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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

Author

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  • Ben Kearns

    (University of Sheffield)

  • John Stevens

    (University of Sheffield)

  • Shijie Ren

    (University of Sheffield)

  • Alan Brennan

    (University of Sheffield)

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.

Suggested Citation

  • Ben Kearns & John Stevens & Shijie Ren & Alan Brennan, 2020. "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 Effective," PharmacoEconomics, Springer, vol. 38(2), pages 193-204, February.
    • Handle: RePEc:spr:pharme:v:38:y:2020:i:2:d:10.1007_s40273-019-00853-x
    DOI: 10.1007/s40273-019-00853-x
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    References listed on IDEAS

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    1. Laura Bojke & Bogdan Grigore & Dina Jankovic & Jaime Peters & Marta Soares & Ken Stein, 2017. "Informing Reimbursement Decisions Using Cost-Effectiveness Modelling: A Guide to the Process of Generating Elicited Priors to Capture Model Uncertainties," PharmacoEconomics, Springer, vol. 35(9), pages 867-877, September.
    2. K. Ishak & Noemi Kreif & Agnes Benedict & Noemi Muszbek, 2013. "Overview of Parametric Survival Analysis for Health-Economic Applications," PharmacoEconomics, Springer, vol. 31(8), pages 663-675, August.
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    Cited by:

    1. Yizhe Xu & Tom H. Greene & Adam P. Bress & Brandon K. Bellows & Yue Zhang & Zugui Zhang & Paul Kolm & William S. Weintraub & Andrew S. Moran & Jincheng Shen, 2022. "An Efficient Approach for Optimizing the Cost-effective Individualized Treatment Rule Using Conditional Random Forest," Papers 2204.10971, arXiv.org.

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