Extrapolating Parametric Survival Models in Health Technology Assessment: A Simulation Study

Extrapolations of parametric survival models fitted to censored data are routinely used in the assessment of health technologies to estimate mean survival, particularly in diseases that potentially reduce the life expectancy of patients. Akaike’s information criterion (AIC) and Bayesian information criterion (BIC) are commonly used in health technology assessment alongside an assessment of plausibility to determine which statistical model best fits the data and should be used for prediction of long-term treatment effects. We compare fit and estimates of restricted mean survival time (RMST) from 8 parametric models and contrast models preferred in terms of AIC, BIC, and log-likelihood, without considering model plausibility. We assess the methods’ suitability for selecting a parametric model through simulation of data replicating the follow-up of intervention arms for various time-to-event outcomes from 4 clinical trials. Follow-up was replicated through the consideration of recruitment duration and minimum and maximum follow-up times. Ten thousand simulations of each scenario were performed. We demonstrate that the different methods can result in disagreement over the best model and that it is inappropriate to base model selection solely on goodness-of-fit statistics without consideration of hazard behavior and plausibility of extrapolations. We show that typical trial follow-up can be unsuitable for extrapolation, resulting in unreliable estimation of multiple parameter models, and infer that selecting survival models based only on goodness-of-fit statistics is unsuitable due to the high level of uncertainty in a cost-effectiveness analysis. This article demonstrates the potential problems of overreliance on goodness-of-fit statistics when selecting a model for extrapolation. When follow-up is more mature, BIC appears superior to the other selection methods, selecting models with the most accurate and least biased estimates of RMST.