Survival Isotonic Distributional Regression

Martin Bladt; Alexander Henzi; Bram van den Heuvel; Johanna Ziegel

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arXiv · 2608.02914

Survival Isotonic Distributional Regression

Martin Bladt·Alexander Henzi·Bram van den Heuvel·Johanna Ziegel

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Abstract

We introduce Survival-IDR (S-IDR), a nonparametric estimator of conditional survival distributions under order restrictions, extending Isotonic Distributional Regression (IDR; Henzi et al., 2021) to right-censored outcomes. S-IDR has no tuning parameters and accommodates continuous, discrete, and partially ordered covariates. We first study the direct Kaplan-Meier adaptation of IDR: it is uniformly consistent at the minimax rate, but only when the conditional outcomes are hazard-rate ordered. We trace this restriction to the Kaplan-Meier estimator's failure to satisfy the Cauchy mean value property on non-i.i.d. samples, and use the diagnosis to construct S-IDR. The S-IDR estimator is uniformly consistent under only stochastic dominance of the conditional outcomes, attains the minimax rate when the smoothness of the conditional CDFs is known, and admits a known cross-threshold PAVA acceleration. We further embed S-IDR in a distributional single-index framework on a benchmark suite, and apply it in a case study that validates the MELD score used for liver-transplant wait list management. Accompanying R, Python and Rust packages are available at https://github.com/AlexanderHenzi/isodistrreg.

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Martin Bladt, Alexander Henzi, Bram van den Heuvel, Johanna Ziegel. 2026-08-03. Survival Isotonic Distributional Regression. https://arxiv.org/abs/2608.02914

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