A Flexible Approach to Time-varying Coefficients in the Cox Regression Setting
- Daniel J. Sargent
- … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
Research on methods for studying time-to-event data (survival analysis) has been extensive in recent years. The basic model in use today represents the hazard function for an individual through a proportional hazards model (Cox, 1972). Typically, it is assumed that a covariate's effect on the hazard function is constant throughout the course of the study. In this paper we propose a method to allow for possible deviations from the standard Cox model, by allowing the effect of a covariate to vary over time. This method is based on a dynamic linear model. We present our method in terms of a Bayesian hierarchical model. We fit the model to the data using Markov chain Monte Carlo methods. Finally, we illustrate the approach with several examples.
- O.O. Aalen, “Nonparametric inference for a family of counting processes,” Annals of Statistics 6, 701–726, 1978.
- H. Akaike, “Information theory and an extension of the entropy maximization principle”, in Proceedings of the Second International Symposium on Information Theory, eds. B.N. Petrov and R. Csak. Kiado: Akademica, 1973.
- P.K. Anderson and R.D. Gill, “Cox's regression model for counting processes: A large sample study,” Annals of Statistics 10, 1100–1120, 1982.
- D.R. Cox, “Regression models and life tables (with discussion),” Journal of the Royal Statistical Society, Series B 34, 187–220, 1972.
- D.R. Cox, “Partial Likelihood,” Biometrika 62, 269–275, 1975. CrossRef
- B. Efron, “The efficiency of Cox's likelihood function for censored data,” Journal of the American Statistical Association 72, 557–565, 1977. CrossRef
- D. Gamerman, “Dynamic Bayesian models for survival data,” Applied Statistics 40, 63–79, 1991. CrossRef
- A.E. Gelfand and A.F.M. Smith, “Sampling based approaches to calculating marginal densities,” Journal of the American Statistical Association 85, 398–409, 1990. CrossRef
- A. Gelman, G. Roberts, W. Gilks, “Efficient Metropolis jumping rules,” in Bayesian Statistics 5, eds. J.O. Berger, J.M. Bernardo, A.P. Dawid, A.F.M. Smith, Oxford: University Press, 1996.
- A. Gelman and D.B. Rubin, “Inference from iterative simulation using multiple sequences (with discussion),” Statistical Science 7, 457–511, 1992.
- I.J. Good and R.A Gaskins, “Density estimation and bump-hunting by the penalized likelihood method exemplified by scattering and meteorite data (with discussion),” Journal of the American Statistical Association 75, 42–56, 1980. CrossRef
- P.M. Grambsch and T.M. Therneau, “Proportional hazards tests and diagnostics based on weighted residuals,” Biometrika 81, 515–526, 1994. CrossRef
- R.J. Gray, “Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis,” Journal of the American Statistical Association 87, 942–951, 1992. CrossRef
- R.J. Gray, “Spline-based tests in survival analysis,” Biometrics 50, 640–652, 1994. CrossRef
- T.J. Hastie and R.J. Tibshirani, Generalized additive models, New York: Chapman and Hall, 1990.
- T.J. Hastie and R.J. Tibshirani, “Varying-coefficient models,” Journal of the Royal Statistical Society, Series B 55, 86-95, 1993.
- S. Johansen, “An extension of Cox's regression model,” International Statistical Review, 51, 165-174, 1983. CrossRef
- J.D. Kalbfleisch, “Nonparametric Bayesian analysis of survival time data,” Journal of the Royal Statistical Society, Series B 40, 214–221, 1978.
- J.D. Kalbfleisch and R.L. Prentice, The Statistical Analysis of Failure Time Data. New York: Wiley, 1978.
- D.Y. Lin, “Goodness-of-fit for the Cox regression model based on a class of parameter estimators,” Journal of the American Statistical Association 86, 725–728, 1991. CrossRef
- D.V. Lindley and A.F.M Smith, “Bayes estimates for the linear model (with discussion),” Journal of the Royal Statistical Society, Series B, 34, 1–41, 1972.
- P. Müller, “A generic approach to posterior integration and Gibbs sampling,” Technical Report 91-009, Department of Statistics, Purdue University.
- F. O'sullivan, “Nonparametric estimation in the Cox model,” The Annals of Statistics 21, 124–145, 1993.
- D.J. Sargent, “A general framework for random effects survival analysis in the Cox proportional hazards setting,” Research Report 95–004, Division of Biostatistics, University of Minnesota, 1995.
- D. Schoenfeld, “Partial residuals for the proportional hazards regression model,” Biometrika 69, 239–241, 1982. CrossRef
- A.F.M. Smith and G.O. Roberts, “Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion),” Journal of the Royal Statistical Society, Series B 55, 3–23, 1993.
- T.M. Therneau, “A package of survival functions for S,” Technical Report No. 53, Section of Biostatistics, Mayo Clinic, 1994.
- L. Tierney, “Markov chains for exploring posterior distributions (with discussion),” Annals of Statistics 22, 1701–1762, 1994.
- P.J.M. Verweij and H.C. van Houwelingen, “Time-dependent effects of fixed covariates in Cox regression,” Biometrics 51 1550–1556, 1995. CrossRef
- M. West, P.J. Harrison, H.S. Migon, “Dynamic generalized linear models and Bayesian forecasting (with discussion),” Journal of the American Statistical Association 80, 73–97, 1985. CrossRef
- D.M. Zucker and A.F. Karr, “Nonparametric survival analysis with time-dependent covariate effects: a penalized partial likelihood approach,” The Annals of Statistics 18, 329–353, 1990.
- A Flexible Approach to Time-varying Coefficients in the Cox Regression Setting
Lifetime Data Analysis
Volume 3, Issue 1 , pp 13-25
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Hierarchical models
- Markov chain Monte Carlo
- Dynamic linear model
- Survival analysis
- Industry Sectors
- Author Affiliations
- 1. Cancer Center Statistics, Plummer 4, Mayo Clinic, 200 1st Street SW, Rochester, MN, 55905