Survival Extrapolation Incorporating General Population Mortality Using Excess Hazard and Cure Models: A Tutorial

Abstract

Background: Different parametric survival models can lead to widely discordant extrapolations and decision uncertainty in cost-effectiveness analyses. The use of excess hazard (EH) methods, which incorporate general population mortality data, has the potential to reduce model uncertainty. This review highlights key practical considerations of EH methods for estimating long-term survival.

Methods: Demonstration of methods used a case study of 686 patients from the German Breast Cancer Study Group, followed for a maximum of 7.3 y and divided into low (1/2) and high (3) grade cancers. Seven standard parametric survival models were fit to each group separately. The same 7 distributions were then used in an EH framework, which incorporated general population mortality rates, and fitted both with and without a cure parameter. Survival extrapolations, restricted mean survival time (RMST), and difference in RMST between high and low grades were compared up to 30 years along with Akaike information criterion goodness-of-fit and cure fraction estimates. The sensitivity of the EH models to lifetable misspecification was investigated.

Results: In our case study, variability in survival extrapolations was extensive across the standard models, with 30-y RMST ranging from 7.5 to 14.3 y. Incorporation of general population mortality rates using EH cure methods substantially reduced model uncertainty, whereas EH models without cure had less of an effect. Long-term treatment effects approached the null for most models but at varying rates. Lifetable misspecification had minimal effect on RMST differences.

Conclusions: EH methods may be useful for survival extrapolation, and in cancer, EHs may decrease over time and be easier to extrapolate than all-cause hazards. EH cure models may be helpful when cure is plausible and likely to result in less extrapolation variability.

Highlights: In health economic modeling, to help anchor long-term survival extrapolation, it has been recommended that survival models incorporate background mortality rates using excess hazard (EH) methods.We present a thorough description of EH methods with and without the assumption of cure and demonstrate user-friendly software to aid researchers wishing to use these methods.EH models are applied to a case study, and we demonstrate that EHs are easier to extrapolate and that the use of the EH cure model, when cure is plausible, can reduce extrapolation variability.EH methods are relatively robust to lifetable misspecification.

Keywords: excess hazard models; health technology assessment; modeling; overall survival; survival extrapolation.

Figure 1

Hypothesised hazard functions in a cancer clinical trial where cure is possible.

Figure 2

All-cause survival extrapolation of 7 parametric models for grades 1/2 breast cancer patients: (a) without external data, (b) with background mortality rates incorporated using an excess hazards model, and (c) with background mortality rates incorporated in a mixture-cure excess hazards model. The black dashed line shows the marginal background survival. The vertical dashed line shows the end-of-study follow-up. The table shows the 30-y restricted mean survival times (RMST) with 95% confidence intervals.

Figure 3

Extrapolation of all-cause hazards estimated from 7 parametric models for grades 1/2 breast cancer patients: (a) without external data, (b) with background mortality rates incorporated using an excess hazards model, and (c) with background mortality rates incorporated in a mixture-cure excess hazards model. The black dashed line shows the marginal background hazard. The vertical dashed line shows end of study follow-up.

Figure 4

All-cause hazard ratios derived from 7 parametric models fitted separately to the 2 cancer grade groups: (a) without external data, (b) with background mortality rates incorporated using an excess hazards model, and (c) with background mortality rates incorporated in a mixture-cure excess hazards model. The table shows the difference in 30-y restricted mean survival times (RMST) with 95% confidence intervals.

Figure 5

All-cause survival extrapolation of the stratified Log-normal excess hazard models with and without cure, where background mortality rates used for model fitting are taken from 1 of 6 countries and predictions are made for the country used in the estimation. The table shows the difference in 30-y restricted mean survival time (RMST) with 95% confidence intervals. (a) Scenario 1: Excess hazard model without cure (same lifetable for estimation and prediction), (b) Scenario 1: Excess hazard model with cure (same lifetable for estimation and prediction).