Doubly Robust Conformalized Survival Analysis with Right-Censored Data

TL;DR

This paper develops DR-COSARC, a doubly robust conformal inference framework for constructing lower prediction bounds on survival times from right-censored data. It combines a survival model for $P_{T|X}$ with a censoring model for $P_{C|X}$, imputes latent censoring times, and applies weighted conformal calibration to obtain approximately valid LPBs at level $1-\alpha$; asymptotic guarantees hold if either model is consistently estimated. Two calibration variants are proposed: a fixed-cutoff method adapting ideas from type-I censoring, and an adaptive-cutoff method inspired by covariate-dependent thresholds, with the latter yielding more informative bounds in practice. Empirical results on synthetic and real data show DR-COSARC achieves near-nominal coverage while delivering informative LPBs, especially in challenging settings where the survival model is imperfect. The work provides practical software and demonstrates a principled path to uncertainty quantification in survival analysis under right-censoring, with potential extensions to upper bounds and robustness to data errors.

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.

Figures (21)

• Figure 1: Performance on synthetic data under three different settings of our method for constructing lower confidence bounds on the true survival time of a new individual based on right-censored data, compared to existing benchmark approaches. Performance is measured by empirical coverage, aiming for 90% nominal coverage (dashed red line), and the average value of the lower bound (higher is better, provided the coverage is valid). The number of training samples available to fit the survival and censoring models is 1000. The three settings correspond to situations in which fitting an accurate survival model is increasingly easy, with rigorous conformal calibration being most essential in setting 1 and less crucial in setting 3.
• Figure 2: Performance on synthetic data of our method as a function of the number of training samples used to fit the censoring model, compared to other benchmark approaches. The number of training samples available to fit the survival model is fixed equal to 1000. These experiments are conducted under setting 1, where fitting an accurate survival model is most difficult. The results demonstrate the double robustness property of our method, which requires only one of the survival or censoring models to be accurate in order to achieve valid coverage. Other details are as in Figure \ref{['fig:exp_fig1']}.
• Figure 3: Distribution of average (estimated) coverage of survival LPBs computed by different methods, across seven real datasets and four survival models. The nominal coverage level is 90%.
• Figure A1: Visualization of the synthetic data distribution under the three experimental settings outlined in Table \ref{['tab:distributions-synthetic']}. The censoring and event times (in different colors) are plotted against the first covariate, $X_1$.
• Figure A2: Performance on synthetic data of our method as a function of the number of training samples used to fit the censoring model, compared to other approaches. The number of training samples available to fit the survival model is fixed equal to 1000. These experiments are conducted under settings 2 and 3 (see Table \ref{['tab:distributions-synthetic']}), where fitting an accurate survival model is easier. Other details are as in Figure \ref{['fig:exp_fig1']}.

Theorems & Definitions (20)

• Proposition 2.2
• Theorem 3.3
• Theorem 3.6
• proof : Proof of Proposition \ref{['prop-1']}
• Lemma A1
• proof : Proof of Lemma \ref{['lemma-dtv']}
• Theorem A2
• proof : Proof of Theorem \ref{['thm:robustness-fs']}
• Theorem A3
• proof : Proof of Theorem \ref{['thm:coverage-fs-candes']}