With new technologies in biomedicine, we are able to generate and collect data of various modalities, including genomics, epigenomics, transcriptomics, and proteomics (Figure 1A). Integrating heterogeneous features on a single set of observations provides a unique opportunity to gain a comprehensive understanding of an outcome of interest. It offers the potential for making discoveries that are hidden in data analyses of a single modality and achieving more accurate predictions of the outcome (Kristensen et al. 2014, Ritchie et al. 2015, Gligorijević et al. 2016, Karczewski & Snyder 2018, Ma et al. 2020). While "multi-view data analysis" can mean different things, we use it here in the context of supervised learning, where the goal is to fuse different data views to model an outcome of interest. To give a concrete example, assume that a researcher wants to predict cancer outcomes from RNA expression and DNA methylation measurements for a set of patients. The researcher suspects that: (1) both data views could potentially have prognostic value; (2) the two views share some underlying relationship with each other, as DNA methylation regulates gene expression and can repress the expression of tumor suppressor genes or promote the expression of oncogenes. Should the researcher use both data views for downstream prediction, or just use one view or the other?

There is currently great interest in applying neural networks to prediction tasks in medicine. It is important for predictive models to be able to use survival data, where each patient has a known follow-up time and event/censoring indicator. This avoids information loss when training the model and enables generation of predicted survival curves. In this paper, we describe a discrete-time survival model that is designed to be used with neural networks. The model is trained with the maximum likelihood method using minibatch stochastic gradient descent (SGD). The use of SGD enables rapid training speed. The model is flexible, so that the baseline hazard rate and the effect of the input data can vary with follow-up time. It has been implemented in the Keras deep learning framework, and source code for the model and several examples is available online. We demonstrated the high performance of the model by using it as part of a convolutional neural network to predict survival for over 10,000 patients with metastatic cancer, using the full text of 1,137,317 provider notes. The model's C-index on the validation set was 0.71, which was superior to a linear baseline model (C-index 0.69).