A scalable discrete-time survival model for neural networks

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.

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References 25

1. 1.
   Improving palliative care with deep learning · 2018

   No notice
2. 2.

   Bottou L. Stochastic gradient learning in neural networks. Proceedings of Neuro-Nimes. 1991;91(8):687-706.

   Not in our library

3. 3.

   Breslow N. Covariance analysis of censored survival data. Biometrics. 1974;30:89-99.

   Not in our library

4. 4.

   Breslow N, Crowley J. A large sample study of the life table and product limit estimates under random censorship. The Annals of Statistics. 1974;2(3):437-453.

   Not in our library10.1214/aos/1176342705

5. 5.

   Brown SF, Branford AJ, Moran W. On the use of artificial neural networks for the analysis of survival data. IEEE Transactions on Neural Networks. 1997;8(5):1071-1077.

   Not in our library10.1109/72.623209

6. 6.
   Cox-nnet: An artificial neural network method for prognosis prediction of high-throughput omics data · 2018

   No notice
7. 7.

   Cooney MT, Dudina AL, Graham IM. Value and limitations of existing scores for the assessment of cardiovascular risk: a review for clinicians. Journal of the American College of Cardiology. 2009;54(14):1209-1227.

   Not in our library10.1016/j.jacc.2009.07.020

8. 8.

   Cox D. Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological). 1972;34(2):187-220.

   Not in our library10.1111/j.2517-6161.1972.tb00899.x

9. 9.

   Cox D, Oakes D. Analysis of survival data. Monographs on statistics & applied probability. 1984.

   Not in our library

10. 10.

    Faraggi D, Simon R. A neural network model for survival data. Statistics in Medicine. 1995;14(1):73-82.

    Not in our library10.1002/sim.4780140108

11. 11.

    Graf E, Schmoor C, Sauerbrei W, Schumacher M. Assessment and comparison of prognostic classification schemes for survival data. Stat Med. 1999;18(17–18):2529-2545.

    Not in our library10.1002/(sici)1097-0258(19990915/30)18:17/18<2529::aid-sim274>3.0.co;2-5

12. 12.

    Harrell Jr FE. Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis (Springer series in statistics). 2015.

    Not in our library

13. 13.

    Jackson CH. flexsurv: a platform for parametric survival modelling in R. Journal of Statistical Software. 2016;70(8):1-33.

    Not in our library10.18637/jss.v070.i08

14. 14.
    DeepSurv: personalized treatment recommender system using a Cox proportional hazards deep neural network · 2018

    No notice
15. 15.

    Knaus WA, Harrell FE, Lynn J, Goldman L, Phillips RS, Connors AF, Dawson NV, Fulkerson WJ, Califf RM, Desbiens N, Layde P, Oye RK, Bellamy PE, Hakim RB, Wagner DP. The SUPPORT prognostic model. Objective estimates of survival for seriously ill hospitalized adults. Annals of Internal Medicine. 1995;122(3):191-203.

    Not in our library10.7326/0003-4819-122-3-199502010-00007

16. 16.

    Kwong C, Ling AY, Crawford MH, Zhao SX, Shah NH. A clinical score for predicting atrial fibrillation in patients with cryptogenic stroke or transient ischemic attack. Cardiology. 2017;138(3):133-140.

    Not in our library10.1159/000476030

17. 17.

    Lecun Y, Bottou L, Bengio Y, Haffner P. Gradient-based learning applied to document recognition. Proceedings of the IEEE. 1998;86(11):2278-2324.

    Not in our library10.1109/5.726791

18. 18.

    Martinsson E. WTTE-RNN: weibull time to event recurrent neural network. Master’s thesis. 2016.

    Not in our library

19. 19.
    Deep Patient: An Unsupervised Representation to Predict the Future of Patients from the Electronic Health Records · 2016

    No notice
20. 20.

    R Core Team. 2017.

    Not in our library

21. 21.
    Scalable and accurate deep learning with electronic health records · 2018

    No notice
22. 22.

    Rodriguez G. Lecture notes for WWS 509: generalized linear statistical models. 2016.

    Not in our library

23. 23.
    External validation of a Cox prognostic model: principles and methods · 2013

    No notice
24. 24.

    Royston P, Parmar MK. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine. 2002;21(15):2175-2197.

    Not in our library10.1002/sim.1203

25. 25.

    Singer JD, Willett JB. It’s about time: using discrete-time survival analysis to study duration and the timing of events. Journal of Educational Statistics. 1993;18(2):155-195.

    Not in our library10.3102/10769986018002155

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