The target of dynamic prediction is to provide individualized risk predictions over time which can be updated as new data become available. Motivated by establishing a dynamic prediction model for the progressive eye disease, age-related macular degeneration (AMD), we proposed a time-dependent Cox model-based survival neural network (tdCoxSNN) to predict its progression on a continuous time scale using longitudinal fundus images. tdCoxSNN extends the time-dependent Cox model by utilizing a neural network to model the non-linear effect of the time-dependent covariates on the survival outcome. Additionally, by incorporating the convolutional neural network (CNN), tdCoxSNN can take the longitudinal raw images as input. We evaluate and compare our proposed method with joint modeling and landmarking approaches through comprehensive simulations using two time-dependent accuracy metrics, the Brier Score and dynamic AUC. 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, in which multiple lab tests were longitudinally collected to predict the time-to-liver transplant. Our approach achieves satisfactory prediction performance in both simulation studies and the two real data analyses. tdCoxSNN was implemented in PyTorch, Tensorflow, and R-Tensorflow.

翻译：动态预测的目标是随时间提供个体化的风险预测，并能在新数据可用时进行更新。受建立进行性眼病——年龄相关性黄斑变性（AMD）动态预测模型的启发，我们提出了一种基于时间相依Cox模型的生存神经网络（tdCoxSNN），利用纵向眼底图像在连续时间尺度上预测其进展。tdCoxSNN通过利用神经网络对时间相依协变量对生存结局的非线性效应进行建模，从而扩展了时间相依Cox模型。此外，通过结合卷积神经网络（CNN），tdCoxSNN能够以纵向原始图像作为输入。我们使用两个时间相依精度指标——Brier评分和动态AUC，通过综合模拟评估了所提方法，并与联合建模和标志性方法进行了比较。我们将所提方法应用于两个真实数据集。一个是一项大型AMD研究——年龄相关性眼病研究（AREDS），该研究在12年期间对4000多名参与者采集了超过5万张眼底图像。另一个是原发性胆汁性胆管炎（PBC）疾病的公开数据集，其中纵向收集了多次实验室检测结果，以预测肝移植时间。我们的方法在模拟研究和两个真实数据分析中均取得了令人满意的预测性能。tdCoxSNN已在PyTorch、Tensorflow和R-Tensorflow中实现。