Biometrika Advance Access originally published online on April 27, 2009
Biometrika 2009 96(2):277-291; doi:10.1093/biomet/asp008
Article |
Gamma frailty transformation models for multivariate survival times
Department of Biostatistics, University of North Carolina, 3105-D McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina, 27516, U.S.A. dzeng{at}bios.unc.edu
Department of Biostatistics, Vanderbilt University, 1161 21st Avenue South, S-2323 Medical Center North, Nashville, Tennessee, 37232, U.S.A. cindy.chen{at}vanderbilt.edu
Department of Biostatistics, University of North Carolina, 3109 McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina, 27516, U.S.A. ibrahim{at}bios.unc.edu
Received for publication 1 March 2008. Revision received 1 October 2008.
We propose a class of transformation models for multivariate failure times. The class of transformation models generalize the usual gamma frailty model and yields a marginally linear transformation model for each failure time. Nonparametric maximum likelihood estimation is used for inference. The maximum likelihood estimators for the regression coefficients are shown to be consistent and asymptotically normal, and their asymptotic variances attain the semiparametric efficiency bound. Simulation studies show that the proposed estimation procedure provides asymptotically efficient estimates and yields good inferential properties for small sample sizes. The method is illustrated using data from a cardiovascular study.
Key Words: Gamma frailty model • Linear transformation model • Proportional hazards model • Semiparametric efficiency
References
-
The ARIC Investigators. The Atherosclerosis Risk in Communities (ARIC) Study: Design and Objectives. Am. J. Epidemiol. (1989) 129:687–702.
Bennett S. Analysis of survival data by the proportional odds model. Statist. Med. (1983) 2:273–7.[CrossRef]
Berkson J., Gage R. P. Survival curve for cancer patients following treatment. J. Am. Statist. Assoc. (1952) 47:501–15.[CrossRef][Web of Science]
Box G. E. P., Cox D. R. An analysis of transformations revisited, rebutted. J. Am. Statist. Assoc. (1982) 77:209–10.[CrossRef][Web of Science]
Chen K., Jin Z., Ying Z. Semiparametric analysis of transformation models with censored data. Biometrika (2002) 89:659–68.
Cheng S. C., Wei L. J., Ying Z. Analysis of transformation models with censored data. Biometrika (1995) 82:835–45.
Clayton D. G., Cuzick J. Multivariate generalizations of the proportional hazards model (with discussion). J. R. Statist. Soc. A (1985) 148:82–117.[CrossRef]
Cox D. R. Regression models and life-tables (with discussion). J. R. Statist. Soc. B (1972) 34:187–220.
Dabrowska D. M., Doksum K. A. Partial likelihood in transformation models with censored data. Scand. J. Statist. (1988) 18:1–23.
Glidden D. V. Pairwise dependence diagnostics for clustered failure-time data. Biometrika (2007) 94:371–85.
Hougaard P. Analysis of Multivariate Survival Data (2000) New York: Springer.
Kalbfleisch J. D., Prentice R. L. The Statistical Analysis of Failure Time Data (2002) 2nd ed. Hoboken, NJ: Wiley.
Klein J. Semiparametric estimation of random effects using the Cox model based on the EM algorithm. Biometrics. 48:795–806.
Lin D. Y. Cox regression analysis of multivariate failure time data: the marginal approach. Statist. Med. (1994) 13:2233–47.[CrossRef]
Louis T. A. Finding the observed information matrix when using the EM algorithm. J. R. Statist. Soc. B (1982) 13:2233–47.
Murphy S. A. Consistency in a proportional hazards model incorporating a random effect. Ann. Statist. (1994) 22:712–31.[CrossRef]
Murphy S. A. Asymptotic theory for the frailty model. Ann. Statist. (1995) 23:182–98.[CrossRef]
Murphy S. A., Rossini A. J., van der Vaart A. W. Maximal likelihood estimation in the proportional odds model. J. Am. Statist. Assoc. (1997) 92:968–76.[CrossRef][Web of Science]
Nielsen G. G., Gill R. D., Andersen P. K., Sorensen T. I. A. A counting process approach to maximum likelihood estimation in frailty models. Scand. J. Statist. (1992) 19:25–43.
Oakes D. Bivariate survival models induced by frailties. J. Am. Statist. Assoc. (1989) 84:487–93.[CrossRef][Web of Science]
Oakes D. Frailty models for multiple event times. Surv. Analysis: State of the Art—Klein J. P., Goel P. K., eds. (1991) 84. Dordrecht: Kluwer. 371–9.
Parner E. Asymptotic theory for the correlated gamma-frailty model. Ann. Statist. (1998) 26:183–214.[CrossRef]
Zeng D., Lin D. Y. Maximum likelihood estimation in semiparametric transformation models for counting processes. Biometrika (2006) 93:627–40.
Zeng D., Lin D. Y. Maximum likelihood estimation in semiparametric regression models with censored data (with discussion). J. R. Statist. Soc. B (2007) 69:507–64.[CrossRef]
Zeng D., Yin G., Ibrahim J. G. Semiparametric transformation models for survival data with a cure fraction. J. Am. Statist. Assoc. (2006) 101:670–84.[CrossRef][Web of Science]
CiteULike 
Connotea 
Del.icio.us What's this?
| ||||||||||||||||||||||||||||||||||||||||||||||||