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Cited by 1,995Machine Learning in HealthcareStatistical Methods and InferenceRecommender Systems and Techniques

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DeepSurv: personalized treatment recommender system using a Cox proportional hazards deep neural network

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Katzman, Jared L., Shaham, Uri, Cloninger, Alexander, Bates, Jonathan, Jiang, Tingting, Kluger, Yuval·2018·BMC Medical Research Methodology
DOI 10.1186/s12874-018-0482-1PMC PMC5828433
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Abstract

BACKGROUND: Medical practitioners use survival models to explore and understand the relationships between patients' covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options. Standard survival models like the linear Cox proportional hazards model require extensive feature engineering or prior medical knowledge to model treatment interaction at an individual level. While nonlinear survival methods, such as neural networks and survival forests, can inherently model these high-level interaction terms, they have yet to be shown as effective treatment recommender systems. METHODS: We introduce DeepSurv, a Cox proportional hazards deep neural network and state-of-the-art survival method for modeling interactions between a patient's covariates and treatment effectiveness in order to provide personalized treatment recommendations. RESULTS: We perform a number of experiments training DeepSurv on simulated and real survival data. We demonstrate that DeepSurv performs as well as or better than other state-of-the-art survival models and validate that DeepSurv successfully models increasingly complex relationships between a patient's covariates and their risk of failure. We then show how DeepSurv models the relationship between a patient's features and effectiveness of different treatment options to show how DeepSurv can be used to provide individual treatment recommendations. Finally, we train DeepSurv on real clinical studies to demonstrate how it's personalized treatment recommendations would increase the survival time of a set of patients. CONCLUSIONS: The predictive and modeling capabilities of DeepSurv will enable medical researchers to use deep neural networks as a tool in their exploration, understanding, and prediction of the effects of a patient's characteristics on their risk of failure.

