• Graduate Group in Biostatistics, University of California - Davis, Davis, California, United States of America.
• Department of Statistics, University of California - Davis, Davis, California, United States of America.

Lung cancer is a major cause of cancer-related deaths, and early diagnosis and treatment are crucial for improving patients' survival outcomes. In this paper, we propose to employ convolutional neural networks to model the non-linear relationship between the risk of lung cancer and the lungs' morphology revealed in the CT images. We apply a mini-batched loss that extends the Cox proportional hazards model to handle the non-convexity induced by neural networks, which also enables the training of large data sets. Additionally, we propose to combine mini-batched loss and binary cross-entropy to predict both lung cancer occurrence and the risk of mortality. Simulation results demonstrate the effectiveness of both the mini-batched loss with and without the censoring mechanism, as well as its combination with binary cross-entropy. We evaluate our approach on the National Lung Screening Trial data set with several 3D convolutional neural network architectures, achieving high AUC and C-index scores for lung cancer classification and survival prediction. These results, obtained from simulations and real data experiments, highlight the potential of our approach to improving the diagnosis and treatment of lung cancer.