Abstract
Score and weighted tests used to compare survival curves: Numerical examples There are many situations where investigators are not able to specify in advance the specific type of the survival differences that may exist between two groups. These differences can be illustrated by drawing graph of the estimated survivorship function. However, the graph gives only a rough idea of the difference between the distributions; therefore, a statistical test is necessary. There are several distribution-free methods available for testing the equality of two survival curves. These non-parametric methods are divided into score and weighted tests. This study presents these score and weighted tests that can be used for data with and without censored observations. And these tests are applied to the two different survival data sets which one of them satisfies the assumption of proportionality, whereas the other one does not..
References
- D. Collett, 2003, Modelling Survival Data in Medical Research, Chapman and Hall, New York.
- D. R. Cox, D. Oakes, 1984, Analysis of Survival Data, Chapman and Hall, London.
- A. Erdoğan, 1993, Orantılı hazard modeli, Bilim Uzmanlığı Tezi, Hacettepe Üniversitesi Fen Bilimleri Enstitüsü, Ankara.
- T. R. Fleming, D. P. Harrington, M. O’Sullivan, 1987, Supremum versions of the log-rank and generalized Wilcoxon statistics”, Journal of the American Statistical Association, 82(397), 312–320.
- T. R. Fleming, D. P. Harrington, 1991, Counting Processes and Survival Analysis, John Wiley, New York. E. A. Gehan, D. G. Thomas , 1969, The performance of some two-sample tests in small samples with and without censoring. Biometrika, 56, 127-132.
- D. Karasoy, N. Ata, M. T. Sözer, 2005, Yaşam çözümlemesinde zamana bağlı açıklayıcı değişkenli Cox regresyon modeli, Ankara Üniversitesi Tıp Fakültesi Mecmuası, 44, 153-158.
- J. P. Klein, M. L. Moeschberger, 1997, Survival Analysis, Techniques for Censored and Truncated Data, Springer-Verlag, New York.
- D. G. Kleinbaum, 1996, Survival Analysis, Springer-Verlag, New York.
- J. F. Lawless, Statistical Models and Methods for Life Time Data, John Wiley, New York (1982).
- E. T. Lee, M. M. Desu, E. A. Gehan, 1975, A Monte-Carlo study of the power of some two-sample tests, Biometrika, 62, 425-432.
- J. W. Lee, 1996, Some versatile tests based on the simultaneous use of weighted log-rank statistics, Biometrics, 52, 721-725.
- E. T. Lee, J. W. Wang, 2003, Statistical Methods for Survival Data Analysis, John Wiley and Sons, New Jersey.
- E. Leton, P. Zuluaga, 2001, Equivalence between score and weighted tests for survival curves, Commun. Statist.–Theory Meth., 30(4), 591-608.
- N. Mantel, 1966, Evaluation of survival data and two new rank order statistics arising in its consideration, Cancer Chemotherapy Reports, 50 (3), 163–70.
- T. Moreau, J. Maccario, J. Lellouch, C. Huber, 1992, Weighted log-rank statistics for comparing two distributions, Biometrika, 79(1), 195–198.
- R. Peto, J. Peto, 1972, Asymptotically efficient rank invariant test procedures, J R Stat Soc Ser A, 135(2), 185-20
- R. L. Prentice, 1978, Linear rank tests with right-censored data, Biometrika, 65, 167–179.
- R. L. Prentice, P. Marek, 1979, A Quantitative discrepancy between censored data rank tests, Biometrics, 35, 861-867.
- D. Schonfeld, 1981, The asymptotic properties of nonparametric tests for comparing survival distribution, Biometrika, 68, 316-319.
- R. E. Tarone, J. Ware, 1977, On distribution-free tests for equality of survival distributions, Biometrika, 64(1), 156–160.
- Y. Terzi, M. A. Cengiz, 2006, Sağdan sansürlü iki sağkalım dağılımının karşılaştırılmasında kullanılan parametrik olmayan yöntemlerin gerçek verilere uygulaması, 15. İstatistik Araştırma Sempozyumu, Ankara, 531-541.
