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

2026-05-19

AI Summary

Traditional meta-analyses rely on the assumption of a constant hazard ratio, which fails to capture time-varying treatment effects under non-proportional hazards. This study proposes a Bayesian time-varying hazard ratio approach that incorporates an interaction term between treatment and log-time within a Cox model, integrated with bivariate or network meta-analysis to jointly estimate both the overall treatment effect and its temporal dynamics. By innovatively combining time-varying modeling with Bayesian multivariate meta-analysis, the method yields intuitive, interpretable, and policy-relevant dynamic efficacy evidence suitable for health technology assessment. Applied to gastric cancer and melanoma datasets, it successfully identified non-proportional hazards—for instance, revealing that the combination of nivolumab and ipilimumab achieved a hazard ratio of 0.24 at five years, demonstrating substantially superior long-term benefit over control, with significant clinical and decision-making implications.

Abstract

Background: Often when undertaking meta-analyses of time-to-event (TTE) outcomes, especially in a Health Technology Assessment context, a hazard ratio (HR) scale is used. However, issues arise when there is evidence of non-proportional hazards in some of the studies included. A number of methods have been advocated, but their use has been limited by either their complexity and/or the ease with which their results can be used in HTA. An alternative approach is to assume a treatment-log(time) interaction within a Cox proportional hazards model for each study, and to then undertake a bivariate meta-analysis of the resulting treatment and interaction coefficients, so that an overall time-varying HR (TVHR) can be obtained. Methods: A TVHR approach was applied to a meta-analysis of chemotherapy compared to Standard of Care for advanced recurrent gastric cancer, and in which Progression-Free Survival (PFS) was an outcome. The approach was also applied to a network meta-analysis (NMA) evaluating overall survival (OS) in advanced BRAF-mutated melanoma. Results: Five trials in the advanced gastric cancer meta-analysis displayed evidence of non-proportional hazards for PFS. Using a TVHR model produced HRs ranging from 0.83 (CrI:0.75-0.91) at 0.5 years to 0.99 (CrI:0.79-1.23) at 3.5 years. Three studies showed evidence of non-proportional hazards in the advanced BRAF-mutated melanoma NMA for OS. Using a TVHR model, nivolumab plus ipilimumab demonstrated consistent superiority from month 7 onwards, with a HR improving from 0.37 (CrI:0.26-0.51) at one year to 0.24 (CrI:0.12-0.45) at five years. Conclusions: A TVHR approach to the meta-analysis or NMA of TTE outcomes when the proportional hazards assumption appears not to hold, produces an intuitive solution which can be readily used in HTA.

Problem

• time-to-event
• non-proportional hazards
• meta-analysis
• network meta-analysis
• hazard ratio

Innovation

• time-varying hazard ratio
• non-proportional hazards
• Bayesian meta-analysis
• treatment-time interaction
• network meta-analysis