Towards the Revival of Survival Ratio
Abstract
The hazard ratio is the most commonly reported measure in survival analysis, yet it suffers from well-documented limitations, including non-collapsibility and susceptibility to selection bias as treatment-specific risk sets change over time. In this article, we revisit the survival ratio and the cumulative incidence ratio as alternative measures that directly compare survival and failure probabilities. We introduce a novel modeling framework that targets these ratio functions and constructs coherent nuisance models so that the target and nuisance parameters are variation independent. The framework yields valid monotone survival and cumulative distribution functions and supports likelihood-based and doubly robust estimation of the target parameters, together with estimation of covariate-specific survival and cumulative incidence curves. We illustrate the proposed frameworks using two clinical-trial datasets. In a prostate cancer trial, the estimated survival ratio for 1.0 mg estrogen versus placebo increased over follow-up, while a descriptive selected-cohort analysis of a breast cancer screening trial yielded a cumulative incidence ratio that crossed one over time.
Related
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BibTeX
@misc{zhao2026towards,
title = {{Towards the Revival of Survival Ratio}},
author = {Ruixuan Zhao and Jingxin Yan and Xiaochuan Shi and Torben Martinussen and Eric Tchetgen Tchetgen and Linbo Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34619},
eprint = {2610.34619},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34619},
}
RIS
TY - UNPB
TI - Towards the Revival of Survival Ratio
AU - Ruixuan Zhao
AU - Jingxin Yan
AU - Xiaochuan Shi
AU - Torben Martinussen
AU - Eric Tchetgen Tchetgen
AU - Linbo Wang
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34619
UR - https://arxiv.org/abs/2610.34619
AB - The hazard ratio is the most commonly reported measure in survival analysis, yet it suffers from well-documented limitations, including non-collapsibility and susceptibility to selection bias as treatment-specific risk sets change over time. In this article, we revisit the survival ratio and the cumulative incidence ratio as alternative measures that directly compare survival and failure probabilities. We introduce a novel modeling framework that targets these ratio functions and constructs coherent nuisance models so that the target and nuisance parameters are variation independent. The framework yields valid monotone survival and cumulative distribution functions and supports likelihood-based and doubly robust estimation of the target parameters, together with estimation of covariate-specific survival and cumulative incidence curves. We illustrate the proposed frameworks using two clinical-trial datasets. In a prostate cancer trial, the estimated survival ratio for 1.0 mg estrogen versus placebo increased over follow-up, while a descriptive selected-cohort analysis of a breast cancer screening trial yielded a cumulative incidence ratio that crossed one over time.
ER -