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| Life Expectancy Estimate with Bivariate Weibull Distribution using Archimedean Copula
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Full
text: |
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Source |
International Journal of Biometrics and Bioinformatics (IJBB) |
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Table of Contents |
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Complete Issue PDF(2.29MB) |
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Volume: 5 Issue: 3 |
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Pages: 149-201 |
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Publication
Date: July / August 2011 |
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ISSN
(Online): 1985-2347 |
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Pages |
149 - 161 |
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Author(s) |
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Published
Date |
05-08-2011 |
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Publisher |
CSC
Journals, Kuala Lumpur,
Malaysia |
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ADDITIONAL
INFORMATION |
| Keywords Abstract References Cited by Related Articles Collaborative
Colleague |
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KEYWORDS: Archimedean Copula, Dependence, Weibull Distribution, Value at Risk |
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| 6. Bielefeld Academic Search Engine (BASE) |
| 7. iSEEK |
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| Archimedean copulas are used to construct bivariate Weibull distributions. Co-movement structures of variables are analyzed through the copulas, where the tail dependence between the variables is explored with more flexibility. Based on the distance between the copula distribution and its empirical version, a copula that may best fit data is selected. With extra computing costs, the adequacy of the copula chosen is then assessed. When multiple myeloma data are considered, it is found that relationship between survival time of a patient and the hemoglobin level is well described by the Clayton copula. The bivariate Weibull distribution constructed by the copula is used to estimate value at risk from which we investigate the anticipated longest life expectancy of a patient with the disease over the treatment period. |
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| 1 |
D.G. Clayton, “A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence”. Biometrika, 65:141-151, 1978
|
|
|
| 2 |
D. Collect, “Modelling Survival Data in Medical Research”. Chapman, 1999
|
|
|
| 3 |
R.D. Cook and M.E. Johnson, “A family of distributions for modeling non-elliptically symmetric multivariate data”. Journal of the Royal Statistical Society, Series B, 43, 210-218, 1981
|
|
|
| 4 |
M. Crouhy, D. Galai, and R. Mark, “Risk Management”. McGraw-Hill, 2001
|
|
|
| 5 |
B.G. Durie and S.E. Salmon, “A clinical staging system for multiple myeloma. Correlation of measured myeloma cell mass with presenting clinical features, response to treatment, and survival”. Cancer, 36(3), 842-854, 1975
|
|
|
| 6 |
V. Durrleman, A. Nikeghbail and T. Roncalli, “Which copula is the right one?”. Credit Lyonnais, Available at SSRN: http://ssm.com/abstract=1032545, 2000
|
|
|
| 7 |
P. Embrechts, A. McNeil and D. Straumann, “Correlation: Pitfall and Alternative”. Risk, 12, 69-71, 1999
|
|
|
| 8 |
M.J. Frank, “On the simultaneous associativity of and ”. Aequationes Mathematicae, 19, 194-226, 1979
|
|
|
| 9 |
M.J. Frees and E. Valdez, “Understanding relationships using copulas”. North American Actuarial Journal, 2, 1-25, 1998
|
|
|
| 10 |
C. Genest and R.J. MacKay, “Copules Archimediennes et Failles de Lois Bidimensionnelles Don’t les Marges Sont Donnees”, The Canadian Journal of Statistics, 14, 145-159, 1986a
|
|
|
| 11 |
C. Genest and R.J. MacKay, “The joy of copulas: Bivariate distributions with uniform marginals”. American Statistician, 40, 280-283, 1986b
|
|
|
| 12 |
C. Genest, and L. Rivest, “Statistical inference procedures for bivariate Archimedean copulas”. Journal of American Statistical Association, 88, 1034-1043, 1993
|
|
|
| 13 |
P.R. Greipp, J. San Miguel, B.G. Durie, J.J. Crowley, B. Barlogie, J. Bladé, M. Boccadoro, J.A. Child, H. Avet-Loiseau, R.A. Kyle, J.J. Lahuerta, H. Ludwig, G. Morgan, R. Powles, K. Shimizu, C. Shustik, P. Sonneveld, P. Tosi, I. Turesson, and J. Westin, “International staging system for multiple myeloma”. Journal of Clinical Oncology, 23, 3412-3420, 2005
|
|
|
| 14 |
E.J. Gumbel, “Bivariate exponential distributions”. Journal of American Statistical Association, 55, 698-707, 1960
|
|
|
| 15 |
P. Hougaard, “A class of multivariate failure time distributions”. Biometrika, 73, 671-678, 1986
|
|
|
| 16 |
H. Joe, “Multivariate Models and Dependence Concepts”. Chapman & Hall, London, 1997
|
|
|
| 17 |
P. Jorion, “Value at Risk: The New Benchmark for Managing Financial Risk”. McGraw-Hill Publication, 2007
|
|
|
| 18 |
J.M. Krall, V.A. Uthoff and J.B. Harley, “A step-up procedure for selecting variables associated with survival”. Biometrics, 31, 49-51, 1975
|
|
|
| 19 |
P. Kumar and M.M. Shoukri, “Evaluating Aortic Stenosis using the Archimedean copula methodology”. Journal of Data Science, 6, 173-187, 2008
|
|
|
| 20 |
R.A. Kyle and S.V. Rajkumar, Multiple myeloma. Blood, 111(6), 2962-2972, 2008
|
|
|
| 21 |
S. Lee, E.-J. Lee and B.O. Omolo, “Using integrated weighted survival difference for the two-sample censored data problem”. Computational Statistics and Data Analysis, 52, 4410-4416, 2008
|
|
|
| 22 |
S. Lee and S. Yang, “Checking the censored two-sample accelerated life model using integrated cumulative hazard difference”. Lifetime Data Analysis, 13, 371-380, 2007
|
|
|
| 23 |
D.Y. Lin, L.J. Wei and Z. Ying, “Checking the cox model with cumulative sums of martingale-based residuals”. Biometrika, 80, 557-72, 1993
|
|
|
| 24 |
A. McNeil, R. Frey and P. Embrechts, “Quantitative Risk Management: Concepts, Techniques and Tools”. Princeton University Press, 2005
|
|
|
| 25 |
M.R. Melchiori, “Which Archimedean copula is the right one?”. Yield Curve, 37, 1-20, 2003
|
|
|
| 26 |
R.B. Nelsen, “An introduction to copulas”. Springer, 1999
|
|
|
| 27 |
L. Rivest and M. Wells, “A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring”. Journal of Multivariate Analysis, 79, 138-155, 2001
|
|
|
| 28 |
A. Sklar, “Functions de repartition a n dimensions et leurs merges”. Publication of the Institute of Statistics, University of Paris, 8, 229-231, 1959
|
|
|
| 29 |
G. Venter, “Tails of copulas”. Proceedings of the Astin Colloquium, 2001.
|
|
|
| 30 |
M. Zheng and J. Klein, “Estimates of marginal survival for dependent competing risks based on an assumed copula”. Biometrika, 82, 127-138, 1995
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| Eun-Joo Lee : Colleagues
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| Chang-Hyun Kim : Colleagues
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| Seung-Hwan Lee : Colleagues
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