Regression on hazard ratios and cross ratios in multivariate failure time analysis

Biometrika

Volumn 84, Issue 2, 1997, Pages 349-363

  Prentice, Ross L ^a   Hsu, L I ^a  

^a Fred Hutchinson Cancer Research Center   (United States)

Author keywords

Censoring; Clayton bivariate survival model; Correlated failure times; Covariance; Cox regression; Cross ratio; Estimating equation; Family cohort study; Genetic epidemiology; Martingale; Multivariate failure times; Regression; Time varying covariate

Indexed keywords

EID: 0000784399     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/84.2.349     Document Type: Article

References (30)

1. ANDERSEN, P. K. & GILL, R. D. (1982). Cox's regression model for counting processes: A large sample study. Ann. Statist. 10, 1100-20.
2. BRESLOW, N. E. (1974). Covariance analysis of censored survival data. Biometrics 30, 89-99.
3. CAI, J. & PRENTICE, R. L. (1995). Estimating equations for hazard ratio parameters based on correlated failure time data. Biometrika 82, 151-64.
4. CLAYTON, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency on chronic disease incidence. Biometrika 65, 144-51.
5. CLAYTON, D. G. & CUZICK, J. (1985). Multivariate generalizations of the proportional hazards model (with Discussion). J. R. Statist. Soc. A 148, 82-117.
6. Cox, D. R. (1972). Regression models and life tables (with Discussion). J. R. Statist. Soc. B 34, 187-220.
7. CROWDER, M. (1995). On the use of a working correlation matrix in using generalised linear models for repeated measures. Biometrika 82, 407-10.
8. DIABETIC RETINOPATHY STUDY RESEARCH GROUP (1981). Diabetic Retinopathy Study. Investig. Ophthal Visual Sci. 21, 149-226.
9. DIGGLE, P. J., LIANG, K. Y. & ZEGER, S. L. (1994). Analysis of Longitudinal Data. New York: Oxford University Press.
10. DUFFY, D. L., MARTIN, N. G. & MATTHEWS, J. D. (1990). Appendectomy in Australian twins. Am. J. Human Genet. 47, 590-2.
11. FITZMAURICE, G. M. & LAIRD, N. (1993). A likelihood-based method for analyzing longitudinal binary responses. Biometrika 80, 141-52.
12. FOUTZ, R. V. (1977). On the unique consistent solution to the likelihood equations. J. Am. Statist. Assoc. 72. 147-8.
13. GENEST, C. (1987). Frank's family of bivariate distributions. Biometrika 74, 549-55.
14. Hsu, L. & PRENTICE, R. L. (1996). On assessing the strength of dependency between failure time variâtes. Biometrika 83, 491-506.
15. HUSTER, W. S., BROOKMEYER, R. & SELF, S. G. (1989). Modeling paired survival data with covariates. Biometrics 45, 145-56.
16. KALBFLEISCH, J. D. & PRENTICE, R. L. (1980). The Statistical Analysis of Failure Time Data. New York: Wiley.
17. LIANG, K. Y., SELF, S. G. & CHANG, Y. C. (1993). Modeling marginal hazards in multivariate failure time data. J. R. Statist. Soc. B 55, 441-53.
18. LIANG, K. Y. & ZEGER, S. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73. 13-22.
19. LIANG, K. Y., ZEGER, S. & QAQISH, B. (1992). Multivariate regression analysis for categorical data (with Discussion). J. R. Statist. Soc. B 54, 3-40.
20. MURPHY, S. A. (1994). Consistency in a proportional hazards model incorporating a random effect. Ann. Statist. 22, 712-31.
21. MURPHY, S. A. (1995). Asymptotic theory for the frailty model. Ann. Statist. 23, 182-98.
22. NLSEN, 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, 25-43.
23. OAKES, D. (1982). A model for association in bivariate survival data. J. R. Statist. Soc. B 44, 414-22.
24. OAKES, D. (1986). Semi-parametric inference in a model for association in bivariate survival data. Biometrika 73, 353-61.
25. OAKES, D. (1989). Bivariate survival models induced by frailties. J. Am. Statist. Assoc. 84, 487-93.
26. PRENTICE, R. L. & CAI, J. (1992). Covariance and survivor function estimation using censored multivariate failure time data. Biometrika 79, 495-512.
27. PRENTICE, R. L. & ZHAO, L. P. (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics 47, 825-39.
28. WEI, L. J., LIN, P. Y. & WEISSFELD, L. (1989). Regression analysis of multivariate incomplete failure time data by modelling marginal distributions. J. Am. Statist. Assoc. 84, 1065-73.
29. ZHAO, L. P. & PRENTICE, R. L. (1990). Correlated binary regression using a quadratic exponential model. Biometrika 77, 642-8.
30. ZHAO, L. P., PRENTICE, R. L. & SELF, S. G. (1992). Multivariate mean parameter estimation by using a partly exponential model. J. R. Statist. Soc. B 54, 805-11.