Deep Learning for Survival Analysis: A Review

The influx of deep learning (DL) techniques into the field of survival analysis in recent years, coupled with the increasing availability of high-dimensional omics data and unstructured data like images or text, has led to substantial methodological progress; for instance, learning from such high-dimensional or unstructured data. Numerous modern DL-based survival methods have been developed since the mid-2010s; however, they often address only a small subset of scenarios in the time-to-event data setting - e.g., single-risk right-censored survival tasks - and neglect to incorporate more complex (and common) settings. Partially, this is due to a lack of exchange between experts in the respective fields. In this work, we provide a comprehensive systematic review of DL-based methods for time-to-event analysis, characterizing them according to both survival- and DL-related attributes. In doing so, we hope to provide a helpful overview to practitioners who are interested in DL techniques applicable to their specific use case as well as to enable researchers from both fields to identify directions for future investigation. We provide a detailed characterization of the methods included in this review as an open-source, interactive table: https://survival-org.github.io/DL4Survival. As this research area is advancing rapidly, we encourage the research community to contribute to keeping the information up to date.

Factorized Structured Regression for Large-Scale Varying Coefficient Models

Recommender Systems (RS) pervade many aspects of our everyday digital life. Proposed to work at scale, state-of-the-art RS allow the modeling of thousands of interactions and facilitate highly individualized recommendations. Conceptually, many RS can be viewed as instances of statistical regression models that incorporate complex feature effects and potentially non-Gaussian outcomes. Such structured regression models, including time-aware varying coefficients models, are, however, limited in their applicability to categorical effects and inclusion of a large number of interactions. Here, we propose Factorized Structured Regression (FaStR) for scalable varying coefficient models. FaStR overcomes limitations of general regression models for large-scale data by combining structured additive regression and factorization approaches in a neural network-based model implementation. This fusion provides a scalable framework for the estimation of statistical models in previously infeasible data settings. Empirical results confirm that the estimation of varying coefficients of our approach is on par with state-of-the-art regression techniques, while scaling notably better and also being competitive with other time-aware RS in terms of prediction performance. We illustrate FaStR's performance and interpretability on a large-scale behavioral study with smartphone user data.

DeepPAMM: Deep Piecewise Exponential Additive Mixed Models for Complex Hazard Structures in Survival Analysis

Survival analysis (SA) is an active field of research that is concerned with time-to-event outcomes and is prevalent in many domains, particularly biomedical applications. Despite its importance, SA remains challenging due to small-scale data sets and complex outcome distributions, concealed by truncation and censoring processes. The piecewise exponential additive mixed model (PAMM) is a model class addressing many of these challenges, yet PAMMs are not applicable in high-dimensional feature settings or in the case of unstructured or multimodal data. We unify existing approaches by proposing DeepPAMM, a versatile deep learning framework that is well-founded from a statistical point of view, yet with enough flexibility for modeling complex hazard structures. We illustrate that DeepPAMM is competitive with other machine learning approaches with respect to predictive performance while maintaining interpretability through benchmark experiments and an extended case study.