Strategies to address non-proportional hazards between survival curves - Lessons from phase III trials in hepatocellular carcinoma

Introduction

Hepatocellular carcinoma (HCC) is a major cause of global cancer mortality, significantly affecting overall survival (OS) due to poor adherence to surveillance programs and frequent late-stage diagnoses.^1,2 Advances in immune checkpoint inhibitor (ICI)-based therapies have reshaped the therapeutic landscape, particularly in advanced stages of disease, and have even shown promising results at earlier HCC stages. ^3–5

Two key considerations in clinical trials are the proportional hazards (PH) assumption when time-to-event endpoints are used and the timing and interpretation of interim analyses (IA). The PH assumption suggests that the hazard ratio (HR) remains constant over time. ⁶ Deviations from this assumption, referred to as non-proportional hazards (NPH), can influence the interpretation of statistical significance and the perceived magnitude of the treatment effect. ⁷ Patterns of NPH in ICI-based oncology trials include diminishing effects over time, delayed treatment effects, and crossing hazards. ⁸ This issue has gained considerable attention in the HCC field following the IMbrave050 phase III randomized controlled trial (RCT), in which the IA demonstrated a positive outcome for recurrence-free survival (RFS) (HR 0.72; 95% CI 0.53–0.98) with adjuvant atezolizumab-bevacizumab vs. surveillance after resection in high-risk HCC. ⁹ These results led to its adoption in American Association for the Study of Liver Diseases (AASLD) clinical practice guidelines. ¹⁰ However, subsequent analysis with more mature RFS data failed to confirm this benefit (HR 0.90; 95% CI 0.72–1.12), ¹¹ resulting in the withdrawal of this recommendation from the major guidelines. This inconsistency in results may be related to the presence of NPH, which poses challenges for determining the optimal timing and robustness of IA.¹²

To address NPH, advanced statistical tools, such as the MaxCombo test ¹³ and restricted mean survival time (RMST) analysis, ¹⁴ offer robust alternatives to assess statistical significance and magnitude of benefit compared with traditional log-rank tests, Cox models and HR estimates. ¹⁵ The MaxCombo test combines several weighted log-rank tests, enhancing detection of treatment effects across different NPH types by providing greater statistical power. ^8,13,15 RMST measures the average survival up to a specified point, akin to a patient’s life expectancy within that period. ¹⁶ This method offers a clear, intuitive summary of survival, relying less on the assumption of PH and providing a more interpretable estimate of treatment benefits when HR fluctuate over time. ¹⁷ Another complementary method to address NPH is the use of piecewise hazard ratios (pHR), which focus on estimating the magnitude of treatment effects within specific time intervals, allowing for a more detailed evaluation of how treatment efficacy evolves over time. ¹³

Given the potential implications of NPH in the interpretation of pivotal phase III trials, we aimed to assess the prevalence and potential impact of NPH. Our analysis focused on evaluating both statistical significance and effect magnitude, while proposing a robust strategy to ensure rigorous interpretation of IA in HCC trials.

Materials and methods

Results

Discussion

The introduction of immunotherapies has transformed the therapeutic landscape of HCC, extending its impact beyond advanced stages. ^3–5 At early stages of the disease, IMbrave050 – the first positive RCT in 40 years – paved the way to improving the outcome of patients undergoing resection/local ablation, when the disease can be cured. The proposed regimen, atezolizumab plus bevacizumab improved RFS vs. surveillance, ⁹ and thus it was adopted by AASLD clinical practice guidelines. ¹⁰ However, a subsequent efficacy analysis with longer FU showed a reduction in the magnitude of clinical benefit, and thus the trial no longer met the primary endpoint. ¹¹ The inconsistency between the interim and subsequent efficacy analyses prompted us to conduct a thorough analysis to understand the reason for such an important switch in the outcome.

The current study identified that inconsistencies in the outcome between the interim and subsequent analyses in the IMbrave050 trial were directly attributable to the presence of NPH, calling for a broader exploration of pivotal practice-changing RCTs reported in HCC. Importantly, our aim was not to reinterpret or challenge the conclusions of individual trials, but to illustrate how statistical significance and effect size may differ under NPH conditions. To this end, we propose a framework based on data maturity and appropriate analytical tools (MaxCombo, RMST, and pHR) to improve the reliability of efficacy assessments.

