A Scalable Discrete-Time Survival Model for Neural Networks (1805.00917v3)

Abstract: There is currently great interest in applying neural networks to prediction tasks in medicine. It is important for predictive models to be able to use survival data, where each patient has a known follow-up time and event/censoring indicator. This avoids information loss when training the model and enables generation of predicted survival curves. In this paper, we describe a discrete-time survival model that is designed to be used with neural networks, which we refer to as Nnet-survival. The model is trained with the maximum likelihood method using minibatch stochastic gradient descent (SGD). The use of SGD enables rapid convergence and application to large datasets that do not fit in memory. The model is flexible, so that the baseline hazard rate and the effect of the input data on hazard probability can vary with follow-up time. It has been implemented in the Keras deep learning framework, and source code for the model and several examples is available online. We demonstrate the performance of the model on both simulated and real data and compare it to existing models Cox-nnet and Deepsurv.

• The paper introduces Nnet-survival, a discrete-time model that integrates with neural networks using maximum likelihood via mini-batch SGD.
• It overcomes proportional hazards limitations by estimating interval-specific hazard probabilities, thereby improving calibration and discrimination.
• Experiments on simulated and clinical datasets, including the SUPPORT study, demonstrate its scalability and potential in personalized medicine.

A Scalable Discrete-Time Survival Model for Neural Networks: Nnet-survival

The paper "A Scalable Discrete-Time Survival Model for Neural Networks" presents a novel approach to survival modeling that integrates seamlessly with neural networks, termed Nnet-survival. This work is significant in the context of applying deep learning methodologies to medical predictive tasks, particularly when handling survival data that traditionally require consideration of events and censoring indicators.

Core Contributions and Methodology

The primary contribution of the paper lies in the development of the Nnet-survival model, which leverages a discrete-time framework compatible with neural networks. This model is optimized using the maximum likelihood method via mini-batch stochastic gradient descent (SGD), thereby accommodating rapid convergence and facilitating the analysis of large datasets that exceed memory capacity. The implementation in the Keras deep learning framework illustrates its practical applicability, with the source code readily available for replication and extension.

Distinctively, Nnet-survival addresses the limitations of previous models that assume proportional hazards, a condition often violated in large clinical datasets due to dynamic changes over time in patient predictors. The Nnet-survival model adapts a theoretically justified negative log likelihood function to compute mini-batch updates, enabling efficient training without the drawbacks associated with batch gradient descent methods utilized in adaptations of the Cox model.

In defining the model, survival time is segmented into intervals, and for each, a conditional hazard probability is estimated—this is achieved in two formulations: a flexible version allowing time-varying effects and a constrained proportional hazards version. Such flexibility ensures that baseline hazard rates and input effects vary with follow-up time, thereby enhancing the model's capability to reflect realistic medical scenarios.

Results and Implications

Through experiments with both simulated data and real-world datasets (e.g., the SUPPORT paper with over 9,000 patients), the Nnet-survival model demonstrated excellent calibration and discrimination performance. Particularly notable is its potential superiority in contexts with known non-proportional hazards, where it may outperform traditional models like the Cox proportional hazards model.

The practical implications of this research are vast, offering methodologies that could enhance predictive modeling in medicine, especially for imaging and text data well-suited to neural network analysis. The model's capacity to handle large datasets also promises substantial utility in clinical studies where data dimensionality and volume are continually increasing.

Future Directions

The paper suggests potential developments, such as integrating flexible parametric modeling approaches like those involving cubic splines, to further refine survival predictions beyond the final time interval used in the current model. This potential amalgamation of parametric models with neural network methods might break new ground in survival analysis.

As computational tools continue to evolve, models like Nnet-survival could be integral in advancing personalized medicine through predictive analytics. Furthermore, the increasing emphasis on large-scale data in other fields—such as genomics—points to the broader applications and relevance of the methodologies introduced in this paper.

In summary, "A Scalable Discrete-Time Survival Model for Neural Networks" contributes significantly to the intersection of deep learning and survival analysis, paving the way for more nuanced modeling capabilities in medical research applications.