Meta-analysis and network meta-analysis of time-to-event outcomes with non-proportional hazards: a Bayesian time-varying hazard ratio approach.
4 affiliations
- 1Swansea University Medical School, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, UK. [email protected].
- 2Department of Statistics, University of Warwick, Mathematical Sciences Building, CV4 7AL, Coventry, England, UK. [email protected].
- 3Warwick Medical School (WMS), University of Warwick, Gibbet Hill, CV4 7AL, Coventry, England, UK. [email protected].
- 4Centre for Health Economics, University of York, Heslington, YO10 5DD, York, England, UK. [email protected].
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.
Related
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BibTeX
@article{owen2026metaanalysis,
title = {{Meta-analysis and network meta-analysis of time-to-event outcomes with non-proportional hazards: a Bayesian time-varying hazard ratio approach.}},
author = {Rhiannon K Owen and Keith R Abrams},
journal = {BMC medical research methodology},
year = {2026},
month = aug,
doi = {10.1186/s12874-026-02963-5},
url = {https://europepmc.org/article/MED/42958094},
note = {CC BY},
}
RIS
TY - JOUR
TI - Meta-analysis and network meta-analysis of time-to-event outcomes with non-proportional hazards: a Bayesian time-varying hazard ratio approach.
AU - Rhiannon K Owen
AU - Keith R Abrams
PY - 2026
DA - 2026/08/01
JO - BMC medical research methodology
DO - 10.1186/s12874-026-02963-5
UR - https://europepmc.org/article/MED/42958094
AB - 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.
SN - 1471-2288
ER -