Similar to other cancers, our findings demonstrated that immunotherapies for HCC are associated with NPH issues in 20% of RCTs (IMbrave050, ¹¹ LEAP-012, ⁵ HIMALAYA ^29,30 and CheckMate 9DW ³¹). This phenomenon highlights the necessity of employing additional statistical tools to accurately evaluate treatment efficacy and appropriately describe the magnitude of effect over time under different patterns of NPH. ^7,13,15,44

To address NPH issues in these trials, we adopted an integrative approach (Fig. 1) that highlights both the need for more mature data (either by ensuring enough FU or number of events) ^8,12,24 and the application of sensitivity analyses using statistical tools for these scenarios. ^13–15 In this regard, we defined mature data as either double the median of the estimated outcome of the primary endpoint for the control arm, or a number of events providing robust information (i.e. ≥60% of events out of the total number of patients randomized). These criteria are essential to ensure that the analysis captures the full impact of the treatment, particularly under the influence of distinct NPH patterns, in which the timing of hazard changes can significantly affect the observed outcomes.^{8, 12,24} In settings with low event rates, the ≥60% threshold may not be achievable; in such cases, reaching at least double the median FU of the control group remains a valid proxy for data maturity under NPH.

In terms of statistical tools, aside from the G-T test to define the presence of NPH, we use the MaxCombo test (instead of the log-rank test) and the RMST analyses (instead of the HR ^{15, 45}), since the latter fails to properly capture the dynamics of treatment benefits under NPH conditions. ⁷ As emphasized by the ICH E9 (R1) addendum, ^12,46 RMST offers a robust alternative, with dRMST quantifying the absolute benefit in time units and rRMST expressing relative benefit. ^16,47,48 Additionally, we used pHRs, which allows a dynamic representation of how treatment benefits evolve over time, offering a nuanced perspective that is particularly relevant in scenarios with varying hazard patterns. ¹³ However, it is important to highlight that MaxCombo and RMST improve analysis under NPH but are not reliable without adequate maturity. Without sufficient FU or events, even these methods may yield misleading results.

Using this approach, we defined four cases of NPH, two of which had a diminishing effect pattern (IMbrave050 and LEAP-012), one with a delayed effect pattern (HIMALAYA trial) and one with a crossover effect pattern (CheckMate 9DW). In all studies, the MaxCombo test yielded results consistent with the log-rank test. Nonetheless, three trials were stopped at the IA (IMbrave050, LEAP-012 and CheckMate 9DW), and one at the final analysis (HIMALAYA). When exploring the robustness of information, only IMbrave050 stands-out as immature for assessing benefit effects in the setting of NPH. Other trials either showed maturity in terms of median FU (LEAP012) or >60% of events (HIMALAYA and Checkmate 9DW). Thus, the only practice-changing pivotal trial that was affected by immature IA was IMbrave050. This has implications for the future of trial design in HCC, as exploring the status of NPH should be mandatory in all IA. In the case of immature data, it is not recommended to stop a study, even in cases where the log-rank test hits the primary endpoint; thus, stopping rules, such as those of O’Brien-Fleming, would not apply in these scenarios.

Therefore, our recommendation is that for cases of NPH at IA, evaluating both the significance and magnitude of treatment benefit requires careful consideration of key parameters, including the minimum FU duration (at least twice the estimated median time of the primary endpoint for the control group) or sufficient events (≥60% of events out of the total number of patients randomized). In our analysis, all four trials with confirmed NPH showed consistent significance across log-rank, MaxCombo, and RMST tests. Notably, MaxCombo consistently yielded smaller p values, suggesting greater sensitivity in detecting time-varying effects. This observation aligns with prior meta-analyses supporting MaxCombo as the preferred test under NPH conditions. ¹⁵ In addition, the application of RMST and pHR analyses allowed us to accurately quantify the magnitude and temporal dynamics of this effect.

The PH assumption is rarely reported in RCTs, even when ICI regimens are tested. ⁶ Recent analysis of 66 RCTs relied on KM curves and the log-rank test (88%), while only 12% checked for NPH. ⁴⁹ In NPH scenarios, the HR depends on the censoring distribution and thus loses clear interpretability, while log-rank tests may fail to detect genuine effects. In support of this, a study found that out of 18 trials with inconclusive log-rank tests, nine found differences when applying NPH-specific methods. ⁵⁰ A similar finding was observed in a RCT assessing acute lymphoblastic leukemia therapies. ^51,52 These insights align with IMbrave050 and underscore the importance of robust FU, sufficient event percentages, and appropriate statistical methods under NPH. Consequently, many recent ICI-based RCTs now incorporate RMST or pHR as sensitivity analyses. ^31,53,54

