A Nonparametric Test For The Grouped And Right Censored Data

Abstract

In this research, we propose a nonparametric test procedure for the right censored and grouped data under the additive hazards model. For deriving the test statistics, we use the likelihood principle. Then we illustrate proposed test with an example and compare the performance with other procedure by obtaining empirical powers. Finally we discuss some interesting features concerning the proposed test. 

Keywords

• Additive hazards model,Grouped data,Log-rank test,Score function

References

1. Aalen, O. O. (1980). A model for non-parametric regression analysis of counting processes. Springer Lecture Notes Statistics 2, 1-25. Mathematical Statistics and Probability Theory, W. Klonecki, A. Kozek and J. Rosinski, editors.
2. Aalen, O. O. (1989). A linear regression model for the analysis of life times. Statistics in Medicine 8, 907-925.
3. Andersen, P. K. and Gill, R. D. (1982). Cox’s regression model for counting processes: A large sample study. Annals of Statistics 10, 1100-1120.
4. Billingsley, P. (1986). Probability and Measure, Second Edition. Wiley and Sons, Inc. New York.
5. Cox, D. R. (1972). Regression models and life-tables. Journal of Royal Statistical Society B 34, 189-220.
6. Efron, B. (1981). Censored data and the bootstrap. Journal of American Statistical Association 76, 312-319.
7. Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
8. Embury, S. H., Elias, L., Heller, P. H., Hood, C. E., Greenberg, P. L. and Schrier, S. L. (1977). Remission maintenance therapy in acute myelogenous leukemia. Western Journal of Medicine 126, 267-272.

9. Flemming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. Wiley and Sons, Inc. New York.
10. Gill, R. D. (1980). Censoring and Stochastic Integrals. Mathematical Centre Tracts, Mathematisch Centrum, Amsterdam.
11. Good, P. (2000). Permutation Tests-A Practical Guide to Resampling Methods for Testing Hypothesis. second Edition. Springer, New York.
12. Heitjan, D. F. (1989). Grouped continuous data. Statistical Sciences 4, 164-183.
13. Huffer, F. W. and McKeague, I. W. (1991). Weighted test squares estimation for Aalen’s additive risk model. Journal of American Statistical Association 86, 114-129.
14. Jones, M. P. and Crowley, J. (1990). Asymptotic properties of a generalized class of nonparametric tests for survival analysis. Annals of Statistics 18, 1203-1220.
15. Kalbfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analysis of Failure Time Data. Wiley and Sons, Inc. New York.
16. Lin and Ying (1994). Semiparametric analysis of the additive risk model. Biometrika 81, 61-71.
17. McKeague, I. W. (1988). A counting process approach to the regression analysis of grouped survival data. Stochastic Process with Applications 28, 221-239.
18. McKeague, I. W. and Sasieni, P. D. (1994). A partly parametric additive risk model. Biometrika 81, 501-514. Neuhaus, G. (1993). Conditional rank tests for the two-sample problem under random censorship. Annals of Statistics 21, 1760-1779.
19. Park, H. I. (1993). Nonparametric rank-order tests for the right censored and grouped data in linear model. Communications in statistics-Theory and Methods 22, 3143-3158.
20. Prentice, R. L. and Gloeckler, L. A. (1978). ”Regression analysis of grouped data with applications to breast cancer data”, Biometrics 34, 57-67.
21. Randles, R. H. and Wolfe, D. A. (1979). Introduction to the Theory of Nonparametric Statistics. Wiley, New York.
22. Reid, N. (1981). Estimating median survival time. Biometrika 68, 601-608.
23. Scheike, T. H. (2002). The additive nonparametric and semiparametric Aalen model as the rate function for a counting process. Lifetime Data Analysis 8, 247-262.
24. Wei, L. J. and Lachin, J. M. (1984). Two-sample asymptotically distribution-free tests for incomplete multivariate observations. Journal of American Statistical Association 79, 653-661.
25. Yin, G. and Cai, J. (2004). Additive hazards model with multivariate failure time data. Biometrika 91, 801-818.