How Uncertain is the Survival Extrapolation? A Study of the Impact of Different Parametric Survival Models on Extrapolated Uncertainty About Hazard Functions, Lifetime Mean Survival and Cost Effectiveness

Abstract

Background and Objective The extrapolation of estimated hazard functions can be an important part of cost-effectiveness analyses. Given limited follow-up time in the sample data, it may be expected that the uncertainty in estimates of hazards increases the further into the future they are extrapolated. The objective of this study was to illustrate how the choice of parametric survival model impacts on estimates of uncertainty about extrapolated hazard functions and lifetime mean survival. Methods We examined seven commonly used parametric survival models and described analytical expressions and approximation methods (delta and multivariate normal) for estimating uncertainty. We illustrate the multivariate normal method using case studies based on four representative hypothetical datasets reflecting hazard functions commonly encountered in clinical practice (constant, increasing, decreasing, or unimodal), along with a hypothetical cost-effectiveness analysis. Results Depending on the survival model chosen, the uncertainty in extrapolated hazard functions could be constant, increasing or decreasing over time for the case studies. Estimates of uncertainty in mean survival showed a large variation (up to sevenfold) for each case study. The magnitude of uncertainty in estimates of cost effectiveness, as measured using the incremental cost per quality-adjusted life-year gained, varied threefold across plausible models. Differences in estimates of uncertainty were observed even when models provided near-identical point estimates. Conclusions Survival model choice can have a significant impact on estimates of uncertainty of extrapolated hazard functions, mean survival and cost effectiveness, even when point estimates were similar. We provide good practice recommendations for analysts and decision makers, emphasizing the importance of considering the plausibility of estimates of uncertainty in the extrapolated period as a complementary part of the model selection process.

Incorporating external trial data to improve survival extrapolations: a pilot study of the COU-AA-301 trial

“…An alternative Bayesian analysis (beyond specifying a prior for the shape parameter of the model under consideration) may also address the problem of potential imbalances noted above (to an extent), and while beyond the scope of this pilot study, is an area for future research to expand upon these findings. Such research could also consider if incorporating external evidence helps to appropriately quantify extrapolation uncertainty (Kearns et al 2020).…”

Estimating life expectancy and years of life lost in epidemiological studies: a review of methods using an example from multimorbidity

“…As most studies predict survival beyond the duration of the study data, further investigations with longer follow-up may explore the impact of the model structural uncertainty on the YLL estimates. 56 Lastly, the minimum sample size of participants and the number of events required to estimate life expectancy and YLL for each method is still yet to be clarified, and further research is needed, possibly through simulation studies. 20 Strengths of this study include the utilisation and illustration of different methods to estimate life expectancy and YLL, with statistical codes reported for the available software.…”

Impact of limited sample size and follow-up on single event survival extrapolation for health technology assessment: a simulation study

“…No study has examined in depth the relationship between sample size, completeness of follow-up, and performance of extrapolation methods for estimation of clinical and economic decision-modelling parameters. Aspects of this study have been evaluated previously, including impact of accrual and follow-up on estimation of relative and non-constant treatment effects [ 21 ], case studies on the impact of survival distribution choice on estimates of extrapolated hazard and mean survival [ 11 ], and performance of IC and bias in RMST estimates in simulated results from clinical trial case study scenarios [ 38 ]. Our simulation study design analyzes several main factors affecting time-to-event outcomes across a full range of sample size and follow-up, across different accrual and event rates, and examines multiple outcomes relevant to HTA.…”

“…Parametric survival analysis methods are used to model event hazards from clinical time-to-event data and extrapolate to lifetime horizons to estimate mean survival for decision modeling [ 6 – 9 ]. Given the large effect extrapolation choices may have on decision model results, emphasis has been placed on robust, systematic approaches for extrapolation choices as best practice [ 1 , 8 , 10 , 11 ].…”