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A bivariate power generalized Weibull distribution: A flexible parametric model for survival analysis

Jones, M. C.; Noufaily, Angela and Burke, Kevin (2019). A bivariate power generalized Weibull distribution: A flexible parametric model for survival analysis. Statistical Methods in Medical Research (Early Access).

DOI (Digital Object Identifier) Link: https://doi.org/10.1177/0962280219890893
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Abstract

We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we argued in favour of an adapted form of the ‘power generalized Weibull’ distribution as an attractive vehicle for univariate parametric survival analysis. Here, we additionally observe a frailty relationship between a power generalized Weibull distribution with one value of the parameter which controls distributional choice within the family and a power generalized Weibull distribution with a smaller value of that parameter. We exploit this relationship to propose a bivariate shared frailty model with power generalized Weibull marginal distributions linked by the BB9 or ‘power variance function’ copula, then change it to have adapted power generalized Weibull marginals in the obvious way. The particular choice of copula is, therefore, natural in the current context, and the corresponding bivariate adapted power generalized Weibull model a novel combination of pre-existing components. We provide a number of theoretical properties of the models. We also show the potential of the bivariate adapted power generalized Weibull model for practical work via an illustrative example involving a well-known retinopathy dataset, for which the analysis proves to be straightforward to implement and informative in its outcomes.

Item Type: Journal Item
Copyright Holders: 2019 The Authors
ISSN: 1477-0334
Keywords: BB9 copula; Gompertz; log-logistic; power variance frailty; shared frailty
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
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Item ID: 68675
SWORD Depositor: Jisc Publications-Router
Depositing User: Jisc Publications-Router
Date Deposited: 06 Jan 2020 16:19
Last Modified: 19 Feb 2020 10:13
URI: http://oro.open.ac.uk/id/eprint/68675
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