Abstract
In a clinical trial to evaluate treatments for a chronic disease, a commonly used regression method for analyzing multiple event times is based on a multivariate Cox model (Wei, Lin and Weissfeld, 1989). However, the Cox model may not fit the data well. For univariate survival analysis, a class of linear transformation models (Cheng, Wei and Ying, 1995a) provides many useful semi-parametric alternatives to the Cox model. In this paper, we take a similar approach as Wei et al. (1989) did for the multivariate case by modeling each marginal failure time with a linear transformation model and derive joint inference procedures for the regression parameters. In addition, we show how to check the adequacy of the fitted model graphically. We apply the proposed methods to data from an AIDS clinical trial and a cancer clinical trial for illustration.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andersen, P. K. and Gill, R. D. (1982). Cox’s regression model for counting processes: A large sample study (Com: p1121-1124). Ann. Statist 10, 1100–1120.
Bennett, S. (1983). Analysis of survival data by the proportional odds model. Statist. Med. 2, 273–277.
Byar, D. P. (1980). The Veterans Administration Study of Chemoprophylaxis for Recurrent Stage I Bladder Tumors: Comparisons of Placebo, Pyridoxine, and Topical Thiotepa. Bladder Tumors and Other Topics in Urological Oncology, eds Pavone-Macaluso, M., Smith, P. H. and Edsmyn, F., New York: Plenum, 363–370.
Cheng, S. C., Wei, L. J. and Ying, Z. (1995a). Analysis of transformation models with censored data. Biometrika 82, 835–845.
Cheng, S. C., Wei, L. J. and Ying, Z. (1995b). Predicting survival probability with non-proportional hazards models, Technical Report, University of Texas, M. D. Anderson Cancer Center, Dept. of Biomathematics.
Cheng, S. C., Wei, L. J. and Ying, Z. (1997). Predicting survival probability with semi-parametric transformation models. To appear in J. Am. Statist. Assoc.
Cox, D. R. (1972). Regression models and life-tables (with discussion). J. R. Statist. Soc. B 34, 187–220.
Cuzick, J. (1988). Rank regression. Ann. Statist. 16, 1369–1389.
Dabrowska, D. M. and Doksum, K. A. (1988a). Estimation and testing in a two-sample generalized odds-rate model. J. Am. Statist. Assoc. 83, 744–749.
Dabrowska, D. M. and Doksum, K. A. (1988b). Partial likelihood in transformation models with censored data. Scand. J. Statist. 15, 1–23.
Fischl, M. A., Stanley, K. et al. (1995). Combination and monotherapy with zidovudine and zalcitabine in patients with advanced HIV disease. Annals of Internal Medicine 122, 24–32.
Gill, R. D. (1980). Censoring and Stochastic Integrals (Mathematical Centre Tract No. 124). Amsterdam: Mathematisch Centrum.
Gray, R. J. (1988). A class of K-sample tests for comparing the cumulative incidence of a competing risk. Ann. Statist. 16, 1140–1154.
Lin, J. S. and Wei, L. J. (1992). Linear regression analysis for multivariate failure time observations. J. Am. Statist. Assoc. 87, 1091–1097.
Pettitt, A. N. (1982). Inference for the linear model using a likelihood based on ranks. J. R. Statist. Soc. C 33, 169–175.
Wei, L. J. (1992). The accelerated failure time model: A useful alternative to the Cox regression model in survival analysis (Disc: p1881-1885). Statist. Med. 11, 1871–1879.
Wei, L. J. and Johnson, W. E. (1985). Combining dependent tests with incomplete repeated measurements. Biometrika 72, 359–364.
Wei, L. J., Lin, D. Y. and Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J. Am. Statist. Assoc. 84, 1065–1073.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Chen, L., Wei, L.J. (1997). Analysis of Multivariate Survival Times with Non-Proportional Hazards Models. In: Lin, D.Y., Fleming, T.R. (eds) Proceedings of the First Seattle Symposium in Biostatistics. Lecture Notes in Statistics, vol 123. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6316-3_3
Download citation
DOI: https://doi.org/10.1007/978-1-4684-6316-3_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94992-5
Online ISBN: 978-1-4684-6316-3
eBook Packages: Springer Book Archive