A Test Procedure for Right Censored Data under the Additive Model

  • Published : 2009.03.30


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.


  1. Aalen, O. O. (1980). A model for non-parametric regression analysis of counting processes, Springer Lecture Notes Statistics, 2, 1-25
  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, The Annals of Statistics, 10, 1100-1120
  4. Billingsley, P. (1986). Probability and Measure, 2nd Edition, John Wiley & Sons, New York
  5. Cox, D. R. (1972). Regression models and life-tables, Journal of the Royal Statistical Society, Series B, 34, 189-220
  6. Efron, B. (1981). Censored data and the bootstrap, Journal of the American Statistical Association, 76, 312-319
  7. Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap, Chapman & Hall/CRC, 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. Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis, John Wiley & Sons, New York
  10. Good, P. (2000). Permutation Tests-A Practical Guide to Resampling Methods for Testing Hypothesis, 2nd Edition, Springer, New York
  11. Heitjan, D. F. (1989). Inference from grouped continuous data, Statistical Sciences, 4, 164-183
  12. Huffer, F. W. and McKeague, I. W. (1991). Weighted least squares estimation for Aalen’s additive risk model, Journal of the American Statistical Association, 86, 114-129
  13. Jones, M. P. and Crowley, J. (1990). Asymptotic properties of a general class of nonparametric tests for survival analysis, The Annals of Statistics, 18, 1203-1220
  14. Kalbfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analysis of Failure Time Data, John Wiley & Sons, New York
  15. Lin, D. Y. and Ying, Z. (1994). Semiparametric analysis of the additive risk model, Biometrika, 81, 61-71
  16. McKeague, I. W. (1988). A counting process approach to the regression analysis of grouped survival data, Stochastic Processes and their Applications, 28, 221-239
  17. McKeague, I. W. and Sasieni, P. D. (1994). A partly parametric additive risk model, Biometrika, 81, 501-514
  18. Neuhaus, G. (1993). Conditional rank tests for the two-sample problem under random censorship, The 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 survival data with appli-cation 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 the median survival time, Biometrika, 68, 601-608
  23. Scheike, T. H. (2002). The additive nonparametric and semiparametric Aalen model as the rate func-tion 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 the 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

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