  The aim of dynamic prediction is to provide individualized risk predictions
over time, which are updated as new data become available. In pursuit of
constructing a dynamic prediction model for a progressive eye disorder,
age-related macular degeneration (AMD), we propose a time-dependent Cox
survival neural network (tdCoxSNN) to predict its progression using
longitudinal fundus images. tdCoxSNN builds upon the time-dependent Cox model
by utilizing a neural network to capture the non-linear effect of
time-dependent covariates on the survival outcome. Moreover, by concurrently
integrating a convolutional neural network (CNN) with the survival network,
tdCoxSNN can directly take longitudinal images as input. We evaluate and
compare our proposed method with joint modeling and landmarking approaches
through extensive simulations. We applied the proposed approach to two real
datasets. 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 years
for more than 4,000 participants. Another is a public dataset of the primary
biliary cirrhosis (PBC) disease, where multiple lab tests were longitudinally
collected to predict the time-to-liver transplant. Our approach demonstrates
commendable predictive performance in both simulation studies and the analysis
of the two real datasets.
