Yaroslav Mukhin, Tereza Oprea, Arielle Anderer, Christina Lee Yu, Jelena Bradic
arXiv 4 Oct 2026 · Mathematics — Statistics Theory
arXiv:2610.05486 · PDF · Extracted main text
Clinical trials with survival endpoints lose information when participants are censored before death is observed. We develop target-preserving estimators that use posttreatment disease history, such as recurrence or progression, to recover information lost to censoring for marginal survival and restricted mean survival effects. The difficulty is that the intermediate event is downstream of treatment: naive adjustment can change the causal estimand, and the useful information enters only through the observed coarsening. We derive observed-data influence functions with and without recurrence history and obtain an exact gain identity. The identity shows that efficiency improvement is driven by the censoring hazard, the split of the alive risk set into recurrence states, and the residual-survival separation between those states. In the no-covariate illness-death model, the Aalen-Johansen estimator realizes the recurrence-augmented efficient score after standardization to the marginal target. With covariates, correctly specified Cox-Breslow transition hazards provide a root-N plug-in benchmark, while a hazard-induced one-step estimator gives rate robustness and, under primitive transition and censoring learner rates, canonical inference with a second-order product remainder. A semi-synthetic metastatic breast cancer study calibrated from digitized progression-free survival and overall survival curves illustrates the gain identity. The framework applies broadly to censored time-to-event studies with informative intermediate histories.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
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| 3 | Moore, T. J. and Zhang, H. and Anderson, G. and Alexander, G. C (2018) Estimated Costs of Pivotal Trials for Novel Therapeutic Agents Approved by the US Food and Drug Administration, 2015–2016 | 0.737 | 3 | 3 | 67% |
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| 7 | Robins, J. M. and Rotnitzky, A. and Zhao, L. P (1995) Analysis of Semiparametric Regression Models for Repeated Outcomes in the Presence of Missing Data | 0.644 | 4 | 1 | 100% |
| 8 | Neyman, J (1990) On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9 | 0.644 | 2 | 2 | 100% |
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