Geodesic
Study of the influence of the distribution law of censoring times and the censoring degree on the power of homogeneity tests
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 3, pp. 122-134.

Voir la notice de l'article provenant de la source Math-Net.Ru

We expose the results of studying the power of statistical tests for checking the hypothesis of homogeneity in randomly censored data for various situations (of different censoring degrees, alternative hypotheses, and laws of distribution of censoring moments). The results of modeling show that the power of the tests depends on the distribution of the censoring times in the case when the survival functions intersect. If they do not intersect then the distribution law for the censoring moments does not have a statistically significant influence on the power of tests. If the survival functions intersect then the Bagdonavičius–Nikulin tests are the most powerful of all those considered but their power decays rapidly as the censoring degree grows. If the survival functions do not intersect then the rank tests are more powerful than the Bagdonavičius–Nikulin tests.
Keywords: randomly censored data, homogeneity hypothesis, Peto's generalized Wilcoxon test, Gehan's generalized Wilcoxon test, logrank test, Bagdonavičius–Nikulin test (single crossing), Bagdonavičius–Nikulin test (multiple crossing).
Mots-clés : Cox–Mantel test, $Q$-test 
@article{SJIM_2014_17_3_a11,
     author = {P. A. Filonenko and S. N. Postovalov},
     title = {Study of the influence of the distribution law of censoring times and the censoring degree on the power of homogeneity tests},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {122--134},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a11/}
}
TY  - JOUR
AU  - P. A. Filonenko
AU  - S. N. Postovalov
TI  - Study of the influence of the distribution law of censoring times and the censoring degree on the power of homogeneity tests
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2014
SP  - 122
EP  - 134
VL  - 17
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a11/
LA  - ru
ID  - SJIM_2014_17_3_a11
ER  - 
%0 Journal Article
%A P. A. Filonenko
%A S. N. Postovalov
%T Study of the influence of the distribution law of censoring times and the censoring degree on the power of homogeneity tests
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2014
%P 122-134
%V 17
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a11/
%G ru
%F SJIM_2014_17_3_a11
P. A. Filonenko; S. N. Postovalov. Study of the influence of the distribution law of censoring times and the censoring degree on the power of homogeneity tests. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 3, pp. 122-134. http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a11/

[1] Smirnov N. V., “Tables for estimating the goodness of fit of empirical distributions”, Ann. Math. Statist., 19:1 (1948), 279–281 | DOI | MR | Zbl

[2] Lehmann E. L., “Consistency and unbiasedness of certain nonparametric tests”, Ann. Math. Statist., 22:1 (1951), 165–179 | DOI | MR | Zbl

[3] Rosenblatt M., “Limit theorems associated with variants of the von Mises statistic”, Ann. Math. Statist., 23:1 (1952), 617–623 | DOI | MR | Zbl

[4] Pettitt A. N., “A two-sample Anderson–Darling rank statistic”, Biometrika, 63:1 (1976), 161–168 | MR | Zbl

[5] Gehan E. A., “A generalized Wilcoxon test for comparing arbitrarily singly-censored samples”, Biometrika, 52:1/2 (1965), 203–223 | DOI | MR | Zbl

[6] Peto R., Peto J., “Asymptotically efficient rank invariant test procedures”, J. Royal Statist. Soc. Ser. A (General), 135:2 (1972), 185–207 | DOI

[7] Lee E. T., Wang J. W., Statistical Methods for Survival Data Analysis, Wiley Series in Probability and Statistics, Wiley, N.Y., 2003 | DOI | MR | Zbl

[8] Pepe M. S., Fleming T. R., “Weighted Kaplan–Meier statistics: A class of distance tests for censored survival data”, Biometrics, 45 (1989), 497–507 | DOI | MR | Zbl

[9] Kaplan E. L., Meier P., “Nonparametric estimator from incomplete observation”, J. Amer. Statist. Assoc., 53 (1958), 457–481 | DOI | MR | Zbl

[10] Fleming T. R., Harrington D. P., Counting Process and Survival Analysis, Wiley, N.Y., 1991 | MR | Zbl

[11] Bagdonavičius V. B., Levuliene R. J., Nikulin M. S., Zdorova-Cheminade O., “Tests for equality of survival distributions against non-location alternatives”, Lifetime Data Anal., 10:4 (2004), 445–460 | DOI | MR | Zbl

[12] Bagdonavičius V. B., Nikulin M., “On goodness-of-fit tests for homogeneity and proportional hazards”, Appl. Stochastic Models in Business and Industry, 22:1 (2006), 607–619 | DOI | MR | Zbl

[13] Martinez Ruvie L. M. C., Naranjo Joshua D., “A pretest for choosing between logrank and Wilcoxon tests in the two-sample problem”, Internat. J. Statist., 68:2 (2010), 111–125 | MR