A Bivariate Power Generalized Weibull Distribution: a Flexible Parametric Model for Survival Analysis Article Swipe
M. C. Jones
,
Angela Noufaily
,
Kevin Burke
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1901.03210
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1901.03210
We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we have extolled the virtues of the "power generalized Weibull" (PGW) distribution as an attractive vehicle for univariate parametric survival analysis: it is a tractable, parsimonious, model which interpretably allows for a wide variety of hazard shapes and, when adapted (to give an adapted PGW, or APGW, distribution), covers a wide variety of important special/limiting cases. Here, we additionally observe a frailty relationship between a PGW distribution with one value of the parameter which controls distributional choice within the family and a PGW distribution with a smaller value of the same parameter. We exploit this frailty relationship to propose a bivariate shared frailty model with PGW marginal distributions: these marginals turn out to be linked by the so-called BB9 or "power variance function" copula. This particular choice of copula is, therefore, a natural one in the current context. We then adapt the bivariate PGW distribution, in turn, to accommodate APGW marginals. We provide a number of theoretical properties of the bivariate PGW and APGW models and show the potential of the latter 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. The novelty in this article is in the appropriate combination of specific ingredients into a coherent and successful whole.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1901.03210
- https://arxiv.org/pdf/1901.03210
- OA Status
- green
- References
- 17
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2910507872
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- OpenAlex ID
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https://openalex.org/W2910507872Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1901.03210Digital Object Identifier
- Title
-
A Bivariate Power Generalized Weibull Distribution: a Flexible Parametric Model for Survival AnalysisWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2019Year of publication
- Publication date
-
2019-01-10Full publication date if available
- Authors
-
M. C. Jones, Angela Noufaily, Kevin BurkeList of authors in order
- Landing page
-
https://arxiv.org/abs/1901.03210Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1901.03210Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/1901.03210Direct OA link when available
- Concepts
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Bivariate analysis, Copula (linguistics), Weibull distribution, Parametric statistics, Univariate, Parametric model, Joint probability distribution, Computer science, Context (archaeology), Marginal distribution, Econometrics, Mathematics, Statistics, Multivariate statistics, Random variable, Biology, PaleontologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- References (count)
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17Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.example | 191 |
| abstract_inverted_index.exploit | 106 |
| abstract_inverted_index.frailty | 74, 108, 115 |
| abstract_inverted_index.natural | 145 |
| abstract_inverted_index.novelty | 213 |
| abstract_inverted_index.observe | 72 |
| abstract_inverted_index.propose | 111 |
| abstract_inverted_index.provide | 165 |
| abstract_inverted_index.smaller | 99 |
| abstract_inverted_index.variety | 46, 64 |
| abstract_inverted_index.vehicle | 28 |
| abstract_inverted_index.virtues | 17 |
| abstract_inverted_index.Weibull" | 22 |
| abstract_inverted_index.analysis | 7, 200 |
| abstract_inverted_index.coherent | 227 |
| abstract_inverted_index.context. | 150 |
| abstract_inverted_index.controls | 87 |
| abstract_inverted_index.dataset, | 196 |
| abstract_inverted_index.extolled | 15 |
| abstract_inverted_index.flexible | 5 |
| abstract_inverted_index.marginal | 119 |
| abstract_inverted_index.specific | 223 |
| abstract_inverted_index.survival | 10, 32 |
| abstract_inverted_index.variance | 134 |
| abstract_inverted_index.analysis: | 33 |
| abstract_inverted_index.bivariate | 9, 113, 155, 173 |
| abstract_inverted_index.concerned | 2 |
| abstract_inverted_index.function" | 135 |
| abstract_inverted_index.implement | 206 |
| abstract_inverted_index.important | 66 |
| abstract_inverted_index.involving | 192 |
| abstract_inverted_index.marginals | 122 |
| abstract_inverted_index.outcomes. | 211 |
| abstract_inverted_index.parameter | 85 |
| abstract_inverted_index.potential | 181 |
| abstract_inverted_index.practical | 186 |
| abstract_inverted_index.so-called | 130 |
| abstract_inverted_index.Elsewhere, | 12 |
| abstract_inverted_index.attractive | 27 |
| abstract_inverted_index.marginals. | 163 |
| abstract_inverted_index.parameter. | 104 |
| abstract_inverted_index.parametric | 6, 31 |
| abstract_inverted_index.particular | 138 |
| abstract_inverted_index.properties | 170 |
| abstract_inverted_index.successful | 229 |
| abstract_inverted_index.therefore, | 143 |
| abstract_inverted_index.tractable, | 37 |
| abstract_inverted_index.univariate | 30 |
| abstract_inverted_index.well-known | 194 |
| abstract_inverted_index.accommodate | 161 |
| abstract_inverted_index.appropriate | 220 |
| abstract_inverted_index.combination | 221 |
| abstract_inverted_index.generalized | 21 |
| abstract_inverted_index.informative | 208 |
| abstract_inverted_index.ingredients | 224 |
| abstract_inverted_index.retinopathy | 195 |
| abstract_inverted_index.theoretical | 169 |
| abstract_inverted_index.additionally | 71 |
| abstract_inverted_index.distribution | 24, 79, 96 |
| abstract_inverted_index.illustrative | 190 |
| abstract_inverted_index.relationship | 75, 109 |
| abstract_inverted_index.distribution, | 157 |
| abstract_inverted_index.interpretably | 41 |
| abstract_inverted_index.parsimonious, | 38 |
| abstract_inverted_index.distribution), | 60 |
| abstract_inverted_index.distributional | 88 |
| abstract_inverted_index.distributions: | 120 |
| abstract_inverted_index.straightforward | 204 |
| abstract_inverted_index.special/limiting | 67 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |