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) – Specified the amount of additional debug information during optimization.
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coef_¶ Coefficients of the model
- Type
ndarray, shape = (n_features,)
-
cum_baseline_hazard_¶ Estimated baseline cumulative hazard function.
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baseline_survival_¶ Estimated baseline survival function.
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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_,)
See also
sksurv.linear_model.CoxnetSurvivalAnalysisCox proportional hazards model with l1 (LASSO) and l2 (ridge) penalty.
References
- 1
Cox, D. R. Regression models and life tables (with discussion). Journal of the Royal Statistical Society. Series B, 34, 187-220, 1972.
- 2
Breslow, N. E. Covariance Analysis of Censored Survival Data. Biometrics 30 (1974): 89–99.
- 3
Efron, B. The Efficiency of Cox’s Likelihood Function for Censored Data. Journal of the American Statistical Association 72 (1977): 557–565.
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__init__(alpha=0, ties='breslow', n_iter=100, tol=1e-09, verbose=0)[source]¶ Initialize self. See help(type(self)) for accurate signature.
Methods
__init__([alpha, ties, n_iter, tol, verbose])Initialize self.
fit(X, y)Minimize negative partial log-likelihood for provided data.
predict(X)Predict risk scores.
Predict cumulative hazard function.
Predict survival function.
score(X, y)Returns the concordance index of the prediction.
Attributes
-
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.
- Returns
- Return type
self
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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,)
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predict_cumulative_hazard_function(X)[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.
- Returns
cum_hazard – Predicted cumulative hazard functions.
- Return type
ndarray of
sksurv.functions.StepFunction, shape = (n_samples,)
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()
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predict_survival_function(X)[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.
- Returns
survival – Predicted survival functions.
- Return type
ndarray of
sksurv.functions.StepFunction, shape = (n_samples,)
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()
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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