Cost-effectiveness analyses of cancer treatments typically require an evidence synthesis of randomised controlled trials reporting progression free survival (PFS) and overall survival (OS). Existing methods often rely on the proportional hazards assumption, or make parametric assumptions which may not capture the diverse survival curve shapes across studies. Motivated by the NICE clinical guideline for Stage IIIA-N2 Non-Small Cell Lung Cancer, our objective 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, to obtain the inputs required for cost-effectiveness models.

Relative treatment effects are pooled as differences or ratios of restricted mean survival time (RMST), i.e., the mean survival time accrued from randomisation up to T years. RMST is estimated by the area under the survival curves (AUCs) for PFS and OS. The correlation between the AUCs of PFS and OS within trials is estimated using non-parametric bootstrap sampling. AUCs for PFS and OS are pooled in a Bayesian framework, with (network) meta-analysis models given for PFS and post-progression survival (PPS), where OS=PFS + PPS. The relative treatment effects are applied to a baseline RMST for PFS and PPS on the reference treatment taken from the most relevant study, to obtain estimates of RMST and discounted RMST for each treatment.

Estimates conformed to the constraint that OS is greater than PFS. Treatments effects on RMST differed for PFS but were comparable for PPS. The method was implemented to provide the inputs required for the cost-effectiveness analysis in the NICE guideline.

The model was simple to implement and fitted the data well. The results may be combined with external registry evidence beyond the restricted follow-up time used in the evidence synthesis, to produce the mean time in PFS and PPS states for the time-horizon required in economic models.