Advertisement

A non-parametric test for composite hypotheses in survival analysis

  • H. Dennis Tolley
Article

Summary

For survival data with several concomitant (regressor) variables a large sample non-parametric procedure is presented which provides significance tests of hypotheses about a subset of the concomitant variables. This non-iterative procedure resembles linear model methodology in simplicity and form. The method is useful to eliminate unimportant concomitant variables prior to estimation of model parameters.

Keywords

Failure Time Noncentrality Parameter Concomitant Variable Composite Hypothesis Linear Rank 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bhapkar, V. P. (1961). A nonparametric test for the problem of several samples,Ann. Math. Statist.,32, 1108–1117.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Chernoff, H. and Savage, I. R. (1958). Asymptotic normality and efficiency of certain non-parametric test statistics,Ann. Math. Statist.,29, 972–994.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Cox, D. R. (1972). Regression models in life tables (with discussion),J. R. Statist. Soc., B,34, 187–220.zbMATHGoogle Scholar
  4. [4]
    Cox, D. R. (1975). Partial likelihood,Biometrika,62, 269–276.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Crowley, J. (1974). A note on some recent likelihoods leading to the log rank test,Biometrika,61, 533–538.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Downton, F. (1972). Discussion of Cox's regression models in life tables,J. R. Statist. Soc., B,34, 202–205.Google Scholar
  7. [7]
    Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance,J. Amer. Statist. Ass.,32, 675–701.CrossRefGoogle Scholar
  8. [8]
    Hájek, J. (1968). Asymptotic normality of simple linear rank statistics under alternatives,Ann. Math. Statist.,39, 325–346.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Hájek, J. and Sidák, Z. (1967).Theory of Rank Tests, Academic Press, New York.zbMATHGoogle Scholar
  10. [10]
    Hoeffding, W. (1973). On the centering of a simple linear rank statistic,Ann. Statist.,1, 54–66.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Kalbfleisch, J. D. and Prentice, R. L. (1973). Marginal likelihoods based on Cox's regression and life model,Biometrika,60, 267–278.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Kruskal, W. H. (1952). A nonparametric test for the several sample problems,Ann. Math. Statist.,23, 525–540.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Ogawa, J. (1974).Statistical Theory of the Analysis of Experimental Designs, Marcel Dekker, Inc., New York.zbMATHGoogle Scholar
  14. [14]
    Puri, M. L. and Sen, P. K. (1973). A note on asymptotic distribution-free tests for subhypotheses in multiple linear regression,Ann. Statist.,1, 553–556.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Puri, M. L. and Sen, P. K. (1969). A class of rank order tests for a general linear hypothesis,Ann. Math. Statist.,40, 1325–1343.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1978

Authors and Affiliations

  • H. Dennis Tolley
    • 1
  1. 1.Radiation Effects Research FoundationHiroshimaJapan

Personalised recommendations