Dynamic and Flexible Survival Models for Extrapolation of Relative Survival: A Case Study and Simulation Study.

BACKGROUND: Extrapolation of survival data is a key task in health technology assessments (HTAs), which may be improved by incorporating general population mortality data via relative survival models. Dynamic survival models are a promising method for extrapolation that may be expanded to dynamic relative survival models (DRSMs), a novel development presented here. There are currently neither examples of dynamic models in HTA nor comparisons of DRSMs with other relative survival models when used for survival extrapolation. METHODS: An existing appraisal, for which there had been disagreement over the approach to survival extrapolation, was chosen and the health economic model recreated. The sensitivity of estimates of cost-effectiveness to different model choices (standard survival models, DSMs, and DRSMs) and specifications was examined. The appraisal informed a simulation study to evaluate DRSMs with relative survival models based on both standard and spline-based (flexible) models. RESULTS: Dynamic models provided insight into the behavior of the trend in the hazard function and how it may vary during the extrapolated phase. DRSMs led to extrapolations with improved plausibility for which model choice may be based on clinical input. In the simulation study, the flexible and dynamic relative survival models performed similarly and provided highly variable extrapolations. LIMITATIONS: Further experience with these models is required to identify settings when they are most useful, and they provide sufficiently accurate extrapolations. CONCLUSIONS: Dynamic models provide a flexible and attractive method for extrapolating survival data and facilitate the use of clinical input for model choice. Flexible and dynamic relative survival models make few structural assumptions and can improve extrapolation plausibility, but further research is required into methods for reducing the variability in extrapolations.

Comparing current and emerging practice models for the extrapolation of survival data: a simulation study and case-study.

BACKGROUND: Estimates of future survival can be a key evidence source when deciding if a medical treatment should be funded. Current practice is to use standard parametric models for generating extrapolations. Several emerging, more flexible, survival models are available which can provide improved within-sample fit. This study aimed to assess if these emerging practice models also provided improved extrapolations. METHODS: Both a simulation study and a case-study were used to assess the goodness of fit of five classes of survival model. These were: current practice models, Royston Parmar models (RPMs), Fractional polynomials (FPs), Generalised additive models (GAMs), and Dynamic survival models (DSMs). The simulation study used a mixture-Weibull model as the data-generating mechanism with varying lengths of follow-up and sample sizes. The case-study was long-term follow-up of a prostate cancer trial. For both studies, models were fit to an early data-cut of the data, and extrapolations compared to the known long-term follow-up. RESULTS: The emerging practice models provided better within-sample fit than current practice models. For data-rich simulation scenarios (large sample sizes or long follow-up), the GAMs and DSMs provided improved extrapolations compared with current practice. Extrapolations from FPs were always very poor whilst those from RPMs were similar to current practice. With short follow-up all the models struggled to provide useful extrapolations. In the case-study all the models provided very similar estimates, but extrapolations were all poor as no model was able to capture a turning-point during the extrapolated period. CONCLUSIONS: Good within-sample fit does not guarantee good extrapolation performance. Both GAMs and DSMs may be considered as candidate extrapolation models in addition to current practice. Further research into when these flexible models are most useful, and the role of external evidence to improve extrapolations is required.

The Extrapolation Performance of Survival Models for Data With a Cure Fraction: A Simulation Study.

OBJECTIVES: Curative treatments can result in complex hazard functions. The use of standard survival models may result in poor extrapolations. Several models for data which may have a cure fraction are available, but comparisons of their extrapolation performance are lacking. A simulation study was performed to assess the performance of models with and without a cure fraction when fit to data with a cure fraction. METHODS: Data were simulated from a Weibull cure model, with 9 scenarios corresponding to different lengths of follow-up and sample sizes. Cure and noncure versions of standard parametric, Royston-Parmar, and dynamic survival models were considered along with noncure fractional polynomial and generalized additive models. The mean-squared error and bias in estimates of the hazard function were estimated. RESULTS: With the shortest follow-up, none of the cure models provided good extrapolations. Performance improved with increasing follow-up, except for the misspecified standard parametric cure model (lognormal). The performance of the flexible cure models was similar to that of the correctly specified cure model. Accurate estimates of the cured fraction were not necessary for accurate hazard estimates. Models without a cure fraction provided markedly worse extrapolations. CONCLUSIONS: For curative treatments, failure to model the cured fraction can lead to very poor extrapolations. Cure models provide improved extrapolations, but with immature data there may be insufficient evidence to choose between cure and noncure models, emphasizing the importance of clinical knowledge for model choice. Dynamic cure fraction models were robust to model misspecification, but standard parametric cure models were not.

Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function.

Background. Parametric modeling of survival data is important, and reimbursement decisions may depend on the selected distribution. Accurate predictions require sufficiently flexible models to describe adequately the temporal evolution of the hazard function. A rich class of models is available among the framework of generalized linear models (GLMs) and its extensions, but these models are rarely applied to survival data. This article describes the theoretical properties of these more flexible models and compares their performance to standard survival models in a reproducible case study. Methods. We describe how survival data may be analyzed with GLMs and their extensions: fractional polynomials, spline models, generalized additive models, generalized linear mixed (frailty) models, and dynamic survival models. For each, we provide a comparison of the strengths and limitations of these approaches. For the case study, we compare within-sample fit, the plausibility of extrapolations, and extrapolation performance based on data splitting. Results. Viewing standard survival models as GLMs shows that many impose a restrictive assumption of linearity. For the case study, GLMs provided better within-sample fit and more plausible extrapolations. However, they did not improve extrapolation performance. We also provide guidance to aid in choosing between the different approaches based on GLMs and their extensions. Conclusions. The use of GLMs for parametric survival analysis can outperform standard parametric survival models, although the improvements were modest in our case study. This approach is currently seldom used. We provide guidance on both implementing these models and choosing between them. The reproducible case study will help to increase uptake of these models.