A non-parametric approach for combining evidence on progression-free and overall survival for partitioned survival models

Background: Cost-effectiveness analyses of cancer treatments typically use a partitioned survival model, which tracks time spent progression free and time spent post-progression. Such models require synthesising evidence from randomised controlled trials (RCTs) reporting time-to-event outcomes, progression free survival (PFS) and overall survival (OS). Traditional approaches pool evidence on these related outcomes separately ignoring the natural constraint that OS must be greater than PFS. Furthermore, existing methods often rely on the proportional hazards assumption, or make parametric assumptions which may not be suitable for capturing diverse survival trends across RCTs. Our objective was to develop a non-parametric approach for jointly synthesising evidence from Kaplan-Meier survival curves of PFS and OS without assuming proportional hazards and that provides the inputs required for a partitioned survival cost-effectiveness model. 

Methods: Relative treatment effects are pooled as differences (additive model) or ratios (multiplicative model) 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 techniques. AUCs are statistically synthesised in a Bayesian framework, based on models of PFS and post-progression survival (PPS), where OS is the sum of PFS and PPS. We show how discounted AUCs can be calculated to obtain discounted RMST estimates to directly use in a partitioned survival cost-effectiveness model. We applied this method to a network of trials evaluating three treatments for Stage IIIA-N2 Non-Small Cell Lung Cancer, where survival curve shapes varied between studies and proportional hazards was violated. 

Results: Models assuming additive and multiplicative treatment effects were comparable in terms of fit. Both models conformed to the natural constraint that OS is always greater than PFS and were simple to implement. We applied the relative treatment effects to a baseline RMST for PFS and OS on the reference treatment taken from the most relevant study, to obtain RMST and discounted RMST for each treatment as required in the cost-effectiveness model. 

Discussion: We discuss how the synthesis model and its output may be adapted to produce the mean time in PFS and PPS states for the time-horizon required in economic models, using external registry evidence beyond the restricted follow-up time used in the evidence synthesis.

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