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Fig. 1 Diagram of DeepSurv. DeepSurv is a configurable feed-forward deep neural network. The input to the network is the baseline data x. The network propagates the inputs through a number of hidden layers with weights θ. The hidden layers consist of fully-connected nonlinear activation functions followed by dropout. The final layer is a single node which performs a linear combination of the hidden features. The output of the network is taken as the predicted log-risk function ĥθ(x). The hyper-parameters of the network (e.g. number of hidden layers, number of nodes in each layer, dropout probability, etc.) were determined from a random hyper-parameter search and are detailed in Table 3
Fig. 1 Diagram of DeepSurv. DeepSurv is a configurable feed-forward deep neural network. The input to the network is the baseline data x. The network propagates the inputs through a number of hidden layers with weights θ. The hidden layers consist of fully-connected nonlinear activation functions followed by dropout. The final layer is a single node which performs a linear combination of the hidden features. The output of the network is taken as the predicted log-risk function ĥθ(x). The hyper-parameters of the network (e.g. number of hidden layers, number of nodes in each layer, dropout probability, etc.) were determined from a random hyper-parameter search and are detailed in Table 3CC BY · PubMed Central
Fig. 2 Simulated Linear Experimental Log-Risk Surfaces. Predicted log-risk surfaces and errors for the simulated survival data with linear log-risk function with respect to a patient’s covariates x0 and x1. a The true log-risk h(x)=x0+2x1 for each patient. b The predicted log-risk surface of ĥβ(x) from the linear CPH model parameterized by β. c The output of DeepSurv ĥθ(x) predicts a patient’s log-risk. d The absolute error between true log-risk h(x) and CPH’s predicted log-risk ĥβ(x). e The absolute error between true log-risk h(x) and DeepSurv’s predicted log-risk ĥθ(x)
Fig. 2 Simulated Linear Experimental Log-Risk Surfaces. Predicted log-risk surfaces and errors for the simulated survival data with linear log-risk function with respect to a patient’s covariates x0 and x1. a The true log-risk h(x)=x0+2x1 for each patient. b The predicted log-risk surface of ĥβ(x) from the linear CPH model parameterized by β. c The output of DeepSurv ĥθ(x) predicts a patient’s log-risk. d The absolute error between true log-risk h(x) and CPH’s predicted log-risk ĥβ(x). e The absolute error between true log-risk h(x) and DeepSurv’s predicted log-risk ĥθ(x)CC BY · PubMed Central
Fig. 3 Simulated Nonlinear Experimental Log-Risk Surfaces. Log-risk surfaces of the nonlinear test set with respect to patient’s covariates x0 and x1. a The calculated true log-risk h(x) (Eq. 9) for each patient. b The predicted log-risk surface of ĥβ(x) from the linear CPH model parameterized on β. The linear CPH predicts a constant log-risk. c The output of DeepSurv ĥθ(x) is the estimated log-risk function
Fig. 3 Simulated Nonlinear Experimental Log-Risk Surfaces. Log-risk surfaces of the nonlinear test set with respect to patient’s covariates x0 and x1. a The calculated true log-risk h(x) (Eq. 9) for each patient. b The predicted log-risk surface of ĥβ(x) from the linear CPH model parameterized on β. The linear CPH predicts a constant log-risk. c The output of DeepSurv ĥθ(x) is the estimated log-risk functionCC BY · PubMed Central
Fig. 4 Simulated Treatment Log-Risk Surface. Treatment Log-Risk Surfaces as a function of a patient’s relevant covariates x0 and x1. a The true log-risk h1(x) if all patients in the test set were given treatment τ=1. We then manually set all treatment groups to either τ=0 or τ=1. b The predicted log-risk ĥ0(x) for patients with treatment group τ=0. c The network’s predicted log-risk ĥ1(x) for patients in treatment group τ=1
Fig. 4 Simulated Treatment Log-Risk Surface. Treatment Log-Risk Surfaces as a function of a patient’s relevant covariates x0 and x1. a The true log-risk h1(x) if all patients in the test set were given treatment τ=1. We then manually set all treatment groups to either τ=0 or τ=1. b The predicted log-risk ĥ0(x) for patients with treatment group τ=0. c The network’s predicted log-risk ĥ1(x) for patients in treatment group τ=1CC BY · PubMed Central
Fig. 5 Simulated Treatment Survival Curves. Kaplan-Meier estimated survival curves with confidence intervals (α=.05) for the patients who were given the treatment concordant with a method’s recommended treatment (Recommendation) and the subset of patients who were not (Anti-Recommendation). We perform a log-rank test to validate the significance between each set of survival curves. a Effect of DeepSurv’s Treatment Recommendations (Simulated Data), b Effect of RSF’s Treatment Recommendations (Simulated Data)
Fig. 5 Simulated Treatment Survival Curves. Kaplan-Meier estimated survival curves with confidence intervals (α=.05) for the patients who were given the treatment concordant with a method’s recommended treatment (Recommendation) and the subset of patients who were not (Anti-Recommendation). We perform a log-rank test to validate the significance between each set of survival curves. a Effect of DeepSurv’s Treatment Recommendations (Simulated Data), b Effect of RSF’s Treatment Recommendations (Simulated Data)CC BY · PubMed Central
Fig. 6 Rotterdam & German Breast Cancer Study Group (GBSG) Survival Curves. Kaplan-Meier estimated survival curves with confidence intervals (α=.05) for the patients who were given the treatment concordant with a method’s recommended treatment (Recommendation) and the subset of patients who were not (Anti-Recommendation). We perform a log-rank test to validate the significance between each set of survival curves. a Effect of DeepSurv’s Treatment Recommendations (GBSG), b Effect of RSF’s Treatment Recommendations (GBSG)
Fig. 6 Rotterdam & German Breast Cancer Study Group (GBSG) Survival Curves. Kaplan-Meier estimated survival curves with confidence intervals (α=.05) for the patients who were given the treatment concordant with a method’s recommended treatment (Recommendation) and the subset of patients who were not (Anti-Recommendation). We perform a log-rank test to validate the significance between each set of survival curves. a Effect of DeepSurv’s Treatment Recommendations (GBSG), b Effect of RSF’s Treatment Recommendations (GBSG)CC BY · PubMed Central

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Metadata

Authors
Katzman, J. L., Shaham, U., Cloninger, A., Bates, J., Jiang, T., & Kluger, Y.
Affiliations
  • Yale University (US)
  • Yale New Haven Hospital (US)
  • Yale Cancer Center (US)
Corresponding author
Kluger, Yuval
ORCID
Venue
BMC Medical Research Methodology
Publisher
Springer Science and Business Media LLC
Published
2018-02-26
Volume
18
Issue
1
Pages
24-24
ISSN
1471-2288 (ISSN-L)
DOI
10.1186/s12874-018-0482-1
PMC
PMC5828433
OpenAlex
W2753919178
Cited by
1,995
References
49
Citations by year
2026: 376 · 2025: 386 · 2024: 321 · 2023: 301 · 2022: 238 · 2021: 206 · 2020: 94 · 2019: 54 · 2018: 18
FWCI
52.41
Type
journal article
Language
en
Open access
Licence
Locations
  • BMC Medical Research Methodology (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Funders
  • National Human Genome Research Institute (1R01HG008383-01A1)
  • Directorate for Mathematical and Physical Sciences (DMS-1402254)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning in Healthcare
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
  • Physical Sciences › Computer Science › Information Systems › Recommender Systems and Techniques
Keywords
DeepSurv, Cox proportional hazards model, deep neural network, survival analysis, personalized treatment recommendations, treatment effectiveness, clinical trials
MeSH terms
Algorithms, Humans, Proportional Hazards Models, Neural Networks, Computer, Outcome Assessment, Health Care, Kaplan-Meier Estimate, Precision Medicine

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