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The aim of dynamic prediction is to provide individualized risk predictionsover time, which are updated as new data become available. In pursuit ofconstructing a dynamic prediction model for a progressive eye disorder,age-related macular degeneration (AMD), we propose a time-dependent Coxsurvival neural network (tdCoxSNN) to predict its progression usinglongitudinal fundus images. tdCoxSNN builds upon the time-dependent Cox modelby utilizing a neural network to capture the non-linear effect oftime-dependent covariates on the survival outcome. Moreover, by concurrentlyintegrating a convolutional neural network (CNN) with the survival network,tdCoxSNN can directly take longitudinal images as input. We evaluate andcompare our proposed method with joint modeling and landmarking approachesthrough extensive simulations. We applied the proposed approach to two realdatasets. One is a large AMD study, the Age-Related Eye Disease Study (AREDS),in which more than 50,000 fundus images were captured over a period of 12 yearsfor more than 4,000 participants. Another is a public dataset of the primarybiliary cirrhosis (PBC) disease, where multiple lab tests were longitudinallycollected to predict the time-to-liver transplant. Our approach demonstratescommendable predictive performance in both simulation studies and the analysisof the two real datasets.

tdCoxSNN: Time-Dependent Cox Survival Neural Network for Continuous-time Dynamic Prediction