The Open UniversitySkip to content

A Flexible Parametric Modelling Framework for Survival Analysis

Burke, Kevin; Jones, M. C. and Noufaily, Angela (2020). A Flexible Parametric Modelling Framework for Survival Analysis. Journal of the Royal Statistical Society: Series C (Applied Statistics), 69(2) pp. 429–457.

Full text available as:
Full text not publicly available (Accepted Manuscript)
Due to publisher licensing restrictions, this file is not available for public download until 19 February 2021
Click here to request a copy from the OU Author.
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (cure models). This generality is achieved using four distributional parameters: two scale-type parameters – which, respectively, relate to accelerated failure time (AFT) and proportional hazards (PH) modelling – and two shape parameters. Furthermore, we advocate “multi-parameter 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, allowing 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/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 using data from lung cancer, melanoma, and kidney function studies. Censoring is accommodated throughout.

Item Type: Journal Item
Copyright Holders: 2020 Royal Statistical Society
ISSN: 1467-9876
Keywords: accelerated failure time; multi-parameter regression; power generalised Weibull distribution; proportional hazards
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:
Item ID: 69193
Depositing User: M. C. Jones
Date Deposited: 12 Feb 2020 13:24
Last Modified: 10 Mar 2020 21:55
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU