Deep survival analysis made easy

TorchSurv is a Python package that serves as a companion tool to perform deep survival modeling within the PyTorch environment. Unlike existing libraries that impose specific parametric forms on users, TorchSurv enables the use of custom PyTorch-based deep survival models. With its lightweight design, minimal input requirements, full PyTorch backend, and freedom from restrictive survival model parameterizations, TorchSurv facilitates efficient survival model implementation, particularly beneficial for high-dimensional input data scenarios.

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This package was developed by Novartis and the US Food and Drug Administration as part of a research collaboration agreement on radiogenomics.

TL;DR

Our idea is to keep things simple. You are free to use any model architecture you want! Our code has 100% PyTorch backend and behaves like any other functions (losses or metrics) you may be familiar with.

Our functions are designed to support you, not to make you jump through hoops. Here's a pseudo code illustrating how easy is it to use TorchSurv to fit and evaluate a Cox proportional hazards model:

```python from torchsurv.loss import cox from torchsurv.metrics.cindex import ConcordanceIndex

Pseudo training loop

for data in dataloader: x, event, time = data estimate = model(x) # shape = torch.Size([64, 1]), if batch size is 64 loss = cox.negpartiallog_likelihood(estimate, event, time) loss.backward() # native torch backend

You can check model performance using our evaluation metrics, e.g, the concordance index with

cindex = ConcordanceIndex() cindex(estimate, event, time)

You can obtain the confidence interval of the c-index

cindex.confidence_interval()

You can test whether the observed c-index is greater than 0.5 (random estimator)

cindex.pvalue(method="noether", alternative="twosided")

You can even compare the metrics between two models (e.g., vs. model B)

cindex.compare(cindexB) ```

Installation and dependencies

First, install the package using either PyPI or Conda

• Using conda (recommended) bash conda install conda-forge::torchsurv

• Using PyPI bash pip install torchsurv

• Using for local installation (latest version)

bash git clone <repo> cd <repo> pip install -e .

Additionally, to build the documentation (notebooks, sphinx) and for package development (tests), please see the development notes and dev/environment.yml. This step is not required to use TorchSurv in your projects but only for optional features.

Getting started

We recommend starting with the introductory guide, where you'll find an overview of the package's functionalities.

Survival data

We simulate a random batch of 64 subjects. Each subject is associated with a binary event status (= True if event occurred), a time-to-event or censoring and 16 covariates.

```python

import torch _ = torch.manual_seed(52) n = 64 x = torch.randn((n, 16)) event = torch.randint(low=0, high=2, size=(n,)).bool() time = torch.randint(low=1, high=100, size=(n,)).float() ```

Cox proportional hazards model

The user is expected to have defined a model that outputs the estimated log relative hazard for each subject. For illustrative purposes, we define a simple linear model that generates a linear combination of the covariates.

```python

from torch import nn modelcox = nn.Sequential(nn.Linear(16, 1)) loghz = modelcox(x) print(loghz.shape) torch.Size([64, 1]) ```

Given the estimated log relative hazard and the survival data, we calculate the current loss for the batch with:

```python

from torchsurv.loss.cox import negpartialloglikelihood loss = negpartialloglikelihood(loghz, event, time) print(loss) tensor(4.1723, gradfn=) ```

We obtain the concordance index for this batch with:

```python

from torchsurv.metrics.cindex import ConcordanceIndex with torch.nograd(): loghz = modelcox(x) cindex = ConcordanceIndex() print(cindex(loghz, event, time)) tensor(0.4872) ```

We obtain the Area Under the Receiver Operating Characteristic Curve (AUC) at a new time t = 50 for this batch with:

```python

from torchsurv.metrics.auc import Auc newtime = torch.tensor(50.) auc = Auc() print(auc(loghz, event, time, new_time=50)) tensor([0.4737]) ```

Weibull accelerated failure time (AFT) model

The user is expected to have defined a model that outputs for each subject the estimated log scale and optionally the log shape of the Weibull distribution that the event density follows. In case the model has a single output, TorchSurv assume that the shape is equal to 1, resulting in the event density to be an exponential distribution solely parametrized by the scale.

