Modelling failure-time associations in data with multiple levels of clustering

Biometrika

Volumn 83, Issue 1, 1996, Pages 29-39

  Bandeen Roche, Karen J ^a   Liang, Kung Yee ^a  

^a JOHNS HOPKINS BLOOMBERG SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Archimedean copula; Conditional hazard ratio; Frailty distribution; Hierarchical; Laplace transform; Multivariate survival function

Indexed keywords

EID: 0003058574     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/83.1.29     Document Type: Article

References (22)

1. CHURCHILL, R. V. (1972). Operational Mathematics, 3rd ed. New York: McGraw-Hill.
2. CLAYTON, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65, 141-51.
3. COX, D. R. (1972). Regression models and life tables (with Discussion). J. R. Statist. Soc. B 34, 187-202.
4. FIELD, M. J. (1976). Differential Calculus and its Applications. New York: Van Nostrand Reinhold.
5. GENEST, C., GHOUDI, K. & RIVEST, L.-P. (1995). A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82, 543-52.
6. GENEST, C. & MACKAY, R. J. (1986a). Copules archimédiennes of et familles de lois bidimensionnelles dont les marges sont données. Can. J. Statist. 14, 145-59.
7. GENEST, C. & MACKAY, J. (1986b). The joy of copulas; bivariate distributions with uniform marginals. Am. Statistician 40, 280-3.
8. GENEST, C. & RIVEST, L.-P. (1993). Statistical inference procedures for bivariate archimedean copulas. J. Am. Statist. Assoc. 88, 1034-43.
9. GONG, G. & SAMANIEGO, F. J. (1981). Pseudo maximum likelihood. Ann. Statist. 9, 861-9.
10. HUTCHINSON, T. P. (1981). Compound gamma bivariate distributions. Metrika 28, 263-71.
11. JOE, H. (1993). Parametric families of multivariate distributions with given margins. J. Mult. Anal. 46, 262-82.
12. LEE, E. W., WEI, L. J. & AMATO, D. A. (1992). Cox-type regression for large numbers of small groups of correlated failure time observations. In Survival Analysis: State of the Art, Ed. J. P. Klein and P. K. Goel, pp. 237-47. Dordrecht: Kluwer Academic.
13. LIANG, K.-Y., SELF, S. G. & CHANG, Y.-C. (1993). Modelling marginal hazards in multivariate failure time data. J. R. Statist. Soc. B 55, 441-53.
14. LIANG, K.-Y. & ZEGER, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73, 13-22.
15. MARSHALL, A. W. & OLKIN, I. (1988). Families of multivariate distributions. J. Am. Statist. Assoc. 83, 834-41.
16. MURPHY, S. (1994). Consistency in a proportional hazards model incorporating a random effect. Ann. Statist. 22, 712-31.
17. NIELSEN, G. G., GILL, R. D., ANDERSEN, P. K. & SORENSEN, T. I. A. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scand. J. Statist. 19, 25-44.
18. OAKES, D. (1989). Bivariate survival models induced by frailties. J. Am. Statist. Assoc. 84, 487-93.
19. PRENTICE, R. L. & CAI, J. (1992). Covariance and survivor function estimation using censored multivariate failure time data. Biometrika 79, 495-512.
20. SHIH, J. H. & LOUIS, T. A. (1996). Inferences on the association parameter in copula models for bivariate survival data. Biometrics To appear.
21. VAUPEL, J. W., MANTON, K. G. & STALLARD, E. (1979). The impact of heterogeneity in individual frailty and the dynamics of mortality. Demography 16, 439-54.
22. WEDDERBURN, R. W. M. (1974). Quasilikelihood functions, generalized linear models and the Gauss-Newton method. Biometrika 61, 439-47.