{
  "abstract": "Background\n\nMeta-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\n\nThe 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\n\nFive 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\n\nThe 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_shown": true,
  "affiliations": [
    "Swansea University Medical School, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, UK. R.K.Owen@Swansea.ac.uk.",
    "Department of Statistics, University of Warwick, Mathematical Sciences Building, CV4 7AL, Coventry, England, UK. Keith.Abrams@warwick.ac.uk.",
    "Warwick Medical School (WMS), University of Warwick, Gibbet Hill, CV4 7AL, Coventry, England, UK. Keith.Abrams@warwick.ac.uk.",
    "Centre for Health Economics, University of York, Heslington, YO10 5DD, York, England, UK. Keith.Abrams@warwick.ac.uk."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Rhiannon K Owen"
    },
    {
      "affs": [
        1,
        2,
        3
      ],
      "name": "Keith R Abrams"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fb2gagv8t6dhn.bib",
  "cited_by": 0,
  "doi": "10.1186/s12874-026-02963-5",
  "fulltext_url": "https://europepmc.org/articles/PMC13721545",
  "id": "fb2gagv8t6dhn",
  "issns": [
    "1471-2288"
  ],
  "landing_url": "https://europepmc.org/article/MED/42958094",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Research"
    ],
    [
      "lcc",
      "R5-920"
    ],
    [
      "openalex",
      "1804|Meta-analysis and systematic reviews"
    ]
  ],
  "openalex": "W7172316280",
  "pdf_url": "https://europepmc.org/articles/PMC13721545?pdf=render",
  "pmcid": "PMC13721545",
  "pmid": "42958094",
  "published": "2026-08-01",
  "publisher": "BMC",
  "ris": "https://research.draconitic.com/paper/fb2gagv8t6dhn.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:21:29Z",
      "native_id": "MED:42958094",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42958094"
    },
    {
      "first_seen": "2026-11-01T14:21:22Z",
      "native_id": "05d1fc06a2dd4e41bbd2a789a21bfe5b",
      "source": "doaj",
      "url": "https://doi.org/10.1186/s12874-026-02963-5"
    },
    {
      "first_seen": "2026-11-03T12:22:13Z",
      "native_id": "PMC13721545",
      "source": "pmc",
      "url": "https://doi.org/10.1186/s12874-026-02963-5"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:2613|Statistical Methods in Epidemiology",
      "subfield": "statistics"
    },
    {
      "field": "medicine",
      "origin": "lcc:R5-920",
      "subfield": "general"
    }
  ],
  "title": "Meta-analysis and network meta-analysis of time-to-event outcomes with non-proportional hazards: a Bayesian time-varying hazard ratio approach.",
  "title_text": "Meta-analysis and network meta-analysis of time-to-event outcomes with non-proportional hazards: a Bayesian time-varying hazard ratio approach.",
  "type": "peer-reviewed",
  "updated_at": "2026-11-03T14:20:49Z",
  "url": "https://research.draconitic.com/paper/fb2gagv8t6dhn",
  "venue": "BMC medical research methodology",
  "versions": []
}