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Journal of Data Science


Neural Network for Correlated Survival Outcomes Using Frailty Model
Pub. online: 26 March 2025      Type: Statistical Data Science      Open accessOpen Access
Received
5 September 2024
Accepted
1 March 2025
Published
26 March 2025

Abstract

Extensive literature has been proposed for the analysis of correlated survival data. Subjects within a cluster share some common characteristics, e.g., genetic and environmental factors, so their time-to-event outcomes are correlated. The frailty model under proportional hazards assumption has been widely applied for the analysis of clustered survival outcomes. However, the prediction performance of this method can be less satisfactory when the risk factors have complicated effects, e.g., nonlinear and interactive. To deal with these issues, we propose a neural network frailty Cox model that replaces the linear risk function with the output of a feed-forward neural network. The estimation is based on quasi-likelihood using Laplace approximation. A simulation study suggests that the proposed method has the best performance compared with existing methods. The method is applied to the clustered time-to-failure prediction within the kidney transplantation facility using the national kidney transplant registry data from the U.S. Organ Procurement and Transplantation Network. All computer programs are available at https://github.com/rivenzhou/deep_learning_clustered.

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Copyright
2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
Open access article under the CC BY license.

Keywords
correlated survival outcomes deep learning prediction random effect

Funding
This research is partly supported by NIH grants R21 EY031884, R21 EY033518, UL1 TR002345, R01 DK129539.

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