The auton-survival Package

The python package auton-survival is repository of reusable utilities for projects involving censored Time-to-Event Data. auton-survival provides a flexible APIs allowing rapid experimentation including dataset preprocessing, regression, counterfactual estimation, clustering and phenotyping and propensity adjusted evaluation.

For complete details on auton-survival see:

• White Paper    • Documentation    • Demo Notebooks

Contents

1. What is Survival Analysis?

2. The Auton Survival Package

3. Survival Regression

4. Phenotyping and Knowledge Discovery

5. Evaluation and Reporting

6. Dataset Loading and Preprocessing

7. Citing and References

8. Compatibility and Installation

9. Contributing

10. License

What is Survival Analysis?

Survival Analysis involves estimating when an event of interest, ( T ) would take places given some features or covariates ( X ). In statistics and ML these scenarious are modelled as regression to estimate the conditional survival distribution, ( P(T>t|X) ). As compared to typical regression problems, Survival Analysis differs in two major ways:

• The Event distribution, ( T ) has positive support, ( T in [0, \infty) ).
• There is presence of censoring (ie. a large number of instances of data are lost to follow up.)

Figure 1. Illustration of Censoring

The Auton Survival Package

The package auton_survival is repository of reusable utilities for projects involving censored Time-to-Event Data. auton_survival allows rapid experimentation including dataset preprocessing, regression, counterfactual estimation, clustering and phenotyping and propensity-adjusted evaluation.

Survival Regression

auton_survival.models

Currently supported Survival Models include:

• auton_survival.models.dsm.DeepSurvivalMachines
• auton_survival.models.dcm.DeepCoxMixtures
• auton_survival.models.cph.DeepCoxPH
• auton_survival.models.cmhe.DeepCoxMixturesHeterogenousEffects

Training a Deep Cox Proportional Hazards Model with auton-survival:

from auton_survival import datasets, preprocessing, models 

# Load the SUPPORT Dataset
outcomes, features = datasets.load_dataset("SUPPORT")

# Preprocess (Impute and Scale) the features
features = preprocessing.Preprocessor().fit_transform(features)

# Train a Deep Cox Proportional Hazards (DCPH) model
model = models.cph.DeepCoxPH(layers=[100])
model.fit(features, outcomes.time, outcomes.event)

# Predict risk at specific time horizons.
predictions = model.predict_risk(features, t=[8, 12, 16])

Figure 2. Violation of the Proportional Hazards Assumption

auton_survival.estimators [Demo Notebook]

This module provides a wrapper auton_survival.estimators.SurvivalModel to model survival datasets with standard survival (time-to-event) analysis methods. The use of the wrapper allows a simple standard interface for multiple different survival regression methods.

auton_survival.estimators also provides convenient wrappers around other popular python survival analysis packages to experiment with Random Survival Forests and Weibull Accelerated Failure Time regression models.

from auton_survival import estimators

# Train a Deep Survival Machines model using the SurvivalModel class.
model = estimators.SurvivalModel(model='dsm')
model.fit(features, outcomes)

# Predict risk at time horizons.
predictions = model.predict_risk(features, times=[8, 12, 16])

auton_survival.experiments [Demo Notebook]

Modules to perform standard survival analysis experiments. This module provides a top-level interface to run auton_survival style experiments of survival analysis, involving options for cross-validation and nested cross-validation style experiments with multiple different survival analysis models.

The module supports multiple model peroformance evaluation metrics and further eases evaluation by automatically computing the censoring adjusted estimates, such as Time Dependent Concordance Index and Brier Score with IPCW adjustment.

# auton_survival cross-validation experiment.
from auton_survival.datasets import load_dataset

outcomes, features = load_dataset(dataset='SUPPORT')
cat_feats = ['sex', 'income', 'race']
num_feats = ['age', 'resp', 'glucose']

from auton_survival.experiments import SurvivalRegressionCV
# Instantiate an auton_survival Experiment 
experiment = SurvivalRegressionCV(model='cph', num_folds=5, 
                                    hyperparam_grid=hyperparam_grid)

# Fit the `experiment` object with the specified Cox model.
model = experiment.fit(features, outcomes, metric='ibs',
                       cat_feats=cat_feats, num_feats=num_feats)

Phenotyping and Knowledge Discovery

auton_survival.phenotyping [Demo Notebook]

auton_survival.phenotyping allows extraction of latent clusters or subgroups of patients that demonstrate similar outcomes. In the context of this package, we refer to this task as phenotyping. auton_survival.phenotyping provides the following phenotyping utilities:

• Intersectional Phenotyping: Recovers groups, or phenotypes, of individuals over exhaustive combinations of user-specified categorical and numerical features.

from auton_survival.phenotyping import IntersectionalPhenotyper

# ’ca’ is cancer status. ’age’ is binned into two quantiles.
phenotyper = IntersectionalPhenotyper(num_vars_quantiles=(0, .5, 1.0),
cat_vars=['ca'], num_vars=['age'])
phenotypes = phenotyper.fit_predict(features)