Anticipating NPH is essential given its frequent association with ICIs, yet predicting its pattern or whether it arises from treatment effects or population heterogeneity remains challenging. ^8,12 Notably, both trials with a delayed effect (HIMALAYA and CheckMate 9DW) included CTLA-4 blockade, suggesting that similar delayed effects may be expected in studies with this mechanism of action. Proactive strategies that account for NPH, such as incorporating sensitivity analyses, enable adjustments in sample size and IA timing, ultimately strengthening study power and reliability. ^8,12 Accounting for NPH from the design phase is key not only to ensure statistical validity but also to optimize sample size, FU duration, and IA schedules. The approaches proposed here can help avoid premature decisions based on incomplete data, as evidenced in the re-analysis of IMbrave050, and further emphasize the critical role of robust trial designs tailored to NPH scenarios.

Addressing the potential challenges posed by NPH in phase III RCTs, particularly of ICI-based regimens, may warrant a closer look at how clinical benefits are currently evaluated. While the methodological approach to NPH is consistent across settings, the clinical interpretation of benefit depends on disease stage and endpoint. For instance, the European Society for Medical Oncology Magnitude of Clinical Benefit Scale (ESMO-MCBS) grading system ⁵⁵ does not incorporate statistical methods tailored to NPH, relying instead on median-based differences, Cox-derived HRs, or landmark timepoints (e.g. 2–3 years) to define meaningful survival gains. In its latest version (v2.0), ESMO-MCBS has introduced stricter criteria for tail-of-the-curve credit, requiring that at least 20% of patients in the experimental arm remain at risk at the evaluation timepoint to ensure robustness.⁵⁶ While such timepoints may partially capture delayed effects, landmark analyses exclude censored patients, lack formal statistical inference, and are sensitive to the number at risk, limitations that reduce their reliability under NPH. ^57,58 In contrast, RMST offers a more robust and interpretable metric in this context.

Adapting these guidelines to better account for NPH scenarios could be worthwhile, especially given that ESMO-MCBS scores have been found to correlate significantly with favorable health technology assessment (HTA) outcomes, potentially increasing the likelihood of positive HTA decisions and reducing the time between marketing authorization and HTA recommendations. ⁵⁹

Our study has several limitations. The absence of individual patient-level data in RCTs required the reconstruction of KM curves from published data, which may introduce estimation inaccuracies. Our re-analysis, however, was consistent with the original findings, providing validation for the methodology employed. Importantly, our proposal based on defining maturity as either twice the median of the estimated outcome for the control arm or the occurrence of ≥60% of events among randomized patients, is not intended as a definitive standard, but rather as a structured, literature-based framework that should be prospectively validated in future phase III trials with time-varying treatment effects. We propose specific statistical tests for NPH scenarios. The MaxCombo test, although useful, may disproportionately weigh events at specific intervals, potentially affecting interpretation in the presence of complex hazard patterns. Similarly, since the MaxCombo and log-rank tests rely on different assumptions, their p values are not directly comparable. However, previous simulations have shown that MaxCombo test performs better in scenarios with time-varying treatment effects. ¹³ Additionally, RMST is constrained to a predefined time horizon and potentially fails to capture long-term effects or delayed treatment benefits, whereas pHR can be challenging to interpret when treatment effects vary significantly over time, particularly in cases of crossing hazards or delayed effects. These considerations underscore the need for the careful interpretation of these statistical tools in the clinical context of NPH. ⁶⁰

In conclusion, the presence of NPH in ICI-based trials requires a paradigm shift in the approach to statistical analysis, particularly at IA bounded by stopping rules. Our proposed strategy focuses on adapting statistical methodologies to address the challenges posed by NPH, ensuring that the IA provides robust and consistent data. By incorporating advanced techniques such as MaxCombo, RMST, and pHR, this approach enables a more accurate detection of treatment effects over time and minimizes the risk of premature or misleading conclusions based on insufficient FU or event maturity. This approach ensures that trial outcomes reflect the true clinical impact of novel therapies and optimizes decision-making during the trial process. Furthermore, this strategy improves the communication of treatment benefits to the scientific community, healthcare professionals, and key stakeholders, ultimately fostering informed decisions that directly benefit patients with HCC.

Supplementary Material

Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jhep.2025.08.042.

Data availability

Data supporting the findings of this study are available upon request from the corresponding author (JML).