For illustrative purposes, we define a simple linear model that estimate two linear combinations of the covariates (log scale and log shape parameters).

```python

from torch import nn modelweibull = nn.Sequential(nn.Linear(16, 2)) logparams = modelweibull(x) print(logparams.shape) torch.Size([64, 2]) ```

Given the estimated log scale and log shape and the survival data, we calculate the current loss for the batch with:

```python

from torchsurv.loss.weibull import negloglikelihood loss = negloglikelihood(logparams, event, time) print(loss) tensor(82931.5078, gradfn=) ```

To evaluate the predictive performance of the model, we calculate subject-specific log hazard and survival function evaluated at all times with:

```python

from torchsurv.loss.weibull import loghazard from torchsurv.loss.weibull import survivalfunction with torch.nograd(): logparams = modelweibull(x) loghz = loghazard(logparams, time) print(loghz.shape) torch.Size([64, 64]) surv = survivalfunction(log_params, time) print(surv.shape) torch.Size([64, 64]) ```

We obtain the concordance index for this batch with:

```python

from torchsurv.metrics.cindex import ConcordanceIndex cindex = ConcordanceIndex() print(cindex(log_hz, event, time)) tensor(0.4062) ```

We obtain the AUC at a new time t = 50 for this batch with:

```python

from torchsurv.metrics.auc import Auc newtime = torch.tensor(50.) loghzt = loghazard(logparams, time=newtime) auc = Auc() print(auc(loghzt, event, time, newtime=newtime)) tensor([0.3509]) ```

We obtain the integrated brier-score with:

```python

from torchsurv.metrics.brierscore import BrierScore brierscore = BrierScore() bs = brierscore(surv, event, time) print(brierscore.integral()) tensor(0.4447) ```

Related Packages

The table below compares the functionalities of TorchSurv with those of auton-survival, pycox, torchlife, scikit-survival, lifelines, and deepsurv. While several libraries offer survival modelling functionalities, no existing library provides the flexibility to use a custom PyTorch-based neural networks to define the survival model parameters.

The outputs of both the log-likelihood functions and the evaluation metrics functions have undergone thorough comparison with benchmarks generated using Python and R packages. The comparisons (at time of publication) are summarised in the Related packages summary.

Survival analysis libraries in R. For obtaining the evaluation metrics, packages survival, riskRegression, SurvMetrics and pec require the fitted model object as input (a specific object format) and RisksetROC imposes a smoothing method. Packages timeROC, riskRegression and pec force the user to choose a form for subject-specific weights (e.g., inverse probability of censoring weighting (IPCW)). Packages survcomp and SurvivalROC do not implement the general AUC but the censoring-adjusted AUC estimator proposed by Heagerty et al. (2000).

Contributing

We value contributions from the community to enhance and improve this project. If you'd like to contribute, please consider the following:

1. Create Issues: If you encounter bugs, have feature requests, or want to suggest improvements, please create an issue in the GitHub repository. Make sure to provide detailed information about the problem, including code for reproducibility, or enhancement you're proposing.

2. Fork and Pull Requests: If you're willing to address an existing issue or contribute a new feature, fork the repository, create a new branch, make your changes, and then submit a pull request. Please ensure your code follows our coding conventions and include tests for any new functionality.

By contributing to this project, you agree to license your contributions under the same license as this project.

Contacts

• Thibaud Coroller (Novartis): (creator, maintainer)
• Mélodie Monod (Imperial College London): (creator, maintainer)
• Peter Krusche (Novartis): (author, maintainer)
• Qian Cao (FDA): (author, maintainer)

If you have any questions, suggestions, or feedback, feel free to reach out the development team us.

Cite

If you use this project in academic work or publications, we appreciate citing it using the following BibTeX entry:

@article{Monod2024, doi = {10.21105/joss.07341}, url = {https://doi.org/10.21105/joss.07341}, year = {2024}, publisher = {The Open Journal}, volume = {9}, number = {104}, pages = {7341}, author = {Mélodie Monod and Peter Krusche and Qian Cao and Berkman Sahiner and Nicholas Petrick and David Ohlssen and Thibaud Coroller}, title = {TorchSurv: A Lightweight Package for Deep Survival Analysis}, journal = {Journal of Open Source Software} }