A Diagnostic for Association in Bivariate Survival Models
 Minchi chen,
 Karen BandeenRoche
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
We propose exploratory, easily implemented methods for diagnosing the appropriateness of an underlying copula model for bivariate failure time data, allowing censoring in either or both failure times. It is found that the proposed approach effectively distinguishes gamma from positive stable copula models when the sample is moderately large or the association is strong. Data from the Women’s Health and Aging Study (WHAS, Guralnik et al., The Womens’s Health and Aging Study: Health and Social Characterisitics of Older Women with Disability. National Institute on Aging: Bethesda, Mayland, 1995) are analyzed to demonstrate the proposed diagnostic methodology. The positive stable model gives a better overall fit to these data than the gamma frailty model, but it tends to underestimate association at the later time points. The finding is consistent with recent theory differentiating ‘catastrophic’ from ‘progressive’ disability onset in older adults. The proposed methods supply an interpretable quantity for copula diagnosis. We hope that they will usefully inform practitioners as to the reasonableness of their modeling choices.
 BandeenRoche, K.J., Liang, K.Y. (2002) “Modelling multivariate failure time associations in the presence of a competing risk,”. Biometrika. 89: pp. 299314
 Brown, B.W., Hollander, M., Korwar, R.M. “Nonparametric tests of independence for censored data, with application to heart transplant studies”. In: Proschan, F., Serfling, R. J. eds. (1974) in Reliability and Biometry: Statistical Analysis of Lifelength. SIAM, Philadelphia, pp. 327353
 Clayton, D.G. (1978) “A model for association in bivariate lifetables and its application in epidemiological studies of familiar tendency in chronic disease incidence,”. Biometrika vol. 65: pp. 141151
 Dabrowska, D.M. (1988) “Kaplan–Meier Estimate on the Plane,”. The Annals of Statistics. 16: pp. 14751489
 Ferrucci, L., Guralnik, J.M., Simonsick, E., Salive, M.E., Corti, C., Langlois, J.R. (1996) “Progressive versus catastrophic disability: a longitudinal view of the disablement process,”. Journal of Gerontology. Series A, Biological Sciences & Medical Sciences. 51: pp. 123130
 Fried, L.P., Ettinger, W.H., Hermanson, B. (1994) “Physical disability in older adults: a physiologic approach,”. Journal of Clinical Epidemiology. 47: pp. 747760
 Geman, S., Hwang, C.R. (1982) “ Nonparametric maximum likelihood estimation by the method of sieves,”. Annals of Statistics. 10: pp. 401411
 Genest, C., MacKay, R.J. (1986) “The joy of copulas: bivariate distributions with given marginals,”. The American Statistician. 40: pp. 280283
 Genest, C., Rivest, L.P. (1993) “Statistical inference procedures for bivariatearchimedan copulas,”. Journal of the American statistical Association. 88: pp. 10341043
 Glidden, D.V. (1999) “Checking the adequacy of the gamma frailty model for multivariate failure times,”. Biometrika. 86: pp. 381393
 Gong, G., Samaniego, F.J. (1981) “Pseudo maximum likelihood estimation: theory and applications,”. The Annals of Statistics. 9: pp. 861869
 Guralnik, J.M., Fried, L.P., Simonsick, E.M., Kasper, J., Lafferty, M.E. eds. (1995) The Women’s Health and Aging Study: Health and Social Characteristics of Older Women with Disability. National Institute on Aging, Bethesda, Maryland
 Hall, P., Park, B.U., Turlach, B.A. (1998) “A note on design transformation and binning in nonparametric curve estimation,”. Biometrika. 85: pp. 469476
 Hougaard, P. (1986a) “Survival models for heterogeneous population derived from stable distributions,”. Biometrika. 73: pp. 387396
 Hougaard, P. (1986b) “A class of multivariate failure time distribution,”. Biometrika 73: pp. 671673
 Huster, W.J., Brookmeyer, R, Self, S.G. (1989) “Modelling paired survival data with covariates,”. Biometrics. 45: pp. 145156
 Kaplan, E.L., Meier, P. (1958) “Nonparametric estimation from incomplete observations,”. Journal of the American Statistical Association. 53: pp. 457481
 Kendall, M.G. (1938) “A new measure of rank correlation,”. Biometrika. 30: pp. 8193
 Liang, K.Y. (1991) “Estimating effects of probands” characteristics on familial risk: I Adjustment for censoring and correlated ages at onset. Genetic Epidemiology. 8: pp. 329338
 Liang, K.Y., Self, S.G., BandeenRoche, K.J., Zeger, S.L. (1995) “Some recent developments for regression analysis of multivariate failure time data,”. Lifetime Data Analysis. 1: pp. 403415
 Lonergan, E.T., Krevans, J.R. (1991) “A national agenda for research on aging,”. New England Journal of Medicine. 1: pp. 18251828
 Manatunga, A.K., Oakes, D. (1996) “A measure of association for bivariate frailty distributions,”. Journal of Multivariate Analysis. 56: pp. 6074
 Marshall, A.W., Olkin, I. (1988) “Families of multivariate distributions,”. Journal of the American Statistical Association. 83: pp. 834841
 Oakes, D. (1989) “Bivariate survival models induced by frailties,”. Journal of the American Statistical Association. 84: pp. 487493
 Pizer, S.M. (1975) “Numerical Computing and Mathematical Analysis,”. Science Research Associates, Inc., Chicago
 Prentice, R.L., Kalbfleisch, J.D., Peterson, A.V., Flournoy, N., Farewell, V.T., Breslow, N.E. (1978) “The analysis of failure times in the presence of competing risk,”. Biometrics. 34: pp. 541554
 Reinsch, C.H. (1967) “Smoothing by spline functions,”. Numerische Mathematik. 10: pp. 177183
 Schweizer B., Sklar A. (1983). Probabilistic Metric Spaces, New York: NorthHolland, 1983.
 Shih, J.H., Louis, T.A. (1995) “ Inference on the association parameter in copula models for bivariate survival data,”. Biometrics. 51: pp. 13841399
 Shih, J.H., Louis, T.A. (1995) “Assessing gamma frailty models for clustered failure time data,”. Lifetime Data Analysis. 1: pp. 205220
 Shih, J.H. (1998) “A goodnessoffit test for association in a bivariate survival model,”. Biometrika. 85: pp. 189200
 Viswanathan, B., Manatunga, A.K. (2001) “Diagnostic plots for assessing the grailty distribution in multivariate survival data,”. Lifetime Data Analysis. 7: pp. 143155
 Wand, M.P. (1997) “Databased choice of histogram bin width,”. The American Statistician. 51: pp. 5964
 Wang, W., Wells, M.T. (2000a) “Model selection and semiparametric inference for bivariate censored data,”. Journal of the American Statistical Association. 95: pp. 6272
 Title
 A Diagnostic for Association in Bivariate Survival Models
 Journal

Lifetime Data Analysis
Volume 11, Issue 2 , pp 245264
 Cover Date
 20050601
 DOI
 10.1007/s1098500403868
 Print ISSN
 13807870
 Online ISSN
 15729249
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Archimedean copula
 bivariate failure time
 copula models
 frailty
 Industry Sectors
 Authors

 Minchi chen ^{(1)}
 Karen BandeenRoche ^{(2)}
 Author Affiliations

 1. Department of Public Health, College of Medicine, Chang Gung University, TaoYuan, 333, Taiwan
 2. Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, 21205, USA