Survival analysis estimates how long until an event occurs — death, failure, relapse. The standard tools — Kaplan-Meier curves, Cox regression, hazard functions — work at the population level. They estimate the probability that a randomly chosen individual from a group will survive past time t. But clinicians and patients don't want population probabilities. They want to know: what is my risk?
The paper (arXiv:2603.24276, March 2026) formalizes why this question cannot be answered. The authors construct a latent hazard framework where each individual has an unobserved, individual-specific hazard mechanism — a personal trajectory of risk over time. The population survival function is an aggregate of these heterogeneous mechanisms. The mathematical question: can you recover the individual mechanisms from the population aggregate?
No. The conditional distribution of latent hazard mechanisms, given covariates, is structurally non-identifiable. This is not a sample size problem or a modeling choice — it is a mathematical impossibility. Even with a perfectly specified population survival function and unlimited data, the individual-level hazard trajectories cannot be determined. Different collections of individual mechanisms produce identical population curves.
The non-identifiability stems from aggregation itself. When you sum heterogeneous individual trajectories into a population average, information about the distribution of trajectories is destroyed. This is not noise or bias. It is information-theoretic: the mapping from distributions-of-trajectories to population-curves is many-to-one, and no amount of additional data can invert a non-injective function.
The consequence is that every survival model embodies an implicit assumption about the distribution of individual mechanisms — an assumption that is untestable from the data. Cox regression assumes one thing; accelerated failure time models assume another. Both fit the same population data. Neither can be distinguished on empirical grounds. The model is not estimating the truth about individual risk. It is choosing a truth, and the data cannot tell you if the choice is wrong.