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A unifying framework for flexible excess hazard modelling with applications in cancer epidemiology

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  • Alessia Eletti
  • Giampiero Marra
  • Manuela Quaresma
  • Rosalba Radice
  • Francisco Javier Rubio

Abstract

Excess hazard modelling is one of the main tools in population‐based cancer survival research. Indeed, this setting allows for direct modelling of the survival due to cancer even in the absence of reliable information on the cause of death, which is common in population‐based cancer epidemiology studies. We propose a unifying link‐based additive modelling framework for the excess hazard that allows for the inclusion of many types of covariate effects, including spatial and time‐dependent effects, using any type of smoother, such as thin plate, cubic splines, tensor products and Markov random fields. In addition, this framework accounts for all types of censoring as well as left truncation. Estimation is conducted by using an efficient and stable penalized likelihood‐based algorithm whose empirical performance is evaluated through extensive simulation studies. Some theoretical and asymptotic results are discussed. Two case studies are presented using population‐based cancer data from patients diagnosed with breast (female), colon and lung cancers in England. The results support the presence of non‐linear and time‐dependent effects as well as spatial variation. The proposed approach is available in the R package GJRM.

Suggested Citation

  • Alessia Eletti & Giampiero Marra & Manuela Quaresma & Rosalba Radice & Francisco Javier Rubio, 2022. "A unifying framework for flexible excess hazard modelling with applications in cancer epidemiology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 1044-1062, August.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:4:p:1044-1062
    DOI: 10.1111/rssc.12566
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    References listed on IDEAS

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    1. Mathieu Fauvernier & Laurent Roche & Zoé Uhry & Laure Tron & Nadine Bossard & Laurent Remontet & and the Challenges in the Estimation of Net Survival Working Survival Group, 2019. "Multi‐dimensional penalized hazard model with continuous covariates: applications for studying trends and social inequalities in cancer survival," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(5), pages 1233-1257, November.
    2. Maja Pohar Perme & Janez Stare & Jacques Estève, 2012. "On Estimation in Relative Survival," Biometrics, The International Biometric Society, vol. 68(1), pages 113-120, March.
    3. Simon N. Wood & Natalya Pya & Benjamin Säfken, 2016. "Smoothing Parameter and Model Selection for General Smooth Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1548-1563, October.
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    1. Petti, Danilo & Eletti, Alessia & Marra, Giampiero & Radice, Rosalba, 2022. "Copula link-based additive models for bivariate time-to-event outcomes with general censoring scheme," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).

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