SurvInt: a simple tool to obtain precise parametric survival extrapolations

Abstract

Background: Economic evaluation of emerging health technologies is mandated by agencies such as the National Institute for Health and Care Excellence (NICE) to ensure their cost is proportional to their benefit. To avoid bias, NICE stipulate that the benefit of a treatment is assessed across the lifetime of the patient population, which can be many decades. Unfortunately, follow-up from a clinical trial will not usually cover the required period and the observed follow-up will require extrapolation. For survival data this is often done by selecting a preferred model from a set of candidate parametric models. This approach is limited in that the choice of model is restricted to those originally fitted. What if none of the models are consistent with clinical prediction or external data?

Method/results: This paper introduces SurvInt, a tool that estimates the parameters of common parametric survival models which interpolate key survival time co-ordinates specified by the user, which could come from external trials, real world data or expert clinical opinion. This is achieved by solving simultaneous equations based on the survival functions of the parametric models. The application of SurvInt is shown through two examples where traditional parametric modelling did not produce models that were consistent with external data or clinical opinion. Additional features include model averaging, mixture cure models, background mortality, piecewise modelling, restricted mean survival time estimation and probabilistic sensitivity analysis.

Conclusions: SurvInt allows precise parametric survival models to be estimated and carried forward into economic models. It provides access to extrapolations that are consistent with multiple data sources such as observed data and clinical predictions, opening the door to precise exploration of regions of uncertainty/disagreement. SurvInt could avoid the need for post-hoc adjustments for complications such as treatment switching, which are often applied to obtain a plausible survival model but at the cost of introducing additional uncertainty. Phase III clinical trials are not designed with extrapolation in mind, and so it is sensible to consider alternative approaches to predict future survival that incorporate external information.

Keywords: External data; Extrapolation; Health technology assessment; Interpolation; Survival analysis.

Fig. 1

Parametric models fitted to recreated OS data for BSC arm of Keynote-045, with none passing near the circle indicating the 5 year survival rate reported by Cancer Research UK

Fig. 2

A Gompertz model obtained from SurvInt interpolating the Cancer Research UK 5 year survival rate and the median survival from the data

Fig. 3

Parametric (dashed) models fitted to observed follow-up compared to predictions made by clinical experts

Fig. 4

Extrapolations of models with parameter values obtained using SurvInt tool