Abstract
The accelerated failuretime (AFT) model is an important alternative to the Cox proportionalhazards model (PHM) in survival analysis. For multivariate failuretime data we propose to use frailties to explicitly account forpossible correlations (and heterogeneity) among failure times.An EM-like algorithm analogous to that in the frailty model forthe Cox model is adapted. Through simulation it is shown thatits performance compares favorably with that of the marginalindependence approach. For illustration we reanalyze a real dataset.
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References
D. G. Clayton, “The analysis of event history data: a review of progress and outstanding problems,” Statistics in Medicine vol. 7 pp. 819–841, 1988.
D. G. Clayton and J. Cuzick, “Multivariate generalizations of the proportional hazards model (with discussion),” Journal of the Royal Statistical Society A vol. 48 pp. 82–117, 1985.
D. R. Cox, “Regression models and life-tables (with discussion),” Journal of the Royal Statistical Society B vol. 34 pp. 187–220, 1972.
D. R. Cox, “Some remarks on the analysis of survival data,” in Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis, Springer: New York, 1997.
B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall: London, 1993.
J. P. Klein, “Semiparametric estimation of random effects using the Cox model based on the EM algorithm,” Biometrics vol. 48 pp. 795–806, 1992.
E. W. Lee, L. J. Wei, and Z. Ying, “Linear regression analysis for highly stratified failure time data,” Journal of the American Statistical Association vol. 88 pp. 557–565, 1993.
S. R. Lipsitz and M. Parzen, “A jackknife estimator of variance for Cox regression for correlated survival data,” Biometrics vol. 52 pp. 291–298, 1996.
D. Y. Lin and C. J. Geyer, “Computational methods for semi-parametric linear regression with censored data,” Journal of Computational and Graphical Statistics vol. 1 pp. 77–90, 1992.
C. A. McGilchrist and C.W. Aisbett, “Regression with frailty in survival analysis,” Biometrics vol. 47 pp. 461–466, 1991.
G. G. Nielsen, R. D. Gill, P. K. Andersen, and T. I. A. Sorensen, “A counting process approach to maximum likelihood estimation in frailty models,” Scand. J. Statist. vol. 19 pp. 25–43, 1992.
W. Pan and J. E. Connett, “A multiple imputation approach to linear regression with clustered censored data,” to appear in Lifetime Data Analysis, 2000.
W. Pan and T. A. Louis, “A linear mixed-effects model for multivariate censored data,” Biometrics vol. 56 pp. 160–166, 2000.
A. A. Tsiatis, “Estimating regression parameters using linear rank tests for censored data,” Annals of Statistics vol. 18 pp. 354–372, 1990.
L. J. Wei, “The accelerated failure time model: A useful alternative to the Cox regression model in survival analysis (with discussion),” Statistics in Medicine vol. 11 pp. 1871–1879, 1992.
C. F. J. Wu, “On the convergence properties of the EM algorithm,” Ann. Statist. vol. 11 pp. 95–103, 1983.
X. Xue and R. Brookmeyer, “Bivariate frailty model for the analysis of multivariate survival time,” Lifetime Data Analysis vol. 2 pp. 277–289, 1996.
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Pan, W. Using Frailties in the Accelerated Failure Time Model. Lifetime Data Anal 7, 55–64 (2001). https://doi.org/10.1023/A:1009625210191
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DOI: https://doi.org/10.1023/A:1009625210191