Abstract
While univariate failure time methods, including Kaplan-Meier survivor function estimators, censored data rank tests, and Cox regression procedures are well developed, corresponding flexible, standardized tools are not available for multivariate failure time analysis. This paper considers methods for the modeling and analysis of clustered failure times, with a focus on the estimation of marginal hazard functions and pairwise cross-ratio functions. First some representations of bivariate failure times are reviewed, along with corresponding nonparametric estimators and summary measures of pairwise dependence. Then procedures are outlined for simultaneous estimation of marginal hazard ratio, and pairwise cross-ratio parameters, for use in more general multivariate failure time regression problems. These estimation procedures are somewhat restrictive concerning the form of pairwise dependencies between failure times. Some approaches to relaxing these restrictions are briefly mentioned.
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., Borgan, O., Gill, R.D. and Keiding, N. (1993). Statistical Models Based on Counting Processes. New York: Springer-Verlag.
Anderson, P.K. and Gill, R.D. (1982). Cox’s regression model for counting processes: A large sample study. Ann. Statist., 10, 1100–1120.
Bickel, P.J., Klassen, C.A., Ritov, Y. and Wellner, J. (1993). Efficient and adaptive estimation for semiparametric models. Baltimore, Maryland: Johns Hopkins University Press.
Breslow, N.E. (1974). Covariance analysis of censored survival data. Biometrics, 30, 89–99.
Cai, J. and Prentice, R.L. (1995). Estimating equations for hazard ratio parameters based on correlated failure time data. Biometrika, 82, 151–164.
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, 144–151.
Clayton, D.G. and Cuzick, J. (1985). Multivariate generalizations of the proportional hazards model (with discussion). J.R. Statist. Soc. A, 148, 82–117.
Cox, D.R. (1972). Regression models and life tables (with discussion). J.R. Statist. Soc. B, 187–220.
Dabrowska, D. (1988). Kaplan-Meier estimate on the plane. Ann. Statist., 16, 1475–1489.
Fleming, T.R. and Harrington, D.P. (1991). Counting Processes and Survival Analysis. New York: Wiley.
Gill, R.D., Van der Laan, M.J. and Wellner, J.A. (1995). Inefficient estimators of the bivariate survival function for three models. Ann. Inst. Henri Poincare, 31, 545–597.
Hsu, L. and Prentice, R.L. (1996). On assessing the strength of dependency between failure time variates. Biometrika, 83, 491–506.
Lee, E., Wei, L.J., and Amato, D.A. (1992). Cox-type regression analysis for large numbers of small groups of correlated failure-time observations. In Survival Analysis: State of the Art, Eds. J.P. Klein and P.K. Goel, pp. 237–247. Klewer Academic Publishers.
Nielsen, G.G., Gill, R.D., Andersen, P.K. and Sorensen, T.I.A. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scand. J. Statist., 19, 25–43.
Oakes, D. (1989). Bivariate survival models induced by frailties. J. Amer. Statist. Assoc, 84 487–493.
Prentice, R.L. and Cai, J. (1992). Covariance and survivor function estimation using censored multivariate failure time data. Biometrika, 79, 495–512.
Prentice, R.L. and Hsu, L. (1997). Regression on hazard ratios and crossratios in multivariate failure time analysis. Biometrika, in press.
Prentice, R.L. and Zhao, L.P. (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics, 47, 825–839.
Wei, L.J., Lin, D.Y. and Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modelling marginal distributions. J. Amer. Statist. Assoc., 84, 1065–1073.
Whittemore, A.S. (1995). Logistic regression of family data from casecontrol studies. Biometrika, 82, 57–67.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Prentice, R.L., Hsu, L. (1997). Multivariate Failure Time Data: Representation and Analysis. 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_2
Download citation
DOI: https://doi.org/10.1007/978-1-4684-6316-3_2
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