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Su, Pei-Fang; Chi, Yunchan; Li, Chung-I; Shyr, Yu; Liao, Yi-De

Analyzing survival curves at a fixed point in time for paired and clustered right-censored data. (English) Zbl 1328.62563

Comput. Stat. Data Anal. 55, No. 4, 1617-1628 (2011).
Summary: In clinical trials, information about certain time points may be of interest in making decisions about treatment effectiveness. Therefore, rather than comparing entire survival curves, researchers may wish to focus the comparison on fixed time points with potential clinical utility. For two independent samples of right-censored data, J. P. Klein et al. [“Analyzing survival curves at a fixed point in time”, Stat. Medicine 26, 4505–4519 (2007; doi:10.1002/sim.2864)] compared survival probabilities at a fixed time point by studying a number of tests based on transformations of the Kaplan-Meier estimators of the survival function. To compare the survival probabilities at a fixed time point for paired right-censored data or clustered right-censored data, however, their approach requires modification. In this paper, we extend the statistics to accommodate possible within-pair and within-cluster correlation. We use simulation studies to present comparative results. Finally, we illustrate the implementation of these methods using two real data sets.

Cited in 4 Documents

MSC:

62N01 Censored data models
62N02 Estimation in survival analysis and censored data
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62-07 Data analysis (statistics) (MSC2010)

Keywords:

right-censored data; Kaplan-Meier estimator; pseudo-value approach; correlated survival data
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References:

[1] Andersen, P. K.; Klein, J. P.; Rosthøj, S., Generalized linear models for correlated pseudo-observations with applications to multi-state models, Biometrika, 90, 15-27 (2003) · Zbl 1034.62062
[2] Bie, O.; Borgan, Ø.; Liestøl, K., Confidence intervals and confidence bands for the cumulative hazard rate function and their small sample properties, Scandinavian Journal of Statistics, 14, 221-233 (1987) · Zbl 0627.62049
[3] Borgan, Ø.; Liestøl, K., A note on confidence intervals and bands for the survival curve based on transformations, Scandinavian Journal of Statistics, 17, 35-41 (1990)
[4] Cai, J.; Shen, Y., Permutation tests for comparing marginal survival functions with clustered failure time data, Statistics in Medicine, 19, 2963-2973 (2000)
[5] Clayton, D.; Cuzick, J., Multivariate generalizations of the proportional hazards model (with discussion), Journal of the Royal Statistical Society, Series A, 148, 82-117 (1985) · Zbl 0581.62086
[6] Dallas, M. J.; Rao, P. V., Testing equality of survival functions based on both paired and unpaired censored data, Biometrics, 56, 154-159 (2000) · Zbl 1060.62593
[7] Gill, R. D., Censoring and Stochastic Integrals, Tract 124 (1980), The Mathematical Centre: The Mathematical Centre Amsterdam · Zbl 0456.62003
[8] Greenwood, M., The Natural Duration of Cancer, Reports on Public Health and Medical Subjects, Vol. 33 (1926), H.M. Stationery Office: H.M. Stationery Office London
[9] Gu, M.; Follmann, D.; Geller, N. L., Monitoring a general class of two-sample survival statistics with applications, Biometrika, 86, 45-57 (1999) · Zbl 1101.62376
[10] Huang, X.; Wolfe, R. A., A frailty model for informative censoring, Biometrics, 58, 510-520 (2002) · Zbl 1210.62129
[11] Huster, W. S.; Brookmeyer, R.; Self, S. G., Modeling paired survival data with covariates, Biometrics, 45, 145-156 (1989) · Zbl 0715.62224
[12] Jung, S. H.; Jeong, J. H., Rank tests for clustered survival data, Lifetime Data Analysis, 9, 21-33 (2003) · Zbl 1116.62415
[13] Kalbfeisch, J. D.; Prentice, R. L., The Statistical Analysis of Failure Time Data (1980), Wiley: Wiley New York · Zbl 0504.62096
[14] Kaplan, E. L.; Meier, P., Nonparametric estimation form incomplete observations, Journal of the American Statistical Association, 53, 457-481 (1958) · Zbl 0089.14801
[15] Klein, J. P.; Andersen, P. K., Regression modeling of competing risks data based on pseudo-values of the cumulative incidence function, Biometrics, 61, 223-229 (2005) · Zbl 1077.62081
[16] Klein, J. P.; Logan, B.; Harhoff, M.; Anderson, P. K., Analyzing survival curves at a fixed point in time, Statistics in Medicine, 26, 4505-4519 (2007)
[17] Le, C. T.; Lindgren, B. R., Duration of ventilating tubes: a test of comparing two clustered samples of censored data, Biometrics, 52, 328-334 (1996) · Zbl 0876.62098
[18] Liang, K. Y.; Zeger, S. L., Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22 (1986) · Zbl 0595.62110
[19] Logan, B. R.; Klein, J. P.; Zhang, M. J., Comparing treatments in the presence of crossing survival curves. An application to bone marrow transplantation, Biometrics, 64, 733-740 (2008) · Zbl 1170.62394
[20] Moran, P. A.P., Testing for correlation between non-negative variates, Biometrika, 54, 385-394 (1967) · Zbl 0166.15101
[21] Murray, S., Using weighted Kaplan-Meier statistics in nonparametric comparisons of paired censored survival outcomes, Biometrics, 57, 361-368 (2001) · Zbl 1209.62106
[22] Nair, V. N., Confidence bands for survival functions with censored data: a comparative study, Technometrics, 26, 265-275 (1984)
[23] Oakes, D., Bivariate survival models induced by frailties, Journal of the American Statistical Association, 84, 487-493 (1989) · Zbl 0677.62094
[24] O’Gorman, J. T.; Akritas, M. G., Nonparametric models and methods for designs with dependent censored data: part II, Journal of Nonparametric Statistics, 16, 613-622 (2004) · Zbl 1148.62305
[25] Parzen, M. I.; Wei, L. J.; Ying, Z., Simultaneous confidence intervals for the difference of two survival functions, Scandinavian Journal of Statistics, 24, 309-314 (1997) · Zbl 0888.62107
[26] Pepe, M. S.; Fleming, T. R., Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data, Biometrics, 45, 497-507 (1989) · Zbl 0715.62087
[27] Perme, M. P.; Andersen, P. K., Checking hazard regression models using pseudo-observations, Statistics in Medicine, 27, 5309-5328 (2008)
[28] Wang, H.; Fygenson, M., Inference for censored quantile regression models in longitudinal studies, Annals of Statistics, 37, 756-781 (2009) · Zbl 1162.62035
[29] Ying, Z.; Wei, L. J., The Kaplan-Meier estimate for dependent failure time observations, Journal of Multivariate Analysis, 50, 17-29 (1994) · Zbl 0798.62048
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