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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
Rethinking Individual Risk and Aggregation in Survival An...
Xijia Liu · 2026-03-25 · via math.ST updates on arXiv.org

Survival analysis provides a well-established framework for modeling time-to-event data, with hazard and survival functions formally defined as population-level quantities. In applied work, however, these quantities are often interpreted as representing individual-level risk, despite the absence of a clear generative account linking individual risk mechanisms to observed survival data. This paper develops a latent hazard framework that makes this relationship explicit by modeling event times as arising from unobserved, individual-specific hazard mechanisms and viewing population-level survival quantities as aggregates over heterogeneous mechanisms. Within this framework, we show that individual hazard trajectories are not identifiable from survival data under partial information. More generally, the conditional distribution of latent hazard mechanisms given covariates is structurally non-identifiable, even when population-level survival functions are fully known. This non-identifiability arises from the aggregation inherent in survival data and persists independently of model flexibility or estimation strategy. Finally, we show that classical survival models can be systematically reinterpreted according to how they handle this unresolved conditional mechanism distribution. This paper provides a unified framework for understanding heterogeneity, identifiability, and interpretation in survival analysis, and clarifies how population-level survival models should be interpreted when individual risk mechanisms are only partially observed, thereby establishing explicit information constraints for principled modeling and inference.