• Unsupervised Phenotyping: Identifies groups of individuals based on structured similarity in the fature space by first performing dimensionality reduction of the input covariates, followed by clustering. The estimated probability of an individual to belong to a latent group is computed as the distance to the cluster normalized by the sum of distance to other clusters.

from auton_survival.phenotyping import ClusteringPhenotyper

# Dimensionality reduction using Principal Component Analysis (PCA) to 8 dimensions.
dim_red_method, = 'pca', 
# We use a Gaussian Mixture Model (GMM) with 3 components and diagonal covariance.
clustering_method, n_clusters = 'gmm', 

# Initialize the phenotyper with the above hyperparameters.
phenotyper = ClusteringPhenotyper(clustering_method=clustering_method,
                                  dim_red_method=dim_red_method,
                                  n_components=n_components,
                                  n_clusters=n_clusters)
# Fit and infer the phenogroups.
phenotypes = phenotyper.fit_predict(features)

• Supervised Phenotyping: Identifies latent groups of individuals with similar survival outcomes. This approach can be performed as a direct consequence of training the Deep Survival Machines and Deep Cox Mixtures latent variable survival regression estimators using the predict latent z method.

from auton_survival.models.dcm import DeepCoxMixtures

# Instantiate a DCM Model with 3 phenogroups and a single hidden layer with size 100.
model = DeepCoxMixtures(k = 3, layers = [100])
model.fit(features, outcomes.time, outcomes.event, iters = 100, learning_rate = 1e-4)

# Infer the latent Phenotpyes
latent_z_prob = model.predict_latent_z(features)
phenotypings = latent_z_prob.argmax(axis=1)

• Counterfactual Phenotyping: Identifies groups of individuals that demonstrate heterogenous treatment effects. That is, the learnt phenogroups have differential response to a specific intervention. Relies on the specially designed auton_survival.models.cmhe.DeepCoxMixturesHeterogenousEffects latent variable model.

from auton_survival.models.cmhe DeepCoxMixturesHeterogenousEffects

# Instantiate the CMHE model
model = DeepCoxMixturesHeterogenousEffects(random_seed=random_seed, k=k, g=g, layers=layers)

model = model.fit(features, outcomes.time, outcomes.event, intervention)
zeta_probs = model.predict_latent_phi(x_tr)
zeta = np.argmax(zeta_probs, axis=1)

• Virtual Twins Phenotyping: Phenotyper that estimates the potential outcomes under treatment and control using a counterfactual Deep Cox Proportional Hazards model, followed by regressing the difference of the estimated counterfactual Restricted Mean Survival Times using a Random Forest regressor.

from auton_survival.phenotyping import SurvivalVirtualTwins

# Instantiate the Survival Virtual Twins
model = SurvivalVirtualTwins(horizon=365)
# Infer the estimated counterfactual phenotype probability.
phenotypes = model.fit_predict(features, outcomes.time, outcomes.event, interventions)

DAG representations of the unsupervised, supervised, and counterfactual probabilitic phenotypers in auton-survival are shown in the below figure. X represents the covariates, T the time-to-event and Z is the phenotype to be inferred.

A. Unsupervised Phenotyping    B. Supervised Phenotyping    C. Counterfactual Phenotyping

Figure 3. DAG Representations of the Phenotypers in auton-survival

Evaluation and Reporting

auton_survival.metrics

Helper functions to generate standard reports for common Survival Analysis tasks with support for bootstrapped confidence intervals.

• Regression Metric: Metrics for survival model performance evaluation:
  • Brier Score
  • Integrated Brier Score
  • Area under the Receiver Operating Characteristic (ROC) Curve
  • Concordance Index

from auton_survival.metrics import survival_regression_metric

# Infer event-free survival probability from model
predictions = model.predict_survival(features, times)
# Compute Brier Score, Integrated Brier Score
# Area Under ROC Curve and Time Dependent Concordance Index
metrics = ['brs', 'ibs', 'auc', 'ctd']
score = survival_regression_metric(metric='brs', outcomes_train, 
                                   outcomes_test, predictions_test,
                                   times=times)

• Treatment Effect: Used to compare treatment arms by computing the difference in the following metrics for treatment and control groups:
  • Time at Risk (TaR)
  • Risk at Time
  • Restricted Mean Survival Time (RMST)

A. Time at Risk                                                  B. RMST                                                  C. Risk at Time

Figure 4. Graphical representation of the Treatment Effect Metrics

from auton_survival.metrics import survival_diff_metric

# Compute the difference in RMST, Risk at Time, and TaR between treatment and control groups
metrics = ['restricted_mean', 'survival_at', 'tar']
effect = survival_diff_metric(metric='restricted_mean', outcomes=outcomes
                              treatment_indicator=treatment_indicator, 
                              weights=None, horizon=120, n_bootstrap=500)

• Phenotype Purity: Used to measure a phenotyper’s ability to extract subgroups, or phenogroups, with differential survival rates by fitting a Kaplan-Meier estimator within each phenogroup followed by estimating the Brier Score or Integrated Brier Score within each phenogroup.

from auton_survival.metrics import phenotype_purity

# Measure phenotype purity using the Brier Score at event horizons of 1, 2 and 5 years.
phenotype_purity(phenotypes, outcomes, strategy='instantaneous', 
                 time=[365,730,1825])
# Measure phenotype purity using the Integrated Brier score at an event horizon of 5 years.
phenotype_purity(phenotypes, outcomes, strategy='integrated', time=1825)

auton_survival.reporting

Helper functions to generate plots for Survival Analysis tasks.

