Nonparametric Survival Analysis
Michael G. Akritas
Source: Statist. Sci. Volume 19, Number 4
(2004), 615-623.
Abstract
Some classes of nonparametric procedures with randomly right-censored data are presented. They include procedures for analysis of variance and analysis of covariance designs with independent and dependent ordinal (continuous and discrete) data.
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Keywords: Censored data; product-limit estimator; k-sample problem; analysis of variance; analysis of covariance; dependent data
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ss/1113832726
Digital Object Identifier: doi:10.1214/088342304000000530
Mathematical Reviews number (MathSciNet): MR2185583
Zentralblatt MATH identifier: 1100.62603
References
Akritas, M. G. (1986). Bootstrapping the Kaplan--Meier estimator. J. Amer. Statist. Assoc. 81 1032--1038.
Mathematical Reviews (MathSciNet): MR867628
Akritas, M. G. (1988). Pearson-type goodness-of-fit tests: The univariate case. J. Amer. Statist. Assoc. 83 222--230.
Mathematical Reviews (MathSciNet): MR941019
Akritas, M. G. (1992). Rank transform statistics with censored data. Statist. Probab. Lett. 13 209--221.
Mathematical Reviews (MathSciNet): MR1158861
Akritas, M. G. and Arnold, S. F. (1994). Fully nonparametric hypotheses for factorial designs. I. Multivariate repeated measures designs. J. Amer. Statist. Assoc. 89 336--343.
Mathematical Reviews (MathSciNet): MR1266303
Akritas, M. G., Arnold, S. F. and Du, Y. (2000). Nonparametric models and methods for nonlinear analysis of covariance. Biometrika 87 507--526.
Mathematical Reviews (MathSciNet): MR1789806
Zentralblatt MATH: 0956.62036
Digital Object Identifier: doi:10.1093/biomet/87.3.507
Akritas, M. G. and Brunner, E. (1997). Nonparametric methods for factorial designs with censored data. J. Amer. Statist. Assoc. 92 568--576.
Mathematical Reviews (MathSciNet): MR1467850
Akritas, M. G. and LaValley, M. P. (1997). Statistical analysis with incomplete data: A selective review. In Robust Inference (G. S. Maddala and C. R. Rao, eds.). Handbook of Statistics 15 551--632. North-Holland, Amsterdam.
Mathematical Reviews (MathSciNet): MR1492725
Zentralblatt MATH: 0908.62041
Andersen, P. K., Borgan, Ø., Gill, R. and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer, New York.
Mathematical Reviews (MathSciNet): MR1198884
Zentralblatt MATH: 0769.62061
Beran, R. (1981). Nonparametric regression with randomly censored survival data. Technical report, Dept. Statistics, Univ. California, Berkeley.
Borgan, Ø. and Liestøl, K. (1990). A note on confidence intervals and bands for the survival function based on transformations. Scand. J. Statist. 17 35--41.
Mathematical Reviews (MathSciNet): MR1062844
Brookmeyer, R. and Crowley, J. J. (1982). A confidence interval for the median survival time. Biometrics 38 29--41.
Cox, D. R. (1972). Regression models and life-tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187--220.
Mathematical Reviews (MathSciNet): MR341758
Du, Y., Akritas, M. G. and Van Keilegom, I. (2003). Nonparametric analysis of covariance for censored data. Biometrika 90 269--287.
Mathematical Reviews (MathSciNet): MR1986646
Zentralblatt MATH: 1036.62037
Digital Object Identifier: doi:10.1093/biomet/90.2.269
Fleming, T. R. and Harrington, D. P. (1981). A class of hypothesis tests for one- and two-sample censored survival data. Comm. Statist. Theory Methods 10 763--794.
Mathematical Reviews (MathSciNet): MR620862
Gill, R. D. (1980). Censoring and Stochastic Integrals. Mathematisch Centrum, Amsterdam.
Mathematical Reviews (MathSciNet): MR596815
Zentralblatt MATH: 0456.62003
Gill, R. D. (1983). Large sample behavior of the product-limit estimator on the whole line. Ann. Statist. 11 49--58.
Mathematical Reviews (MathSciNet): MR684862
JSTOR: links.jstor.org
Greenwood, M. (1926). The natural duration of cancer. Reports on Public Health and Medical Subjects 33 1--26. Her Majesty's Stationery Office, London.
Hall, W. J. and Wellner, J. A. (1980). Confidence bands for a survival curve from censored data. Biometrika 67 133--143.
Mathematical Reviews (MathSciNet): MR570515
Zentralblatt MATH: 0423.62078
Digital Object Identifier: doi:10.2307/2335326
Hjort, N. L. (1990). Goodness-of-fit tests in models for life history data based on cumulative hazard rates. Ann. Statist. 18 1221--1258.
Mathematical Reviews (MathSciNet): MR1062707
JSTOR: links.jstor.org
Hollander, M. and Peña, E. A. (1992). A chi-squared goodness-of-fit test for randomly censored data. J. Amer. Statist. Assoc. 87 458--463.
Mathematical Reviews (MathSciNet): MR1173810
Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53 457--481.
Mathematical Reviews (MathSciNet): MR93867
Kim, J. H. (1993). Chi-square goodness-of-fit tests for randomly censored data. Ann. Statist. 21 1621--1639.
Mathematical Reviews (MathSciNet): MR1241282
JSTOR: links.jstor.org
Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data. Wiley, New York.
Mathematical Reviews (MathSciNet): MR640866
Zentralblatt MATH: 0541.62081
Li, G. and Doss, H. (1993). Generalized Pearson--Fisher chi-square goodness-of-fit tests, with applications to models with life history data. Ann. Statist. 21 772--797.
Mathematical Reviews (MathSciNet): MR1232519
JSTOR: links.jstor.org
Lin, D. Y. (1994). Cox regression analysis of multivariate failure time data: The marginal approach. Statistics in Medicine 13 2233--2247.
Mantel, N. (1966). Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemotherapy Reports Part 1 50 163--170.
O'Gorman, J. T. and Akritas, M. G. (2001). Nonparametric models and methods for designs with dependent censored data. Biometrics 57 88--95.
Mathematical Reviews (MathSciNet): MR1833293
Digital Object Identifier: doi:10.1111/j.0006-341X.2001.00088.x
Pepe, M. S. and Fleming, T. R. (1991). Weighted Kaplan--Meier statistics: Large sample and optimality considerations. J. Roy. Statist. Soc. Ser. B 53 341--352.
Mathematical Reviews (MathSciNet): MR1108331
Tarone, R. E. and Ware, J. H. (1977). On distribution-free tests for equality of survival distributions. Biometrika 64 156--160.
Mathematical Reviews (MathSciNet): MR461830
Zentralblatt MATH: 0352.62046
Digital Object Identifier: doi:10.2307/2335790
Thomas, D. R. and Grunkemeier, G. L. (1975). Confidence interval estimation of survival probabilities for censored data. J. Amer. Statist. Assoc. 70 865--871.
Mathematical Reviews (MathSciNet): MR405766
Wei, L. J. and Lachin, J. M. (1984). Two-sample asymptotically distribution-free tests for incomplete multivariate observations. J. Amer. Statist. Assoc. 79 653--661.
Mathematical Reviews (MathSciNet): MR763584
Woolson, R. F. and O'Gorman, T. W. (1992). A comparison of several tests for censored paired data. Statistics in Medicine 11 193--208.
