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Background <p>Meta-analyses of time-to-event (TTE) outcomes, particularly in Health Technology Assessment (HTA), commonly use a hazard ratio (HR) scale. However, non-proportional hazards in included trials create difficulties. Existing methods are either too complex or not easily incorporated into economic decision models for cost-effectiveness assessment.</p> <p>An alternative approach assumes a treatment-log(time) interaction within a Cox proportional hazards model, allowing the log HR to vary linearly with log(time). A bivariate meta-analysis of the resulting treatment and interaction coefficients then yields an overall time-varying HR (TVHR) with appropriate uncertainty.</p> Methods <p>The TVHR approach was applied to a meta-analysis of 20 trials (4,069 patients) comparing chemotherapy to Standard of Care (SoC) for advanced recurrent gastric cancer, with Progression-Free Survival (PFS) as an outcome (median follow-up 1.2 years). It was also applied to a network meta-analysis (NMA) of 13 treatments across 13 Randomised Controlled Trials (RCTs) in previously untreated advanced BRAF-mutated melanoma (3,913 deaths in 6,378 participants) evaluating Overall Survival (OS). Both applications were compared against standard Bayesian meta-analysis assuming proportional hazards.</p> Results <p>Five trials in the gastric cancer meta-analysis showed non-proportional hazards for PFS. A standard Bayesian random-effects meta-analysis yielded a pooled HR of 0.78 (95% CrI: 0.70–0.86). The TVHR model produced a pooled interaction effect of 0.09 (95% CrI: -0.005-0.193), with HRs ranging from 0.83 (95% CrI: 0.75-0.91) at 0.5 years to 0.99 (95% CrI: 0.79-1.23) at 3.5 years. Three studies in the melanoma NMA showed non-proportional hazards for OS. Using the TVHR model, nivolumab plus ipilimumab demonstrated consistent superiority from month 7, with improving HRs from 0.37 (95% CrI: 0.26-0.51) at one year to 0.24 (95% CrI: 0.12-0.45) at five years (mean rank 1.18, 95% CrI: 1-2). Dabrafenib- and vemurafenib-based regimens showed evidence of waning treatment effects, potentially becoming inferior to dacarbazine (HR&gt;1) at five years.</p> Conclusions <p>The TVHR approach offers a simple, intuitive solution for meta-analysis of TTE outcomes when proportional hazards do not hold, and are readily incorporated into economic decision models. Extensions to a fully Bayesian one-stage model, and spline-based interaction effects are also feasible.</p>

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Meta-analysis and network meta-analysis of time-to-event outcomes with non-proportional hazards: a Bayesian time-varying hazard ratio approach

  • 期刊论文

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  • 发表日期：

    2026年8月4日

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  • Rhiannon K. Owen,
  • Keith R. Abrams

摘要

Background

Meta-analyses of time-to-event (TTE) outcomes, particularly in Health Technology Assessment (HTA), commonly use a hazard ratio (HR) scale. However, non-proportional hazards in included trials create difficulties. Existing methods are either too complex or not easily incorporated into economic decision models for cost-effectiveness assessment.

An alternative approach assumes a treatment-log(time) interaction within a Cox proportional hazards model, allowing the log HR to vary linearly with log(time). A bivariate meta-analysis of the resulting treatment and interaction coefficients then yields an overall time-varying HR (TVHR) with appropriate uncertainty.

Methods

The TVHR approach was applied to a meta-analysis of 20 trials (4,069 patients) comparing chemotherapy to Standard of Care (SoC) for advanced recurrent gastric cancer, with Progression-Free Survival (PFS) as an outcome (median follow-up 1.2 years). It was also applied to a network meta-analysis (NMA) of 13 treatments across 13 Randomised Controlled Trials (RCTs) in previously untreated advanced BRAF-mutated melanoma (3,913 deaths in 6,378 participants) evaluating Overall Survival (OS). Both applications were compared against standard Bayesian meta-analysis assuming proportional hazards.

Results

Five trials in the gastric cancer meta-analysis showed non-proportional hazards for PFS. A standard Bayesian random-effects meta-analysis yielded a pooled HR of 0.78 (95% CrI: 0.70–0.86). The TVHR model produced a pooled interaction effect of 0.09 (95% CrI: -0.005-0.193), with HRs ranging from 0.83 (95% CrI: 0.75-0.91) at 0.5 years to 0.99 (95% CrI: 0.79-1.23) at 3.5 years. Three studies in the melanoma NMA showed non-proportional hazards for OS. Using the TVHR model, nivolumab plus ipilimumab demonstrated consistent superiority from month 7, with improving HRs from 0.37 (95% CrI: 0.26-0.51) at one year to 0.24 (95% CrI: 0.12-0.45) at five years (mean rank 1.18, 95% CrI: 1-2). Dabrafenib- and vemurafenib-based regimens showed evidence of waning treatment effects, potentially becoming inferior to dacarbazine (HR>1) at five years.

Conclusions

The TVHR approach offers a simple, intuitive solution for meta-analysis of TTE outcomes when proportional hazards do not hold, and are readily incorporated into economic decision models. Extensions to a fully Bayesian one-stage model, and spline-based interaction effects are also feasible.