Adjusting Survival Curves to Incorporate External Evidence: A Simplified Approach without Patient-Level Data

Cost-effectiveness modelling often requires the extrapolation of survival data from clinical trials. The choice of extrapolation method is often uncertain and can have a profound effect on the results. We propose an approach that incorporates external evidence (eg, from published studies, registries, or elicited clinical opinion) into the extrapolation process to reduce uncertainty. This method can be applied to adjust previously fitted parametric curves as a secondary analysis, without access to the underlying patient-level data. Adjusted curves can be easily exported and used in spreadsheet-based models.

Standard parametric survival curves are fitted to time-to-event data using maximum likelihood estimation (MLE). These are combined with external evidence on expected cohort-level survival at a future time point(s), formulated as a probability distribution, to generate adjusted survival curves that simultaneously incorporate both observed data and external evidence. Parameter estimation uses importance sampling and multivariate normal approximations of the likelihood. We apply our method to a case study of survival extrapolation from immuno-oncology.

Our method resulted in extrapolated survival predictions that were more closely aligned with the external evidence compared with the standard (MLE-based) approach. The incorporation of external evidence decreased the between-distribution variance (reduced structural uncertainty) and for most distributions also decreased within-distribution variance (reduced parametric uncertainty).

Our extrapolation method can reduce uncertainty when valid external evidence is available. Only MLE-based parameter estimates are required to implement our method; thus, secondary model users such as health technology assessment bodies can adjust survival extrapolations from existing cost-effectiveness models without access to patient-level data. Implementation is straightforward and computationally efficient, and outputs are easily incorporated into existing cost-effectiveness models.