sksurv.tree.SurvivalTree#

class sksurv.tree.SurvivalTree(*, splitter='best', max_depth=None, min_samples_split=6, min_samples_leaf=3, min_weight_fraction_leaf=0.0, max_features=None, random_state=None, max_leaf_nodes=None)[source]#

A survival tree.

The quality of a split is measured by the log-rank splitting rule.

See 1, 2 and 3 for further description.

Parameters

splitter ({'best', 'random'}, default: 'best') – The strategy used to choose the split at each node. Supported strategies are ‘best’ to choose the best split and ‘random’ to choose the best random split.
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.
random_state (int, RandomState instance or None, optional, default: None) – Controls the randomness of the estimator. The features are always randomly permuted at each split, even if splitter is set to "best". When max_features < n_features, the algorithm will select max_features at random at each split before finding the best split among them. But the best found split may vary across different runs, even if max_features=n_features. That is the case, if the improvement of the criterion is identical for several splits and one split has to be selected at random. To obtain a deterministic behavior during fitting, random_state has to be fixed to an integer.
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.

event_times_#

Unique time points where events occurred.

Type: array of shape = (n_event_times,)

max_features_#

The inferred value of max_features.

Type: int,

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_,)

tree_#

The underlying Tree object. Please refer to help(sklearn.tree._tree.Tree) for attributes of Tree object.

Type: Tree object

See also

sksurv.ensemble.RandomSurvivalForest: An ensemble of SurvivalTrees.

References

1: Leblanc, M., & Crowley, J. (1993). Survival Trees by Goodness of Split. Journal of the American Statistical Association, 88(422), 457–467.
2: Ishwaran, H., Kogalur, U. B., Blackstone, E. H., & Lauer, M. S. (2008). Random survival forests. The Annals of Applied Statistics, 2(3), 841–860.
3: 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__(*, splitter='best', max_depth=None, min_samples_split=6, min_samples_leaf=3, min_weight_fraction_leaf=0.0, max_features=None, random_state=None, max_leaf_nodes=None)[source]#

Methods

`__init__`(*[, splitter, max_depth, ...])
`apply`(X[, check_input])	Return the index of the leaf that each sample is predicted as.
`decision_path`(X[, check_input])	Return the decision path in the tree.
`fit`(X, y[, sample_weight, check_input])	Build a survival tree from the training set (X, y).
`get_params`([deep])	Get parameters for this estimator.
`predict`(X[, check_input])	Predict risk score.
`predict_cumulative_hazard_function`(X[, ...])	Predict cumulative hazard function.
`predict_survival_function`(X[, check_input, ...])	Predict survival function.
`score`(X, y)	Returns the concordance index of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

apply(X, check_input=True)[source]#

Return the index of the leaf that each sample is predicted as.

Parameters

X (array-like or sparse matrix, shape = (n_samples, n_features)) – The input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csr_matrix.
check_input (bool, default: True) – Allow to bypass several input checking. Don’t use this parameter unless you know what you do.

Returns

X_leaves – For each datapoint x in X, return the index of the leaf x ends up in. Leaves are numbered within [0; self.tree_.node_count), possibly with gaps in the numbering.

Return type

array-like, shape = (n_samples,)

decision_path(X, check_input=True)[source]#

Return the decision path in the tree.

Parameters

X (array-like or sparse matrix, shape = (n_samples, n_features)) – The input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csr_matrix.
check_input (bool, default=True) – Allow to bypass several input checking. Don’t use this parameter unless you know what you do.

Returns

indicator – Return a node indicator CSR matrix where non zero elements indicates that the samples goes through the nodes.

Return type

sparse matrix, shape = (n_samples, n_nodes)

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

Build a survival tree from the training set (X, y).

Parameters

X (array-like or sparse matrix, 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.
check_input (boolean, default: True) – Allow to bypass several input checking. Don’t use this parameter unless you know what you do.

Return type

self

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, check_input=True)[source]#

Predict risk score.

The risk score is the total number of events, which can be estimated by the sum of the estimated cumulative hazard function \(\hat{H}_h\) in terminal node \(h\).

\[\sum_{j=1}^{n(h)} \hat{H}_h(T_{j} \mid x) ,\]

where \(n(h)\) denotes the number of distinct event times of samples belonging to the same terminal node as \(x\).

Parameters

X (array-like or sparse matrix, shape = (n_samples, n_features)) – Data matrix.
check_input (boolean, default: True) – Allow to bypass several input checking. Don’t use this parameter unless you know what you do.

Returns

risk_scores – Predicted risk scores.

Return type

ndarray, shape = (n_samples,)

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

Predict cumulative hazard function.

The cumulative hazard function (CHF) for an individual with feature vector \(x\) is computed from all samples of the training data that are in the same terminal node as \(x\). It is estimated by the Nelson–Aalen estimator.

Parameters

X (array-like or sparse matrix, shape = (n_samples, n_features)) – Data matrix.
check_input (boolean, default: True) – Allow to bypass several input checking. Don’t use this parameter unless you know what you do.
return_array (boolean, default: False) – 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 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.tree import SurvivalTree

Load and prepare the data.

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

Fit the model.

>>> estimator = SurvivalTree().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, check_input=True, return_array=False)[source]#

Predict survival function.

The survival function for an individual with feature vector \(x\) is computed from all samples of the training data that are in the same terminal node as \(x\). It is estimated by the Kaplan-Meier estimator.

Parameters

X (array-like or sparse matrix, shape = (n_samples, n_features)) – Data matrix.
check_input (boolean, default: True) – Allow to bypass several input checking. Don’t use this parameter unless you know what you do.
return_array (boolean, default: False) – 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 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.tree import SurvivalTree

Load and prepare the data.

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

Fit the model.

>>> estimator = SurvivalTree().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

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

Survival Trees

Utilities