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A flexible parametric modelling framework for survival analysis

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  • Kevin Burke
  • M. C. Jones
  • Angela Noufaily

Abstract

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard functions (constant; increasing; decreasing; up then down; down then up) and various common survival distributions (log‐logistic; Burr type XII; Weibull; Gompertz) and includes defective distributions (cure models). This generality is achieved by using four distributional parameters: two scale‐type parameters—one of which relates to accelerated failure time (AFT) modelling; the other to proportional hazards (PH) modelling—and two shape parameters. Furthermore, we advocate ‘multiparameter regression’ whereby more than one distributional parameter depends on covariates—rather than the usual convention of having a single covariate‐dependent (scale) parameter. This general formulation unifies the most popular survival models, enabling us to consider the practical value of possible modelling choices. In particular, we suggest introducing covariates through just one or other of the two scale parameters (covering AFT and PH models), and through a ‘power’ shape parameter (covering more complex non‐AFT or non‐PH effects); the other shape parameter remains covariate independent and handles automatic selection of the baseline distribution. We explore inferential issues and compare with alternative models through various simulation studies, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by using data from lung cancer, melanoma and kidney function studies. Censoring is accommodated throughout.

Suggested Citation

  • Kevin Burke & M. C. Jones & Angela Noufaily, 2020. "A flexible parametric modelling framework for survival analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(2), pages 429-457, April.
    • Handle: RePEc:bla:jorssc:v:69:y:2020:i:2:p:429-457
    DOI: 10.1111/rssc.12398
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    Cited by:

    1. Jie Min & Yili Hong & Caleb B. King & William Q. Meeker, 2022. "Reliability analysis of artificial intelligence systems using recurrent events data from autonomous vehicles," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 987-1013, August.
    2. Chrys Caroni, 2022. "Regression Models for Lifetime Data: An Overview," Stats, MDPI, vol. 5(4), pages 1-11, December.
    3. Muschinski, Thomas & Mayr, Georg J. & Simon, Thorsten & Umlauf, Nikolaus & Zeileis, Achim, 2024. "Cholesky-based multivariate Gaussian regression," Econometrics and Statistics, Elsevier, vol. 29(C), pages 261-281.
    4. Anaya-Izquierdo, Karim & Jones, M.C. & Davis, Alice, 2021. "A family of cumulative hazard functions and their frailty connections," Statistics & Probability Letters, Elsevier, vol. 172(C).
    5. Adam Braima S. Mastor & Abdulaziz S. Alghamdi & Oscar Ngesa & Joseph Mung’atu & Christophe Chesneau & Ahmed Z. Afify, 2023. "The Extended Exponential-Weibull Accelerated Failure Time Model with Application to Sudan COVID-19 Data," Mathematics, MDPI, vol. 11(2), pages 1-26, January.

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