Parametric analysis and model selection for economic evaluation of survival data

Health technology assessments of interventions impacting survival often require extrapolating current data to gain a better understanding of the interventions’ long-term benefits. Both a comprehensive examination of the trial data up to the maximum follow-up period and the fitting of parametric models are required for extrapolation. It is standard practice to visually compare the parametric curves to the Kaplan-Meier survival estimate (or comparison of hazard estimates) and to assess the parametric models using likelihood-based information criteria. In place of these two steps, this work demonstrates how to minimize the squared distance of parametric estimators to the Kaplan-Meier estimate. This is in line with the selection of the model using Mean Squared Error, with the modification that the unknown true survival is replaced by the Kaplan-Meier estimate. We would assure the internal validity of the extrapolated model and its appropriate representation of the data by adhering to this procedure. We use both simulation and real-world data with a scenario where no model that properly fits the data could be found to illustrate how this process can aid in model selection.