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Estimation of the joint conditional distribution for repeatedly measured bivariate cholesterol data using nonparametric copula
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 Title & Authors
Estimation of the joint conditional distribution for repeatedly measured bivariate cholesterol data using nonparametric copula
Kwak, Minjung;
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 Abstract
We study estimation and inference of the joint conditional distributions of bivariate longitudinal outcomes using regression models and copulas. For the estimation of marginal models we consider a class of time-varying transformation models and combine the two marginal models using nonparametric empirical copulas. Regression parameters in the transformation model can be obtained as the solution of estimating equations and our models and estimation method can be applied in many situations where the conditional mean-based models are not good enough. Nonparametric copulas combined with time-varying transformation models may allow quite flexible modeling for the joint conditional distributions for bivariate longitudinal data. We apply our method to an epidemiological study of repeatedly measured bivariate cholesterol data.
 Keywords
Bivariate longitudinal data;empirical copula;joint conditional distribution;time-varying transformation models;
 Language
Korean
 Cited by
 References
1.
Anderson, K. M., Castelli, W. P. and Levy, D. (1987). Cholesterol and mortality. 30 years of follow-up from the Framingham study. Journal of American Medical Association, 257, 2176-2180. crossref(new window)

2.
Cheng, S. C., Wei, L. J. and Ying, Z. (1995). Analysis of transformation models with censored data. Biometrika, 82, 835-845. crossref(new window)

3.
Cho, G. Y. and Dashnyam, O. (2013). Generalized methods of moments in marginal models for longitudinal data with time-dependent covariates. Journal of the Korean Data & Information Science Society, 24, 877-883. crossref(new window)

4.
Daniels, S. R., McMahon, R .P., Obarzanek, E., Waclawiw, M. A., Similo, S. L., Biro, F. M., Schreiber, G. B., Kimm, S. Y., Morrison, J. A. and Barton, B. A. (1998). Longitudinal correlates of change in blood pressure in adolescent girls. Hypertension, 31, 97-103. crossref(new window)

5.
Diggle, P. J., Liang, K. Y. and Zeger S. L. (1994). Analysis of longitudinal data, Oxford University Press, Oxford.

6.
Genest, C., Ghoudi, K. and Rivest, L. P. (1995). A semiparametric estimation procedures of dependence parameters in multivariate families of distributions. Biometrika, 82, 543-552. crossref(new window)

7.
Genest, C. and MacKay, J. (1986). A joy of copulas: Bivariate distributions with uniform marginals. The American Statistician, 40, 280-283.

8.
Jeon J. Y. and Lee K. (2014) Review and discussion of marginalized random effects models. Journal of the Korean Data & Information Science Society, 25, 1263-1272. crossref(new window)

9.
Joe, H. (1993). Parametric families of multivariate distributions with given margins. Journal of Multivariate Analysis, 46, 262-282. crossref(new window)

10.
Leon, A.R. andWu, B. (2011). Copula-based regression models for a bivariate mixed discrete and continuous outcome. Statistics in Medicine, 30, 175-185. crossref(new window)

11.
Lindsey, J. K. (1993). Models for repeated measurements, Oxford University Press, Oxford.

12.
Molenberghs, G. and Verbeke, G. (2005). Models for Discrete Longitudinal Data, Springer, New York.

13.
National Heart, Lung, and Blood Institute Growth and Health Research Group (NGHSRG) (1992). Obesity and cardiovascular disease risk factors in black and white girls: The NHLBI growth and health study. Americal Journal of Public Health, 82, 1613-1620. crossref(new window)

14.
National High Blood Pressure Education Program Working Group on High Blood Pressure in Children and Adolescents (NHBPEP Working Group) (2004). The fourth report on the diagnosis, evaluation, and treatment of high blood pressure in children and adolescents. Pediatrics, 114, 555-576. crossref(new window)

15.
Oakes, D. (1986). Semiparametric inference in a model for association in bivariate survival data. Biometrika, 73, 353-361.

16.
Obarzanek, E.,Wu, C. O., Cutler, J. A., Kavey, R. W., Pearson, R. W. and Daniels, S. R. (2010). Prevalence and incidence of hypertension in adolescent girls. Journal of Pediatrics, 157, 461-467. crossref(new window)

17.
Sklar, A. (1959). Fonctions de repartition an dimensions et leurs marges. Publications de L'Institute de Statistique de L'Universite de Paris, 8, 229-231.

18.
Song, P. X. K., Li, M. and Yuan, Y. (2009). Joint regression analysis of correlated data using Gaussian Copulas. Biometrics, 65, 60-68. crossref(new window)

19.
Thompson, D. R., Obarzanek, E., Franko, D. L., Barton, B. A., Morrison, J., Biro, F. M., Daniels, S. R. and Striegel-Moore, R. H. (2007). Childhood overweight and cardiovascular disease risk factors: The national heart, lung, and blood institute growth and health study. Journal of Pediatrics, 150, 18-25. crossref(new window)

20.
Wu, C. O. and Tian, X. (2013). Nonparametric estimation of conditional distribution functions and ranktracking probabilities with time-varying transformation models in longitudinal studies. Journal of the American Statistical Association, 108, 971-982. crossref(new window)