# Plot separate Kaplan Meier survival estimates for phenogroups.
auton_survival.reporting.plot_kaplanmeier(outcomes, groups=phenotypes)

# Plot separate Nelson-Aalen estimates for phenogroups.
auton_survival.reporting.plot_nelsonaalen(outcomes, groups=phenotypes)

Dataset Loading and Preprocessing

Helper functions to load and preprocess various time-to-event data like the popular SUPPORT, FRAMINGHAM and PBC dataset for survival analysis.

auton_survival.datasets

# Load the SUPPORT Dataset
from auton_survival.datasets import load_dataset
datasets = ['SUPPORT', 'PBC', 'FRAMINGHAM', 'MNIST', 'SYNTHETIC']
features, outcomes = datasets.load_dataset('SUPPORT')

auton_survival.preprocessing

This module provides a flexible API to perform imputation and data normalization for downstream machine learning models. The module has 3 distinct classes, Scaler, Imputer and Preprocessor. The Preprocessor class is a composite transform that does both Imputing and Scaling with a single function call.

# Preprocessing loaded Datasets
from auton_survival import datasets
features, outcomes = datasets.load_topcat()

from auton_survival.preprocessing import Preprocessing
features = Preprocessor().fit_transform(features,
                    cat_feats=['GENDER', 'ETHNICITY', 'SMOKE'],
                    num_feats=['height', 'weight'])

# The `cat_feats` and `num_feats` lists would contain all the categorical and numerical features in the dataset.

Citing and References

Please cite the following paper if you use the auton-survival package:

[1] auton-survival: an Open-Source Package for Regression, Counterfactual Estimation, Evaluation and Phenotyping with Censored Time-to-Event Data. arXiv (2022)

  @article{nagpal2022auton,
    title={auton-survival: an Open-Source Package for Regression, Counterfactual Estimation, Evaluation and Phenotyping with Censored Time-to-Event Data},
    author={Nagpal, Chirag and Potosnak, Willa and Dubrawski, Artur},
    journal={arXiv preprint arXiv:2204.07276},
    year={2022}
  }

Additionally, auton-survival implements the following methodologies:

[2] Counterfactual Phenotyping with Censored Time-to-Events. ACM Conference on Knowledge Discovery and Data Mining (KDD) 2022

  @article{nagpal2022counterfactual,
  title={Counterfactual Phenotyping with Censored Time-to-Events},
  author={Nagpal, Chirag and Goswami, Mononito and Dufendach, Keith and Dubrawski, Artur},
  journal={arXiv preprint arXiv:2202.11089},
  year={2022}
  }

[3] Deep Cox Mixtures for Survival Regression. Conference on Machine Learning for Healthcare (2021)

  @inproceedings{nagpal2021dcm,
  title={Deep Cox mixtures for survival regression},
  author={Nagpal, Chirag and Yadlowsky, Steve and Rostamzadeh, Negar and Heller, Katherine},
  booktitle={Machine Learning for Healthcare Conference},
  pages={674--708},
  year={2021},
  organization={PMLR}
  }

[4] Deep Parametric Time-to-Event Regression with Time-Varying Covariates. AAAI Spring Symposium (2021)

  @InProceedings{pmlr-v146-nagpal21a,
  title={Deep Parametric Time-to-Event Regression with Time-Varying Covariates},
  author={Nagpal, Chirag and Jeanselme, Vincent and Dubrawski, Artur},
  booktitle={Proceedings of AAAI Spring Symposium on Survival Prediction - Algorithms, Challenges, and Applications 2021},
  series={Proceedings of Machine Learning Research},
  publisher={PMLR},
  }

[5] Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks. IEEE Journal of Biomedical and Health Informatics (2021)

  @article{nagpal2021dsm,
  title={Deep survival machines: Fully parametric survival regression and representation learning for censored data with competing risks},
  author={Nagpal, Chirag and Li, Xinyu and Dubrawski, Artur},
  journal={IEEE Journal of Biomedical and Health Informatics},
  volume={25},
  number={8},
  pages={3163--3175},
  year={2021},
  publisher={IEEE}
  }

Compatibility and Installation

auton_survival requires python 3.5+ and pytorch 1.1+.

To evaluate performance using standard metrics auton_survival requires scikit-survival.

To install auton_survival, clone the following git repository:

foo@bar:~$ git clone https://github.com/autonlab/auton-survival.git
foo@bar:~$ pip install -r requirements.txt

Contributing

auton_survival is on GitHub. Bug reports and pull requests are welcome.

License

MIT License

Copyright (c) 2022 Carnegie Mellon University, Auton Lab

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.