Time series methods for extrapolating survival data in health technology assessment

Extrapolating survival data is an important task in health technology assessment (HTA). Current approaches can lack flexibility and there is a tension between using all the data and restricting analyses to the more recent observations. Dynamic survival models (DSMs) exploit the temporal structure of survival data, are very flexible, have interpretable extrapolations, and use all the data whilst providing more weight to more recent observations when generating extrapolations. DSMs have not previously been used in HTA; this thesis evaluated the performance and usefulness of dynamic models in this context. Extensive simulation studies compared DSMs with both current practice and other flexible (emerging practice) models. Results indicated that, compared with current practice, DSMs can more accurately model the data, providing improved extrapolations. However, with small sample sizes or short follow-up there was a danger of providing worse extrapolations. Of emerging practice models, spline-based models often had similar performance to DSMs whilst fractional polynomials provided very poor extrapolations. Two novel extensions to DSMs were developed to incorporate external data in the form of relative survival and cure models. Both extensions helped to reduce the variation in extrapolations. Dynamic cure models were assessed in a simulation study and provided good extrapolations that were robust to model misspecification. A case-study demonstrated that extrapolations from an interim analysis can be poor for all the methods considered when the observed data is not representative of the future. A case-study demonstrated the feasibility of using DSMs in HTA, and an extension to incorporate time-varying treatment effects. DSMs should be considered as a potential method when analysing and extrapolating survival data. These flexible models and their extensions show promise but have the danger of providing poor extrapolations in data-poor scenarios. More research is needed into identifying situations when use of these should be the default approach in HTA.