, RandomSurvivalForest currently does not support controlling the depth of a tree based on the log-rank test statistics or it’s associated p-value, i.e., the parameters min_impurity_decrease or min_impurity_split are absent. In addition, the feature_importances_ attribute is not available. It is recommended to estimate feature importances via permutation-based methods.

The features are always randomly permuted at each split. Therefore, the best found split may vary, even with the same training data, max_features=n_features and bootstrap=False, if the improvement of the criterion is identical for several splits enumerated during the search of the best split. To obtain a deterministic behavior during fitting, random_state has to be fixed.

References

1

Ishwaran, H., Kogalur, U. B., Blackstone, E. H., & Lauer, M. S. (2008). Random survival forests. The Annals of Applied Statistics, 2(3), 841–860.

2

Ishwaran, H., Kogalur, U. B. (2007). Random survival forests for R. R News, 7(2), 25–31. https://cran.r-project.org/doc/Rnews/Rnews_2007-2.pdf.

__init__(n_estimators=100, max_depth=None, min_samples_split=6, min_samples_leaf=3, min_weight_fraction_leaf=0.0, max_features='auto', max_leaf_nodes=None, bootstrap=True, oob_score=False, n_jobs=None, random_state=None, verbose=0, warm_start=False, max_samples=None)[source]

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

Methods

 __init__([n_estimators, max_depth, …]) Initialize self. fit(X, y[, sample_weight]) Build a forest of survival trees from the training set (X, y). Predict risk score. Predict cumulative hazard function. predict_survival_function(X[, return_array]) Predict survival function. score(X, y) Returns the concordance index of the prediction.

Attributes

 feature_importances_ Not implemented
property feature_importances_

Not implemented

fit(X, y, sample_weight=None)[source]

Build a forest of survival trees from the training set (X, y).

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)[source]

Predict risk score.

The ensemble risk score is the total number of events, which can be estimated by the sum of the estimated ensemble cumulative hazard function $$\hat{H}_e$$.

$\sum_{j=1}^{n} \hat{H}_e(T_{j} \mid x) ,$

where $$n$$ denotes the total number of distinct event times in the training data.

Parameters

X (array-like, shape = (n_samples, n_features)) – Data matrix.

Returns

risk_scores – Predicted risk scores.

Return type

ndarray, shape = (n_samples,)

predict_cumulative_hazard_function(X, return_array=False)[source]

Predict cumulative hazard function.

For each tree in the ensemble, the cumulative hazard function (CHF) for an individual with feature vector $$x$$ is computed from all samples of the bootstrap sample that are in the same terminal node as $$x$$. It is estimated by the Nelson–Aalen estimator. The ensemble CHF at time $$t$$ is the average value across all trees in the ensemble at the specified time point.

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.event_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.event_times_, otherwise an array of sksurv.functions.StepFunction will be returned.

Return type

ndarray

Examples

>>> import matplotlib.pyplot as plt
>>> from sksurv.ensemble import RandomSurvivalForest


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


Fit the model.

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


Estimate the cumulative hazard function for the first 5 samples.

>>> chf_funcs = estimator.predict_cumulative_hazard_function(X.iloc[:5])


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.

For each tree in the ensemble, the survival function for an individual with feature vector $$x$$ is computed from all samples of the bootstrap sample that are in the same terminal node as $$x$$. It is estimated by the Kaplan-Meier estimator. The ensemble survival function at time $$t$$ is the average value across all trees in the ensemble at the specified time point.

Parameters
• X (array-like, shape = (n_samples, n_features)) – Data matrix.

• return_array (boolean) – If set, return an array with the probability of survival for each self.event_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.event_times_, otherwise an array of sksurv.functions.StepFunction will be returned.

Return type

ndarray

Examples

>>> import matplotlib.pyplot as plt
>>> from sksurv.ensemble import RandomSurvivalForest


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


Fit the model.

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


Estimate the survival function for the first 5 samples.

>>> surv_funcs = estimator.predict_survival_function(X.iloc[:5])


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