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

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.

arXiv comment23 pages, 13 figures, 3 tables & Presented as an Oral Contribution at International Society for Clinical Biostatistics (ISCB) Conference (ISCB-46), Basel, August 27, 2025