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

Mixture and Non-mixture Cure Models for Health Technology Assessment: What You Need to Know

There is increasing interest in the use of cure modelling to inform health technology assessment (HTA) due to the development of new treatments that appear to offer the potential for cure in some patients. However, cure models are often not included in evidence dossiers submitted to HTA agencies, and they are relatively rarely relied upon to inform decision-making. This is likely due to a lack of understanding of how cure models work, what they assume, and how reliable they are. In this tutorial we explain why and when cure models may be useful for HTA, describe the key characteristics of mixture and non-mixture cure models, and demonstrate their use in a range of scenarios, providing Stata code. We highlight key issues that must be taken into account by analysts when fitting these models and by reviewers and decision-makers when interpreting their predictions. In particular, we note that flexible parametric non-mixture cure models have not been used in HTA, but they offer advantages that make them well suited to an HTA context when a cure assumption is valid but follow-up is limited.

Informing Structural Assumptions for Three State Oncology Cost-Effectiveness Models through Model Efficiency and Fit

The characteristics and relative strengths and weaknesses of partitioned survival models (PSMs) and state transition models (STMs) for three state oncology cost-effectiveness models have previously been studied. Despite clear and longstanding economic modeling guidelines, more than one structure is rarely presented, and the choice of structure appears correlated more with audience or precedent than disease, decision problem, or available data. One reason may be a lack of guidance and tools available to readily compare measures of internal validity such as the model fit and efficiency of different structures, or sensitivity of results to those choices. To address this gap, methods are presented to evaluate the fit and efficiency of three structures, with an accompanying R software package, psm3mkv. The methods are illustrated by analyzing interim and final analysis datasets of the KEYNOTE-826 randomized controlled trial. At both interim and final analyses, the STM Clock Reset structure provided the best and most efficient fit. Structural uncertainties had been reduced from interim to final analysis. Beyond measures of internal validity, guidelines highlight the importance of reflecting all available data, avoiding model selection purely on the basis of goodness of fit and strongly considering external validity. The method and software allow modelers to more easily evaluate and report model fit and efficiency, examine implicit assumptions, and reveal sensitivities to structural choices.

Comparing Survival Extrapolation within All-Cause and Relative Survival Frameworks by Standard Parametric Models and Flexible Parametric Spline Models Using the Swedish Cancer Registry

BACKGROUND

In health technology assessment, restricted mean survival time and life expectancy are commonly evaluated. Parametric models are typically used for extrapolation. Spline models using a relative survival framework have been shown to estimate life expectancy of cancer patients more reliably; however, more research is needed to assess spline models using an all-cause survival framework and standard parametric models using a relative survival framework.

AIM

To assess survival extrapolation using standard parametric models and spline models within relative survival and all-cause survival frameworks.

METHODS

From the Swedish Cancer Registry, we identified patients diagnosed with 5 types of cancer (colon, breast, melanoma, prostate, and chronic myeloid leukemia) between 1981 and 1990 with follow-up until 2020. Patients were categorized into 15 cancer cohorts by cancer and age group (18-59, 60-69, and 70-99 y). We right-censored the follow-up at 2, 3, 5, and 10 y and fitted the parametric models within an all-cause and a relative survival framework to extrapolate to 10 y and lifetime in comparison with the observed Kaplan-Meier survival estimates. All cohorts were modeled with 6 standard parametric models (exponential, Weibull, Gompertz, log-logistic, log-normal, and generalized gamma) and 3 spline models (on hazard, odds, and normal scales).

RESULTS

For predicting 10-y survival, spline models generally performed better than standard parametric models. However, using an all-cause or a relative survival framework did not show any distinct difference. For lifetime survival, extrapolating from a relative survival framework agreed better with the observed survival, particularly using spline models.

CONCLUSIONS

For extrapolation to 10 y, we recommend spline models. For extrapolation to lifetime, we suggest extrapolating in a relative survival framework, especially using spline models.

HIGHLIGHTS

For survival extrapolation to 10 y, spline models generally performed better than standard parametric models did. However, using an all-cause or a relative survival framework showed no distinct difference under the same parametric model.Survival extrapolation to lifetime within a relative survival framework agreed well with the observed data, especially using spline models.Extrapolating parametric models within an all-cause survival framework may overestimate survival proportions at lifetime; models for the relative survival approach may underestimate instead.

SurvInt: a simple tool to obtain precise parametric survival extrapolations

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.

Evaluation of Flexible Parametric Relative Survival Approaches for Enforcing Long-Term Constraints When Extrapolating All-Cause Survival

OBJECTIVES

Parametric models are used to estimate the lifetime benefit of an intervention beyond the range of trial follow-up. Recent recommendations have suggested more flexible survival approaches and the use of external data when extrapolating. Both of these can be realized by using flexible parametric relative survival modeling. The overall aim of this article is to introduce and contrast various approaches for applying constraints on the long-term disease-related (excess) mortality including cure models and evaluate the consequent implications for extrapolation.

METHODS

We describe flexible parametric relative survival modeling approaches. We then introduce various options for constraining the long-term excess mortality and compare the performance of each method in simulated data. These methods include fitting a standard flexible parametric relative survival model, enforcing statistical cure, and forcing the long-term excess mortality to converge to a constant. We simulate various scenarios, including where statistical cure is reasonable and where the long-term excess mortality persists.

RESULTS

The compared approaches showed similar survival fits within the follow-up period. However, when extrapolating the all-cause survival beyond trial follow-up, there is variation depending on the assumption made about the long-term excess mortality. Altering the time point from which the excess mortality is constrained enables further flexibility.

CONCLUSIONS

The various constraints can lead to applying explicit assumptions when extrapolating, which could lead to more plausible survival extrapolations. The inclusion of general population mortality directly into the model-building process, which is possible for all considered approaches, should be adopted more widely in survival extrapolation in health technology assessment.