On When and How to Use External Data to Inform Long-Term Survival Curve Extrapolation

OBJECTIVES: Economic evaluation to support HTA dossier typically requires long term survival extrapolation. Respective economic models may then need external data to inform or validate the extrapolation. Validation in oncology may be particularly challenging due to many limitations in real-world evidence. This study discusses when and how to use external data to inform long-term survival extrapolation in a Bayesian framework.

METHODS: Firstly, discussion around “when” is conducted based on survey of recent literature and summary of our empirical experience in the past years. Secondly, we elaborate on the Bayesian procedure of how to incorporate external data directly into survival modelling for long term extrapolation, built on Guyot et al 2017 and recently emerged spline model on hazard.

RESULTS: On “when”, our suggestions are summarized in three-fold: (1) when to use external data for modeling directly versus for model validation, (2) example sources of external data with hinged pitfalls, and (3) key points to consider when assessing the appropriateness of external data sources. On “how” in a Bayesian framework, we (I) categorize external data into three types, and make explicit on how to incorporate each type into likelihood function or an informative prior, (II) discuss about the pros and cons of natural cubic spline model on log-cumulative hazard (Royston-Parmar model) and spline model directly on hazard, (III) discuss what available R packages exist for each model with some highlight on limitation, (IV) demonstrate implementation for different types of external data, using a simulated dataset (code will be made available in a public GitHub repository).

CONCLUSIONS: There are many factors to be considered before incorporating external data directly into survival model for long term extrapolation. Once deemed appropriate, there might be a more systematic approach to implement it in a Bayesian framework.