ARTICLE
ABSTRACT
Recently, tests for comparing survival distributions become more and more popular and used in applied economics. Unemployment duration, time needed to find a new job, enterprise survival or waiting for a commodity to be sold are good examples. There are a number of tests to compare survival distributions proposed in statistical literature. The aim of this research was to analyze, by the means of computer simulations, the effectiveness of survival tests as implemented in STATISTICA software. The following tests have been outlined and compared: Wilcoxon, Geehan, Cox-Mantel, Peto & Peto and log rank. Random samples were generated from Weibull distribution.
KEYWORDS
survival function, comparing survival, Monte Carlo research
REFERENCES
[1] Altshuler B., (1970), Theory for the Measurement of Competing Risks in Animal Experiments, Math. Biosciences, 6, 1-11.
[2] Balicki A., (2006), Analiza przeżycia i tablice wymieralności, PWE, Warszawa.
[3] Blossfeld H-P., Golsch K., Rohwer G., (2007), Event History Analysis with Stata, New Jersey: Lawrence Erlbaum Associates.
[4] Cox D. R., (1959), The Analysis of Exponentially Distributed Life-times with Two Types of Failure, Journal of the Royal Statistical Society, Series B (Methodological), 21, 411-421.
[5] Cox D. R., (1964), Some Applications of Exponential Ordered Scores, Journal of the Royal Statistical Society, Series B (Methodological), 26 (1), 103-110.
[6] Cox D. R., (1972), Regression Models and Life-Tables, Journal of the Royal Statistical Society, Series B (Methodological), 34 (2), 187-220.
[7] Deszczyńska A., (2011), Model hazardów proporcjonalnych Coxa, Matematyka stosowana, tom, 13/54, Instytut Matematyczny PAN, Warszawa.
[8] Gehan, E. A., (1965), A Generalized Wilcoxon Test for Comparing Arbitrarily Singly-censored Samples, Biometrika, 52, 203-223.
[9] Halabi S., Singh B., (2004), Sample Size Determination for Comparing Several Survival Curves with Unequal Allocations, Statistics in Medicine, 23, 1793-1815.
[10] Jurkiewicz T., Wycinka E., (2011), Signifi cance Tests of Differences Between Two Crossing Survival Curves for Small Samples, w: Domański Cz., Zielińska-Sitkiewicz K. (red.), Methodological Aspects of Multivariate Statistical Analysis, Statistical Models and Applications, Łódź.
[11] Latta R. B., (1981), Monte Carlo Study of Some Two-Sample Rank Tests With Censored Data, Journal of Statistical Association, 76 (375), 713-719.
[12] Lee E.T., Desu M. M., Gehan E. A., (1975), A Monte Carlo Study of the Power of Some Twosample Tests, Biometrika, 62 (2), 425-432.
[13] Lininger L., Gail M. H., Green S. B., Byar D. P., (1979), Comparison of Four Tests for Equality of Survival Curves in the Presence of Stratification and Censoring, Biometrika, 66 (3), 419-428.
[14] Magel R. C., (1991), Estimating the Power of the Gehan Test, Biometrical Journal, 88 (8), 985-997.
[15] Mantel N., (1966), Evaluation of Survival Data and Two New Rank Order Statistics Arising in its Consideration, Cancer Chemotherapy Reports, 50, 163-170.
[16] Mantel N., (1967), Ranking Procedure for Arbitrarily Restricted Observation, Biometrics, 23 (1), 65-78.
[17] Mantel N., Haenszel W., (1959), Statistical Aspects of the Analysis of Data from Retrospective Studies of Disease, Journal of the National Cancer Institute, 22, 719-748.
[18] Peto R., Peto J., (1972), Asymptotically Effi cient Rank Invariant Procedures, Journal of the Royal Statistical Society, Series A (General), 135 (2), 185-207.
[19] Peto R., Pike M. C., (1973), Conservatism of the Aproximation in the Logrank Test for Survival Data or Tumor Incidence Data, Biometrics, 29 (3), 579-84.
[20] Pyke D. A., Thompson J. N., (1986), Statistical Analysis of Survival and Remotal Rate Experiments, Ecology, 67 (1), Ecological Society of America, 240-245.
[21] http://bio.research.ucsc.edu/people/thompson/PublPDFs/025Statistical.pdf
[22] Stanisz A., (2007), Przystępny kurs statystyki z zastosowaniem STATISTICA PL na przykładach z medycyny, t. 3, StatSoft.
[23] Suciu G. P., Lemeshow S., Moeschberger M., (2004), Statistical Tests of the Equality of Survival Curves: Reconsidering the options, w: Balakrishnan N., Rao C. R. (red.), Handbook of Statistics 23, Advances in Survival Analysis, Elsevier B. V.
