Rethinking survival visualisation: moving beyond Kaplan-Meier curves and hazard ratios in urology

Immune checkpoint inhibitors (ICIs) have transformed the treatment landscape in urological oncology. In advanced urothelial carcinoma, pembrolizumab has become a standard option after platinum-based chemotherapy (1), and ICIs are now routinely applied across renal cell carcinoma and other genitourinary malignancies. The efficacy of these agents is conventionally summarised by pairing Kaplan-Meier curves with hazard ratios (HRs) derived from Cox proportional hazards regression—a framework that presupposes the relative risk of events remains constant over the study period. For urologists who translate pivotal trial results into day-to-day treatment decisions, recognising when this single-number summary is potentially misleading is increasingly important.

Unlike cytotoxic chemotherapy, ICIs do not produce immediate tumour regression in all responders; rather, they act by reactivating adaptive immunity, a process that can take months before clinical benefit is observed (2). The Kaplan-Meier curves from landmark ICI trials often reveal delayed separation, late divergence, or crossing of survival curves—patterns that violate the proportional hazards assumption. In such settings, a single HR may obscure clinically meaningful temporal dynamics. A trial may report a favourable HR even though the experimental arm shows little benefit initially, only for a durable effect to emerge among long-term survivors. Despite these known limitations, the majority of urological ICI trials continue to be analysed using conventional proportional hazards methods, often without explicitly testing whether the assumption holds (3).

Restricted mean survival time (RMST) offers a complementary estimand that does not require proportional hazards. RMST quantifies the average survival time accrued up to a prespecified clinically meaningful time horizon, τ, and can be estimated directly from Kaplan–Meier curves by integrating the area under the survival function (4). The difference in RMST between arms provides an absolute measure of survival gain or loss—expressed in units of time—that remains interpretable regardless of whether hazards are proportional. In urological oncology, several recent analyses have adopted RMST to summarise ICI efficacy (5). Reporting RMST alongside HR allows clinicians to gauge both relative risk reduction and absolute survival benefit, which is particularly informative in shared decision-making.

Figure 1 illustrates how RMST-based visualisation can simultaneously capture two important dimensions: the time-dependent nature of ICI efficacy and the continuous relationship between a prognostic covariate and treatment benefit. By plotting ΔRMST against a continuous covariate [neutrophil-to-lymphocyte ratio (NLR)] across multiple time horizons (τ=6 to 60 months), two patterns become immediately apparent. First, the coloured bands widen progressively as τ increases, directly visualising the delayed-effect phenomenon characteristic of ICIs: benefit accrues disproportionately in later follow-up. Second, the continuous covariate axis avoids the information loss inherent in dichotomised subgroup analyses, preserving the smooth relationship between NLR and expected benefit (6).

Figure 1 RMST-based visualisation capturing time-dependent treatment effects and continuous covariate relationships. This illustrative example displays ΔRMST (ICI minus control) as a function of NLR across time horizons from 6 to 60 months. The progressive widening of coloured bands as τ increases (blue to red) directly demonstrates the delayed-effect pattern characteristic of ICIs: survival benefit accumulates disproportionately at longer follow-up. The continuous covariate axis preserves the smooth dose-response relationship that would be lost in dichotomised subgroup analyses. ICI, immune checkpoint inhibitor; NLR, neutrophil-to-lymphocyte ratio; RMST, restricted mean survival time.

None of this is to suggest that Kaplan-Meier curves or HRs should be abandoned. Rather, we advocate for a broader visualisation toolkit that matches the analytic approach to the biological behaviour of the therapy under study. When proportional hazards hold, the HR remains a parsimonious and valid summary. Indeed, conventional Kaplan-Meier analysis and HRs continue to yield clinically meaningful results in settings where time-constant risk stratification is the relevant estimand—as demonstrated, for example, in recent studies of circulating tumour cell-expressed biomarkers as prognostic markers in prostate cancer (7). The recommendation is simply that proportional hazards should be treated as a testable working assumption rather than an unspoken prerequisite. Testing methods such as Schoenfeld residuals or graphical diagnostics should be reported, and when violations are identified, alternative measures such as RMST should be provided.

Urologists are now prescribing therapies of which its mechanisms demand time-varying models. The survival analysis community has long recognised this challenge; the clinical urology community should follow suit. Embracing RMST alongside traditional methods will make our evidence base more transparent, more robust, and ultimately more useful for the patients we serve.

In conclusion, we propose three practical recommendations for urologists and trialists working with ICI data. First, the proportional hazards assumption may warrant formal testing and reporting in all ICI trials, using methods such as Schoenfeld residuals or log-log plots. Second, when violations are identified or delayed treatment effects are anticipated, we suggest reporting RMST alongside the HR to provide an absolute, time-horizon-specific measure of survival benefit. Third, continuous covariate-based RMST visualisation, as illustrated in Figure 1, may be considered to preserve the full biological gradient of prognostic biomarkers, thereby avoiding the information loss inherent in dichotomised subgroup analyses.

Acknowledgments

None.

Footnote

Provenance and Peer Review: This article was a standard submission to the journal. The article has undergone external peer review.

Peer Review File: Available at https://tau.amegroups.com/article/view/10.21037/tau-2026-1-0102/prf

Funding: None.

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://tau.amegroups.com/article/view/10.21037/tau-2026-1-0102/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

References

1. Bellmunt J, de Wit R, Vaughn DJ, et al. Pembrolizumab as Second-Line Therapy for Advanced Urothelial Carcinoma. N Engl J Med 2017;376:1015-26. [Crossref] [PubMed]
2. Robert C. A decade of immune-checkpoint inhibitors in cancer therapy. Nat Commun 2020;11:3801. [Crossref] [PubMed]
3. Mick R, Chen TT. Statistical Challenges in the Design of Late-Stage Cancer Immunotherapy Studies. Cancer Immunol Res 2015;3:1292-8. [Crossref] [PubMed]
4. Royston P, Parmar MK. Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Med Res Methodol 2013;13:152. [Crossref] [PubMed]
5. Rivano M, Cancanelli L, Spazio LD, et al. Restricted mean survival time as outcome measure in advanced urothelial bladder cancer: analysis of 4 clinical studies. Immunotherapy 2021;13:95-101. [Crossref] [PubMed]
6. Tian L, Zhao L, Wei LJ. Predicting the restricted mean event time with the subject's baseline covariates in survival analysis. Biostatistics 2014;15:222-33. [Crossref] [PubMed]
7. Cho H, Byun SS, Son NH, et al. Impact of Circulating Tumor Cell-Expressed Prostate-Specific Membrane Antigen and Prostate-Specific Antigen Transcripts in Different Stages of Prostate Cancer. Clin Cancer Res 2024;30:1788-800. [Crossref] [PubMed]