Abstract
We propose new two andk-sample tests for evaluating the equality of survival distributions against alternatives that include crossing of survival functions, and proportional and monotone hazard ratios. The tests allow for right censored data. The asymptotic power against local alternatives is investigated. Simulation results demonstrate that the new tests are more powerful than known tests when survival functions cross. We apply the tests to a well known study of chemo- and radio-therapy conducted by the Gastrointestinal Tumor Study Group. TheP-values for both proposed tests are much smaller than for other known tests.
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References
O. Aalen (1978) ArticleTitleNonparametric inference for the family of counting processes’‘ Annals of Statistics 6 701–726
P. Andersen, O. Borgan, R. Gill, and N. Keiding, ‘‘Linear non-parametric tests for comparison of counting processes, with application to censored survival data (with discussion)’’, International Statistical Review vol. 50 pp. 219–258, 1982. (Amendment: vol. 52 p. 225 1984.).
P. Andersen (1983) ArticleTitleComparing survival distributions with hazard ratio estimates Scandinavian Journal of Statistics 10 77–85
P. Andersen O. Borgan R. Gill N. Keiding (1993) Statistical Models Based on Counting Processes Springer New York
V Bagdonavičius M. Nikulin (2002) Accelerated Life Models.Modeling and Statistical Analysis Chapman Hall/CRC Boca Raton
N. Breslow (1970) ArticleTitleA generalized Kruskal-Wallis test for comparing K samples subject to unequal patterns of censorship Biometrika 57 579–594
R. Brookmeyere J. Crowley (1982) ArticleTitleA k -sample median test for censored data Journal of American Statistics Association 77 433–440
T. Fleming J. O’Fallon P. O’Brien D. Harrington (1980) ArticleTitleModified Kolmogorov-Smirnov test procedures with application to arbitrary right censored data Biometrics 36 607–626
T. Fleming D. Harrington (1981) ArticleTitleA class of hypothesis tests for one and two samples of censored survival data Communications of Statistic 10 763–794
T. Fleming D. Harrington M. O’Sullivan (1987) ArticleTitleSupremum versions of the log-rank and generalised Wilcoxon statistical Journal of American Statistic Association 82 312–320
Gastrointestinal Tumor Study Group: P. Schein, D. Stablein, H. Bruckner, H. Douglas et al., ‘‘A comparison of combination chemotherapy and combined modality therapy for locally advanced gastric carcinoma,’’ Cancer vol. 49 pp. 1771–1777, 1982.
E. Gehan (1965) ArticleTitleA generalized Wilcoxon test for comparing arbitrary singly censored samples Biometrika 52 203–223 Occurrence Handle1:STN:280:CCqC2cnhslI%3D Occurrence Handle14341275
R. Gill (1980) Censoring and Stochastic Integrals, Mathematical Centre Tracts 124 Mathematisch Centrum Amsterdam
P Nikulin M. Greenwood (1996) A Guide to Chi-squared Testing John Wiley Sons New York
D. Harrington T. Fleming (1982) ArticleTitleA class of rank test procedures for censored survival data Biometrika 69 133–143
F. Hsieh (2001) ArticleTitleOn heteroscedastic hazards regression models: Theory and application Journal of the Royal Statistical Society, Series B 63 63–79
J Kalbfleisch R. Prentice (1980) The Statistical Analysis of Failure Time Data John Wiley Sons New York
J Klein M. Moeschenberger (1997) Survival Analysis .Techniques for Censored and Truncated Data Springer New York
J. Koziol (1978) ArticleTitleA two-sample cramer-Von Mises test for randomly censored data Biometrical Journal 20 603–608
R. Peto J. Peto (1972) ArticleTitleAsymptotically efficient rank invariant test procedures (with discussion) Journal of Royal Statistical Society A 135 185–206
R. Prentice (1978) ArticleTitleLinear rank tests with right censored data Biometrika 65 167–179
M. Schumacher (1984) ArticleTitleTwo-sample tests of Cramer-von Mises and Kolmogorov-Smirnov type for random censored data International Statistical Review 52 263–281
D. Stablein I. Koutrouvelis (1985) ArticleTitleA two sample test sensitive to crossing hazards in uncensored and singly censored data Biometrics 41 643–652
R. Tarone J. Ware (1977) ArticleTitleOn distribution-free tests for equality for survival distributions Biometrika 64 156–160
H.-D. I. Wu F. Hsieh C.-H. Chen (2001) ArticleTitleValidation of a heteroscedastic hazards regression model Lifetime Data Analysis 8 21–34
H.-D.I. Wu (2004) Effect of ignoring heterogeneity in hazards regression in Parametric and Semipametric Models with Applicatiions to Reliability Survival Analysis, and Quality of Life Boston,Birkhauser 239–252
H.-D. I. Wu, A Partial Score Test for Difference Among Heteroscedastic Populations. Preprint of The School of Public Health, China Medical College, Taichung, Taiwan, 21 October, 2002.
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Bagdonavičius, V.B., Levuliene, R.J., Nikulin, M.S. et al. Tests for Equality of Survival Distributions Against Non-Location Alternatives. Lifetime Data Anal 10, 445–460 (2004). https://doi.org/10.1007/s10985-004-4777-7
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DOI: https://doi.org/10.1007/s10985-004-4777-7