A non-parametric approach for jointly combining evidence on progression free and overall survival time in network meta-analysis

Caitlin H Daly, Ross Maconachie, A E Ades, Nicky J Welton*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
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Randomised controlled trials of cancer treatments typically report progression free survival (PFS) and overall survival (OS) outcomes. Existing methods to synthesise evidence on PFS and OS either rely on the proportional hazards assumption or make parametric assumptions which may not capture the diverse survival curve shapes across studies and treatments. Furthermore, PFS and OS are not independent: OS is the sum of PFS and post-progression survival (PPS). Our aim was to develop a non-parametric approach for jointly synthesising evidence from published Kaplan-Meier survival curves of PFS and OS without assuming
proportional hazards. Restricted mean survival times (RMST) are estimated by the area under the survival curves (AUCs) up to a restricted follow-up time. The correlation between AUCs due to the constraint that OS>PFS is estimated using bootstrap re-sampling. Network meta-analysis models are given for RMST for PFS and PPS and ensure that OS=PFS + PPS. Both additive and multiplicative network meta-analysis models are presented to obtain relative treatment effects as either differences or ratios of RMST. The methods are illustrated with a network
meta-analysis of treatments for Stage IIIA-N2 Non-Small Cell Lung Cancer.
The approach has implications for health economic models of cancer treatments which require estimates of the mean time spent in the PFS and PPS health-states. The methods can be applied to a single time-to-event outcome, and so have wide applicability in any field where time-to-event outcomes are reported, the proportional hazards assumption is in doubt, and survival curve shapes differ across studies and interventions.
Original languageEnglish
Number of pages12
JournalResearch Synthesis Methods
Early online date12 Dec 2021
Publication statusE-pub ahead of print - 12 Dec 2021

Bibliographical note

Funding Information:
CHD, AEA, and NJW were supported by the National Institute of Health and Care Excellence (NICE) Guidelines Technical Support Unit at the University of Bristol, with funding from the NICE Centre for Guidelines, and RM was employed by NICE for the period when this work was conducted. NJW and AEA were also partly funded by the UK Medical Research Council grant MR/R025223/1.

Publisher Copyright:
© 2021 The Authors. Research Synthesis Methods published by John Wiley & Sons Ltd.

Structured keywords

  • HEHP@Bristol


  • network meta-analysis
  • oncology
  • restricted mean survival time
  • survival analysis
  • time-toevent outcomes


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