Meta-analysis and network meta-analysis of time-to-event outcomes with non-proportional hazards: a Bayesian time-varying hazard ratio approach
In brief
Nivolumab plus ipilimumab's estimated death hazard fell from 0.37 to 0.24
A Bayesian time-varying analysis of trial data found nivolumab plus ipilimumab's estimated hazard of death, relative to other treatments in the network, declined from 0.37 at one year to 0.24 at five years. The method also suggested gastric cancer chemotherapy's progression benefit waned over time, showing why a single hazard ratio can mislead; findings come from two applications of the approach.
- Journal
- BMC medical research methodology (Q1)
- Published
- 4 August 2026
- Study design
- Systematic review / meta-analysis of RCTs
- Evidence level
- Level 1, High (CEBM 1a)
- Authors
- Rhiannon K Owen, Keith R Abrams
- PMID
- 42958094
- DOI
- 10.1186/s12874-026-02963-5
Why clinicians should know about it
- Picked for Epidemiology (paper of the day, 1 November 2026): Methods paper addresses non-proportional hazards in evidence synthesis
- Picked for Dermatology (top studies of the week, 1 November 2026): Comparative treatment survival evidence for advanced melanoma
Abstract
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.
Abstract as published, via PubMed.
For healthcare professionals. The summary is generated by AI from the published abstract, and the evidence level is assigned automatically from the study design on the Oxford CEBM hierarchy. Neither is medical advice. Read the full paper before changing practice.