Raphael Sonabend

Raphael Sonabend, Florian Pfisterer, Alan Mishler et al.

Algorithmic fairness is an increasingly important field concerned with detecting and mitigating biases in machine learning models. There has been a wealth of literature for algorithmic fairness in regression and classification however there has been little exploration of the field for survival analysis. Survival analysis is the prediction task in which one attempts to predict the probability of an event occurring over time. Survival predictions are particularly important in sensitive settings such as when utilising machine learning for diagnosis and prognosis of patients. In this paper we explore how to utilise existing survival metrics to measure bias with group fairness metrics. We explore this in an empirical experiment with 29 survival datasets and 8 measures. We find that measures of discrimination are able to capture bias well whereas there is less clarity with measures of calibration and scoring rules. We suggest further areas for research including prediction-based fairness metrics for distribution predictions.

Raphael Sonabend, John Zobolas, Riccardo Be Bin et al.

Scoring rules promote rational and honest decision-making, which is important for model evaluation and becoming increasingly important for automated procedures such as `AutoML'. In this paper we survey common squared and logarithmic scoring rules for survival analysis, with a focus on their theoretical and empirical properness. We introduce a marginal definition of properness and show that both the Integrated Survival Brier Score (ISBS) and the Right-Censored Log-Likelihood (RCLL) are theoretically improper under this definition. We also investigate a new class of losses that may inform future survival scoring rules. Simulation experiments reveal that both the ISBS and RCLL behave as proper scoring rules in practice. The RCLL showed no violations across all settings, while ISBS exhibited only minor, negligible violations at extremely small sample sizes, suggesting one can trust results from historical experiments. As such we advocate for both the RCLL and ISBS in external validation of models, including in automated procedures. However, we note practical challenges in estimating these losses including estimation of censoring distributions and densities; as such further research is required to advance development of robust and honest evaluation in survival analysis.

Lukas Burk, John Zobolas, Bernd Bischl et al.

This work presents the first large-scale neutral benchmark experiment focused on single-event, right-censored, low-dimensional survival data. Benchmark experiments are essential in methodological research to scientifically compare new and existing model classes through proper empirical evaluation. Existing benchmarks in the survival literature are smaller in scale regarding the number of used datasets and extent of empirical evaluation. They often lack appropriate tuning or evaluation procedures, while other comparison studies focus on qualitative reviews rather than quantitative comparisons. This comprehensive study aims to fill the gap by neutrally evaluating a broad range of methods and providing generalizable guidelines for practitioners. We benchmark 19 models, ranging from classical statistical approaches to many common machine learning methods, on 34 publicly available datasets. The benchmark tunes models using both a discrimination measure (Harrell's C-index) and a scoring rule (Integrated Survival Brier Score), and evaluates them across six metrics covering discrimination, calibration, and overall predictive performance. Despite superior average ranks in overall predictive performance from individual learners like oblique random survival forests and likelihood-based boosting, and better discrimination rankings from multiple boosting- and tree-based methods as well as parametric survival models, no method significantly outperforms the commonly used Cox proportional hazards model for either tuning measure. We conclude that for predictive purposes in the standard survival analysis setting of low-dimensional, right-censored data, the Cox Proportional Hazards model remains a simple and robust method, sufficient for most practitioners. All code, data, and results are publicly available on GitHub https://github.com/slds-lmu/paper_2023_survival_benchmark

Simon Wiegrebe, Philipp Kopper, Raphael Sonabend et al.

The influx of deep learning (DL) techniques into the field of survival analysis in recent years has led to substantial methodological progress; for instance, learning from unstructured or high-dimensional data such as images, text or omics data. In this work, we conduct a comprehensive systematic review of DL-based methods for time-to-event analysis, characterizing them according to both survival- and DL-related attributes. In summary, the reviewed methods often address only a small subset of tasks relevant to time-to-event data - e.g., single-risk right-censored data - and neglect to incorporate more complex settings. Our findings are summarized in an editable, open-source, interactive table: https://survival-org.github.io/DL4Survival. As this research area is advancing rapidly, we encourage community contribution in order to keep this database up to date.

Raphael Sonabend, Andreas Bender, Sebastian Vollmer

In this paper we consider how to evaluate survival distribution predictions with measures of discrimination. This is a non-trivial problem as discrimination measures are the most commonly used in survival analysis and yet there is no clear method to derive a risk prediction from a distribution prediction. We survey methods proposed in literature and software and consider their respective advantages and disadvantages. Whilst distributions are frequently evaluated by discrimination measures, we find that the method for doing so is rarely described in the literature and often leads to unfair comparisons. We find that the most robust method of reducing a distribution to a risk is to sum over the predicted cumulative hazard. We recommend that machine learning survival analysis software implements clear transformations between distribution and risk predictions in order to allow more transparent and accessible model evaluation. The code used in the final experiment is available at https://github.com/RaphaelS1/distribution_discrimination.

