Abstract
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.
Highlights
Evidence synthesis within a decision-making framework aims to pool and compare all relevant evidence on the efficacy of treatments within a decision set
If proportional hazards do not hold across all studies and treatment comparisons, pooling hazard ratios (HRs) can lead to misleading results, and can be problematic when the results of the synthesis are used in extrapolations to predict long-term survival.[4,8,9,10]
For both the additive and multiplicative models there was no improvement in the posterior mean deviance when the consistency assumption was relaxed, and the network meta-analysis (NMA) model was preferred based on the deviance information criterion (DIC) (Table 2)
Summary
Evidence synthesis within a decision-making framework aims to pool and compare all relevant evidence on the efficacy of treatments within a decision set. Whilst pooling HRs obtained from proportional hazards models has the advantage that it does not make any assumptions about the parametric form of the survival curves in the studies,[7] it does make the strong assumption that the HR is constant over time within each study and treatment comparison (the proportional hazards assumption). If proportional hazards do not hold across all studies and treatment comparisons, pooling HRs can lead to misleading results, and can be problematic when the results of the synthesis are used in extrapolations to predict long-term survival.[4,8,9,10] if HRs are not constant over time, they will be confounded with study follow-up time, which will introduce heterogeneity in pairwise meta-analysis and may introduce inconsistency in network meta-analysis
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