Doubly Robust Conformalized Survival Analysis with Right-Censored Data

Matteo Sesia, Vladimir Svetnik

TL;DR: This paper presents a conformal inference method for constructing lower prediction bounds for survival times from right-censored data.

Abstract: We present a conformal inference method for constructing lower prediction bounds for survival times from right-censored data, extending recent approaches designed for more restrictive type-I censoring scenarios. The proposed method imputes unobserved censoring times using a machine learning model, and then analyzes the imputed data using a survival model calibrated via weighted conformal inference. This approach is theoretically supported by an asymptotic double robustness property. Empirical studies on simulated and real data demonstrate that our method leads to relatively informative predictive inferences and is especially robust in challenging settings where the survival model may be inaccurate.

Lay Summary:

Survival analysis is a subfield of data science focused on modeling and predicting when an event will occur, such as a patient’s death or a device’s failure. These problems are common in fields like medicine and engineering. A major challenge in survival analysis is that the data are usually incomplete: we often don’t observe the true event time for every individual. For example, in a clinical study, some patients may still be alive when the study ends or may leave early. In such cases, we only know that the event hasn’t happened yet, not when it eventually will. This kind of missing information makes survival analysis more difficult than many other prediction tasks.

Nowadays, researchers increasingly use complex machine learning models in many areas of data science, including survival analysis. While these models can be accurate, they can also fail in unpredictable ways as they still often struggle to provide reliable insight into how confident we should be in their predictions. This lack of transparency tends to be a serious limitation in applications where the model may inform high-stakes decisions, such as treatment prioritization in healthcare.

Our work introduces a new method, compatible with any machine learning model, to obtain uncertainty-aware predictions for survival times based on censored data. This method builds on a statistical framework called conformal inference, and it seeks to adjust a model’s output to generate a likely lower bound (as opposed to a single estimate) for the survival time of each individual, accompanied by a formal guarantee that the true survival time falls above this bound with a specified level of confidence.

Unlike existing methods, which rely on overly restrictive assumptions about how the data are censored, our approach is more practical because it is designed to handle the kinds of incomplete data commonly seen in real-world applications of survival analysis.

Link To Code: https://github.com/msesia/conformal_survival

Primary Area: Probabilistic Methods

Keywords: Conformal inference, Survival analysis, Uncertainty Estimation

Submission Number: 2249