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 mini-batch 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.
Highlights
With the popularization of deep learning and the increasing size of medical datasets, there has been increasing interest in the use of machine learning to improve medical care
The outcome measure is generally evaluated at one follow-up time point, and there is often little discussion of how to deal with censored data
This is potentially attractive since the Cox model has been shown to be very useful and is familiar to most medical researchers. One issue with this approach is that the partial likelihood for each individual depends on the model output for that individual, and on the output for all individuals with longer survival. This would preclude the use of stochastic gradient descent (SGD) since with SGD only a small number of individuals are visible to the model at a time
Summary
With the popularization of deep learning and the increasing size of medical datasets, there has been increasing interest in the use of machine learning to improve medical care. The outcome measure is generally evaluated at one follow-up time point, and there is often little discussion of how to deal with censored data (e.g., patients lost to follow-up before the follow-up time point) This is not ideal, as information about censored patients is lost and the model would need to be re-trained to make predictions at different time points. Because of these issues, modern predictive models generally use Cox proportional hazards regression or a parametric survival model instead of simpler methods such as logistic regression that discard time-to-event information (Cooney et al, 2009). Several authors have described solutions for modeling time-to-event data with neural networks These are generally adaptations of linear models such as the Cox proportional hazards model (Cox, 1972). In the modern era of datasets of thousands or millions of patients, it will usually be possible to demonstrate violation of the proportional hazards assumption, either by plotting residuals or with a statistical test
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