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Updated: Aug 5, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
Estimating overall survival treatment effects in oncology trials: hazard ratio instability and RMST as a robust,
Mingye Zhao1, Taihang Shao2, Hanqiao Shao1
1Department of Pharmacoeconomics, School of International Pharmaceutical Business, China Pharmaceutical University, Nanjing, Jiangsu, China; Center for Pharmacoeconomics and Outcomes Research, China Pharmaceutical University, Nanjing, Jiangsu, China.
Objectives:
Overall survival (OS) is the definitive end point in oncology randomized controlled trials (RCTs), yet OS is often immature at interim analyses. Hazard ratio (HR) remains the dominant OS effect measure, but it depends on proportional hazards (PHs) assumption and can be sensitive to follow-up duration. We evaluated whether a time-anchored alternative OS estimand provides better concordance, greater initial-to-updated stability, and improved prediction of updated OS effects compared with HR.
Study Design And Setting:
We identified phase Ⅱ-Ⅲ oncology RCTs supporting US FDA approvals (January 2006-September 2025), given their decision relevance, clinical representativeness, and global influence. We restricted inclusion to trials reporting OS both initially and in later updates. Individual patient data (IPD) were reconstructed from Kaplan-Meier curves. For each comparison, we estimated HR (Cox-PH model) and restricted mean survival time ratio (RMST-r) using reconstructed IPD. Concordance between RMST-r and log-rank test was assessed using P value comparisons. Stability between initial and updated reports was quantified primarily by symmetric relative change (SRC). Association and predictive performance were evaluated using Pearson correlation and linear models with repeated 10-fold cross-validation.
Results:
We included 150 pairwise comparisons, yielding 300 OS comparisons across initial and updated reports. OS differences were significant in 88/150 comparisons initially by log-rank tests. RMST-r and log-rank test were discordant only in 7.33% of OS comparisons, more often with PH violations than without (12.16% vs 5.75%). RMST-r showed smaller changes between initial and updated reports than HR (mean SRC 0.056 vs 0.18; P < .001). Consistency between initial and updated estimates was stronger for RMST-r than HR (r, 0.87 vs 0.59). RMST-r consistently outperformed HR for predicting updated effects (cross-validated R2, 0.748-0.771 vs 0.232-0.296) and showed better calibration (slope 0.961-0.996 vs 0.733-0.853).
Conclusion:
HR-based OS signals at early readouts were often unstable relative to later updates. In contrast, RMST-r showed smaller initial-to-updated changes, stronger association between early and later estimates, and consistently better predictive performance for updated OS effects, though external validation is still needed, while remaining largely concordant with log-rank test. These findings support routinely reporting time-anchored, clinically interpretable RMST estimands alongside the HR to strengthen early interpretation and decision-making.
Plain Language Summary:
Overall survival (OS) is the key measure of whether a cancer treatment helps patients live longer. It is usually summarized by the hazard ratio (HR), but HR estimates can change substantially as trials mature, making early results hard to interpret. We analyzed 140 randomized cancer trials supporting FDA approvals (2006-2025) that reported OS both initially and in later updates. We compared HR with an alternative measure the restricted mean survival time ratio (RMST-r). Compared with HR, RMST-r changed less between initial and updated analyses, agreed more closely across time points, and better predicted later results while still matching standard test conclusions. Reporting RMST-r alongside HR could give a more stable and clinically meaningful picture of survival benefit when trial data are still immature.
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