HΛZΛRDOUS#

Survival Analysis with Competing Risks#

  • Survival Analysis, Competing Risks

  • scikit-learn compatible

  • scalable gradient boosting

hazardous is a Python library for survival analysis -i.e. time-to-event prediction- and competing risks settings. It introduces SurvivalBoost, a scalable gradient-boosting model designed for this task.

With a scikit-learn-compatible API, the library also ships a suite of evaluation metrics specifically adapted to the competing risks setting.

What is the difference between Survival Analysis and the Competing risks setting?#

In contrast to the Survival Analysis setting, the Competing Risks setting accounts for the possibility that multiple event of interest may occur, not just a single event.

It focuses on predicting which event will occur first and when, based on data where some events have not yet been observed.

_images/competing_risk_diagram.svg

What is SurvivalBoost?#

SurvivalBoost is a gradient-boosting variant, that offers prediction for survival and competing risks settings, fully compatible with scikit-learn. It can be used with scikit-learn tools such as pipelines, column transformers, cross-validation, hyper-parameter search tools, etc. Using a novel strictly proper scoring rule, the model is trained to predict the cumulative incidence function and the survival function at any horizon. SurvivalBoost puts a focus on predictive the accuracy -defined as the ability to predict the observed event- rather than on inference.

Additional theoretical details about the model can be found in Survival Models: Proper Scoring Rule and Stochastic Optimization with Competing Risks.

Evaluating competing-risks models#

A trustworthy model has to get three different things right: rank patients by risk, predict the right probabilities, and stay calibrated across the whole follow-up. hazardous provides one family of metrics for each question.

Discrimination

C-index for competing risks This metric can be used to answer the question: Does the model rank individuals in the right order?

See concordance_index_incidence()

Accuracy

Integrated Brier Score (IBS) This metric can be used to answer the question: Are the predicted probabilities close to the observed outcomes?

Accuracy in Time This metric can be used to answer the question: Is the current predicted class correct?

See integrated_brier_score_incidence(), brier_score_incidence() and accuracy_in_time()

Calibration

AJ & KM calibration

Are the predicted probabilities trustworthy on average?

See aj_calibration() and km_calibration()

See also

The library relies on lifelines for the Kaplan-Meier estimator used in SurvivalBoost. We extend our gratitude to the authors of lifelines for their significant contributions to the survival analysis community, including the implementation of models such as the Kaplan-Meier, Cox model, and Aalen-Johansen, as well as metrics like the C-index and Brier Score.

Note

Quantifying the statistical association or causal effect of covariates on the cumulative event incidence or instantaneous hazard rate is currently beyond the scope of this library.