Abstract
İki grup arasında var olan yaşamsal farklılıkların araştırmacılar tarafından tam olarak belirlenemediği ya da açıklanamadığı durumlar vardır. Bu farklılıklar tahmin edilen yaşam fonksiyonunun grafiği çizilerek ortaya konabilir. Fakat bu grafikler, dağılımlar arasındaki farka dair kabaca bir fikir verdiğinden istatistiksel bir testin kullanılması gerekir. İki yaşam eğrisinin eşitliğini test etmek için uygun olan çeşitli parametrik olmayan testler vardır. Bu testler, skor ve ağırlıklı testler olarak ikiye ayrılmıştır. Bu çalışmada, durdurulmuş gözlem içeren ve içermeyen veriler için kullanılan bu testler ele alınmış ve orantılı tehlikeler varsayımını sağlayan ve sağlamayan iki farklı yaşam verilerine uygulanmıştır.
References
- D. Collett, 2003, Modelling Survival Data in Medical Research, Chapman and Hall, New York.
- D. R. Cox, D. Oakes, 1984, Analysis of Survival Data, Chapman and Hall, London.
- A. Erdoğan, 1993, Orantılı hazard modeli, Bilim Uzmanlığı Tezi, Hacettepe Üniversitesi Fen Bilimleri Enstitüsü, Ankara.
- T. R. Fleming, D. P. Harrington, M. O’Sullivan, 1987, Supremum versions of the log-rank and generalized Wilcoxon statistics”, Journal of the American Statistical Association, 82(397), 312–320.
- T. R. Fleming, D. P. Harrington, 1991, Counting Processes and Survival Analysis, John Wiley, New York. E. A. Gehan, D. G. Thomas , 1969, The performance of some two-sample tests in small samples with and without censoring. Biometrika, 56, 127-132.
- D. Karasoy, N. Ata, M. T. Sözer, 2005, Yaşam çözümlemesinde zamana bağlı açıklayıcı değişkenli Cox regresyon modeli, Ankara Üniversitesi Tıp Fakültesi Mecmuası, 44, 153-158.
- J. P. Klein, M. L. Moeschberger, 1997, Survival Analysis, Techniques for Censored and Truncated Data, Springer-Verlag, New York.
- D. G. Kleinbaum, 1996, Survival Analysis, Springer-Verlag, New York.
- J. F. Lawless, Statistical Models and Methods for Life Time Data, John Wiley, New York (1982).
- E. T. Lee, M. M. Desu, E. A. Gehan, 1975, A Monte-Carlo study of the power of some two-sample tests, Biometrika, 62, 425-432.
- J. W. Lee, 1996, Some versatile tests based on the simultaneous use of weighted log-rank statistics, Biometrics, 52, 721-725.
- E. T. Lee, J. W. Wang, 2003, Statistical Methods for Survival Data Analysis, John Wiley and Sons, New Jersey.
- E. Leton, P. Zuluaga, 2001, Equivalence between score and weighted tests for survival curves, Commun. Statist.–Theory Meth., 30(4), 591-608.
- N. Mantel, 1966, Evaluation of survival data and two new rank order statistics arising in its consideration, Cancer Chemotherapy Reports, 50 (3), 163–70.
- T. Moreau, J. Maccario, J. Lellouch, C. Huber, 1992, Weighted log-rank statistics for comparing two distributions, Biometrika, 79(1), 195–198.
- R. Peto, J. Peto, 1972, Asymptotically efficient rank invariant test procedures, J R Stat Soc Ser A, 135(2), 185-20
- R. L. Prentice, 1978, Linear rank tests with right-censored data, Biometrika, 65, 167–179.
- R. L. Prentice, P. Marek, 1979, A Quantitative discrepancy between censored data rank tests, Biometrics, 35, 861-867.
- D. Schonfeld, 1981, The asymptotic properties of nonparametric tests for comparing survival distribution, Biometrika, 68, 316-319.
- R. E. Tarone, J. Ware, 1977, On distribution-free tests for equality of survival distributions, Biometrika, 64(1), 156–160.
- Y. Terzi, M. A. Cengiz, 2006, Sağdan sansürlü iki sağkalım dağılımının karşılaştırılmasında kullanılan parametrik olmayan yöntemlerin gerçek verilere uygulaması, 15. İstatistik Araştırma Sempozyumu, Ankara, 531-541.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | March 1, 2013 |
| Published in Issue | Year 2013 Volume: 6 Issue: 1 |