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Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function

Author

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  • Benjamin Kearns

    (The University of Sheffield, Sheffield, UK)

  • Matt D. Stevenson

    (The University of Sheffield, Sheffield, UK)

  • Kostas Triantafyllopoulos

    (The University of Sheffield, Sheffield, UK)

  • Andrea Manca

    (The University of Sheffield, Sheffield, UK
    The University of York, York, UK)

Abstract

Background. Parametric modeling of survival data is important, and reimbursement decisions may depend on the selected distribution. Accurate predictions require sufficiently flexible models to describe adequately the temporal evolution of the hazard function. A rich class of models is available among the framework of generalized linear models (GLMs) and its extensions, but these models are rarely applied to survival data. This article describes the theoretical properties of these more flexible models and compares their performance to standard survival models in a reproducible case study. Methods. We describe how survival data may be analyzed with GLMs and their extensions: fractional polynomials, spline models, generalized additive models, generalized linear mixed (frailty) models, and dynamic survival models. For each, we provide a comparison of the strengths and limitations of these approaches. For the case study, we compare within-sample fit, the plausibility of extrapolations, and extrapolation performance based on data splitting. Results. Viewing standard survival models as GLMs shows that many impose a restrictive assumption of linearity. For the case study, GLMs provided better within-sample fit and more plausible extrapolations. However, they did not improve extrapolation performance. We also provide guidance to aid in choosing between the different approaches based on GLMs and their extensions. Conclusions. The use of GLMs for parametric survival analysis can outperform standard parametric survival models, although the improvements were modest in our case study. This approach is currently seldom used. We provide guidance on both implementing these models and choosing between them. The reproducible case study will help to increase uptake of these models.

Suggested Citation

  • Benjamin Kearns & Matt D. Stevenson & Kostas Triantafyllopoulos & Andrea Manca, 2019. "Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function," Medical Decision Making, , vol. 39(7), pages 867-878, October.
  • Handle: RePEc:sae:medema:v:39:y:2019:i:7:p:867-878
    DOI: 10.1177/0272989X19873661
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    References listed on IDEAS

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    1. Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    2. Patrick Royston & Paul C. Lambert, 2011. "Flexible Parametric Survival Analysis Using Stata: Beyond the Cox Model," Stata Press books, StataCorp LP, number fpsaus, March.
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    Cited by:

    1. Arantzazu Arrospide & Oliver Ibarrondo & Rubén Blasco-Aguado & Igor Larrañaga & Fernando Alarid-Escudero & Javier Mar, 2024. "Using Age-Specific Rates for Parametric Survival Function Estimation in Simulation Models," Medical Decision Making, , vol. 44(4), pages 359-364, May.
    2. Adeniyi Francis Fagbamigbe & Emma Norrman & Christina Bergh & Ulla-Britt Wennerholm & Max Petzold, 2021. "Comparison of the performances of survival analysis regression models for analysis of conception modes and risk of type-1 diabetes among 1985–2015 Swedish birth cohort," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-23, June.

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