Abstract
This chapter introduces some fundamental results in survival analysis. We first describe what is censored failure time data and how to interpret the failure time distribution. Two nonparametric methods for estimating the survival curve, the life table estimator and the Kaplan-Meier estimator, are demonstrated. We then discuss the two-sample problem and the usage of the log-rank test for comparing survival distributions between groups. Lastly, we discuss in some detail the proportional hazards model, which is a semiparametric regression model specifically developed for censored data. All methods are illustrated with artificial or real data sets.
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Cox, D. R., and Oakes, D. (1984) Analysis of Survival Data. London, Chapman & Hall, pp. 52–53.
Ware, J. H., and DeMets, D. L. (1976) Reanalysis of some baboon descent data. Biometrics. 32, 459–463.
Kalbfleisch, J. D., and Prentice, R. L. (2002) The Statistical Analysis of Failure Time Data. New York, Chichester, John Wiley & Sons.
Klein, J. P., and Moeschberger, M. L. (1997) Survival Analysis Techniques for Censored and Truncated Data. New York, Springer-Verlag, pp. 100–103.
Kaplan, E. L., and Meier, P. (1958) Nonparametric estimation from incomplete observations. J. Am. Stat. Assoc. 53, 457–481.
Efron, B. (1967) The two sample problem with censored data. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. New York, Prentice-Hall, 4, pp. 831–853.
Gill, R. D. (1980) Censoring and Stochastic Integrals, Mathematical Center Tracts 124. Amsterdam, Mathematisch Centrum.
Klein, J. P. (1991) Small-sample moments of some estimators of the variance of the Kaplan-Meier and Nelson-Aalen estimators, Scand. J. Stat. 18, 333–340.
Greenwood, M. (1926) The errors of sampling of the survivorship tables. In: Reports on Public Health and Statistical Subjects, no. 33. London, HMSO, Appendix 1.
Gehan, E. A. (1965) A generalized Wilcoxon test for comparing arbitrarily singlycensored samples. Biometrika 52, 203–223.
Harrington, D. P., and Fleming, T. R. (1982) A class of rank test procedures for censored survival data. Biometrika 69, 553–566.
Cox, D. R. (1972) Regression models and life-tables (with discussion). J. R. Stat. Soc. Ser. B Methodol. 34, 187–220.
Cox, D. R. (1975) Partial likelihood. Biometrika 62, 269–276.
Breslow, N. E. (1975) Analysis of survival data under the proportional hazards model. Int. Stat. Rev. 43, 45–58.
Cox, D. R., and Snell, E. J. (1968) A general definition of residuals (with discussion). J. R. Stat. Soc. Ser. B Methodol. 30, 248–275.
Schoenfeld, D. (1982) Partial residuals for the proportional hazards regression model. Biometrika 69, 239–241.
Lin, D. Y. Wei, L. J., and Ying, Z. (1993) Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika. 80, 557–572.
Therneau, T. M., and Grambsch, P. M. (2000) Modeling survival data: extending the Cox model. Berlin, New York, Springer-Verlag.
Freireich, E. J., Gehan, E., Frei, E., Schroeder, L. R., Wolman, I. J., Anbari, R., Burgert, E. O., Mills, S. D., Pinkel, D., Selawry, O. S., and others. (1963) The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukemia: a model for evaluation of other potentially useful therapy. Blood 21, 699–716.
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© 2007 Humana Press Inc., Totowa, NJ
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Jiang, H., Fine, J.P. (2007). Survival Analysis. In: Ambrosius, W.T. (eds) Topics in Biostatistics. Methods in Molecular Biology™, vol 404. Humana Press. https://doi.org/10.1007/978-1-59745-530-5_15
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DOI: https://doi.org/10.1007/978-1-59745-530-5_15
Publisher Name: Humana Press
Print ISBN: 978-1-58829-531-6
Online ISBN: 978-1-59745-530-5
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