Philipp Kopper, David Rügamer, Raphael Sonabend et al.

Scoring rules are an established way of comparing predictive performances across model classes. In the context of survival analysis, they require adaptation in order to accommodate censoring. This work investigates using scoring rules for model training rather than evaluation. Doing so, we establish a general framework for training survival models that is model agnostic and can learn event time distributions parametrically or non-parametrically. In addition, our framework is not restricted to any specific scoring rule. While we focus on neural network-based implementations, we also provide proof-of-concept implementations using gradient boosting, generalized additive models, and trees. Empirical comparisons on synthetic and real-world data indicate that scoring rules can be successfully incorporated into model training and yield competitive predictive performance with established time-to-event models.

Franz J. Király, Markus Löning, Anthony Blaom et al.

Machine learning (ML) and AI toolboxes such as scikit-learn or Weka are workhorses of contemporary data scientific practice -- their central role being enabled by usable yet powerful designs that allow to easily specify, train and validate complex modeling pipelines. However, despite their universal success, the key design principles in their construction have never been fully analyzed. In this paper, we attempt to provide an overview of key patterns in the design of AI modeling toolboxes, taking inspiration, in equal parts, from the field of software engineering, implementation patterns found in contemporary toolboxes, and our own experience from developing ML toolboxes. In particular, we develop a conceptual model for the AI/ML domain, with a new type system, called scientific types, at its core. Scientific types capture the scientific meaning of common elements in ML workflows based on the set of operations that we usually perform with them (i.e. their interface) and their statistical properties. From our conceptual analysis, we derive a set of design principles and patterns. We illustrate that our analysis can not only explain the design of existing toolboxes, but also guide the development of new ones. We intend our contribution to be a state-of-art reference for future toolbox engineers, a summary of best practices, a collection of ML design patterns which may become useful for future research, and, potentially, the first steps towards a higher-level programming paradigm for constructing AI.

Raphael Sonabend, Franz Kiraly

distr6 is an object-oriented (OO) probability distributions interface leveraging the extensibility and scalability of R6, and the speed and efficiency of Rcpp. Over 50 probability distributions are currently implemented in the package with `core' methods including density, distribution, and generating functions, and more `exotic' ones including hazards and distribution function anti-derivatives. In addition to simple distributions, distr6 supports compositions such as truncation, mixtures, and product distributions. This paper presents the core functionality of the package and demonstrates examples for key use-cases. In addition this paper provides a critical review of the object-oriented programming paradigms in R and describes some novel implementations for design patterns and core object-oriented features introduced by the package for supporting distr6 components.

Raphael Sonabend, Franz J. Király, Andreas Bender et al.

As machine learning has become increasingly popular over the last few decades, so too has the number of machine learning interfaces for implementing these models. Whilst many R libraries exist for machine learning, very few offer extended support for survival analysis. This is problematic considering its importance in fields like medicine, bioinformatics, economics, engineering, and more. mlr3proba provides a comprehensive machine learning interface for survival analysis and connects with mlr3's general model tuning and benchmarking facilities to provide a systematic infrastructure for survival modeling and evaluation.

Franz J Király, Bilal Mateen, Raphael Sonabend

Objective: To determine the completeness of argumentative steps necessary to conclude effectiveness of an algorithm in a sample of current ML/AI supervised learning literature. Data Sources: Papers published in the Neural Information Processing Systems (NeurIPS, née NIPS) journal where the official record showed a 2017 year of publication. Eligibility Criteria: Studies reporting a (semi-)supervised model, or pre-processing fused with (semi-)supervised models for tabular data. Study Appraisal: Three reviewers applied the assessment criteria to determine argumentative completeness. The criteria were split into three groups, including: experiments (e.g real and/or synthetic data), baselines (e.g uninformed and/or state-of-art) and quantitative comparison (e.g. performance quantifiers with confidence intervals and formal comparison of the algorithm against baselines). Results: Of the 121 eligible manuscripts (from the sample of 679 abstracts), 99\% used real-world data and 29\% used synthetic data. 91\% of manuscripts did not report an uninformed baseline and 55\% reported a state-of-art baseline. 32\% reported confidence intervals for performance but none provided references or exposition for how these were calculated. 3\% reported formal comparisons. Limitations: The use of one journal as the primary information source may not be representative of all ML/AI literature. However, the NeurIPS conference is recognised to be amongst the top tier concerning ML/AI studies, so it is reasonable to consider its corpus to be representative of high-quality research. Conclusion: Using the 2017 sample of the NeurIPS supervised learning corpus as an indicator for the quality and trustworthiness of current ML/AI research, it appears that complete argumentative chains in demonstrations of algorithmic effectiveness are rare.