Conformal Survival Bands for Risk Screening under Right-Censoring

We propose a method to quantify uncertainty around individual survival distribution estimates using right-censored data, compatible with any survival model. Unlike classical confidence intervals, the survival bands produced by this method offer predictive rather than population-level inference, making them useful for personalized risk screening. For example, in a low-risk screening scenario, they can be applied to flag patients whose survival band at 12 months lies entirely above 50%, while ensuring that at least half of flagged individuals will survive past that time on average. Our approach builds on recent advances in conformal inference and integrates ideas from inverse probability of censoring weighting and multiple testing with false discovery rate control. We provide asymptotic guarantees and show promising performance in finite samples with both simulated and real data.

💡 Research Summary

The paper introduces a novel statistical tool—Conformal Survival Bands (CSB)—designed for risk‑screening applications when survival data are subject to right‑censoring. Traditional survival analysis methods (parametric, semi‑parametric, or non‑parametric such as Kaplan–Meier) either rely on strong model assumptions or provide only population‑level curves, making it difficult to quantify uncertainty around individualized predictions generated by modern black‑box models (e.g., random survival forests, deep neural networks). The authors address this gap by combining three ideas: conformal inference, inverse‑probability‑of‑censoring weighting (IPCW), and false‑discovery‑rate (FDR) control.

The setting consists of a calibration set of n i.i.d. observations ((X_i,\tilde T_i,E_i)) where (E_i) indicates whether the true event time (T_i) was observed before censoring time (C_i). Two pre‑trained black‑box models are assumed: a survival model (\widehat M_T) that outputs (\widehat S_T(t\mid x)), an estimate of (P(T>t\mid X=x)), and a censoring model (\widehat M_C) that estimates (\widehat S_C(t\mid x)=P(C>t\mid X=x)). The censoring model supplies IPCW weights (w_i=1/\widehat S_C(\tilde T_i\mid X_i)) that correct the calibration data for the missing information caused by censoring.

For each test individual (j) (with covariates (X_j) only) and for a user‑specified time horizon (t) and probability threshold (q), the method formulates two one‑sided hypotheses: (H_{L}(t;j): T_j\ge t) and (H_{R}(t;j): T_j\le t). Using the IPCW‑adjusted calibration set, conformal p‑values are computed for each hypothesis by ranking a conformity score (typically the absolute deviation between the predicted survival probability and the threshold) and applying the standard conformal quantile formula. These p‑values are valid under exchangeability after weighting, even though the raw data are censored.

The two‑sided p‑values are then combined to produce an interval (