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Biometrika Advance Access published online on June 4, 2008
Biometrika, doi:10.1093/biomet/asn003
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© 2008 Biometrika Trust

Articles

Improving the efficiency of the log-rank test using auxiliary covariates

Xiaomin Lu

Department of Epidemiology and Biostatistics, College of Public Health and Health Professions, University of Florida Gainesville, Florida 32611, U.S.A
xlu2{at}phhp.ufl.edu

Anastasios A. Tsiatis

Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, U.S.A
tsiatis{at}stat.ncsu.edu

Received for publication 1 June 2006. Revision received 1 February 2007.

Under the assumption of proportional hazards, the log-rank test is optimal for testing the null hypothesis H0: β = 0, where β denotes the logarithm of the hazard ratio. However, if there are additional covariates that correlate with survival times, making use of their information will increase the efficiency of the log-rank test. We apply the theory of semiparametrics to characterize a class of regular and asymptotically linear estimators for β when auxiliary covariates are incorporated into the model, and derive estimators that are more efficient. The Wald tests induced by these estimators are shown to be more powerful than the log-rank test. Simulation studies are used to illustrate the gains in efficiency.

Key Words: Efficient estimator • Influence function • Log-rank test • Nuisance tangent space • Proportional hazard model • Regular and asymptotically linear estimator



References

    Begun J. M., Hall W. J., Huang W. M., Wellner J. A. Information and asymptotic efficiency in parametric-nonparametric models. Ann. Statist. (1983) 11:432–52.[CrossRef]

    Bickel P. J., Klaassen C. A. J., Ritov Y., Wellner J. A. Efficient and Adaptive Estimation for Semiparametric Models (1993) Baltimore: The Johns Hopkins University Press.

    Cox D. R. Regression models and life tables (with Discussion. J. R. Statist. Soc. (1972) B 34:187–220.

    Cox D. R. Partial likelihood. Biometrika (1975) 62:269–75.[Abstract/Free Full Text]

    Fleming T. R., Harrington D. P. Counting Processes and Survival Analysis (1991) New York: John Wiley and Sons.

    Hammer S. M., Katzenstein D. A., Hughes M. D., et al. A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200-500 per cubic millimeter. New Engl. J. Med. (1996) 335:1081–90.[Abstract/Free Full Text]

    Mantel N. Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemo. Rep. (1966) 50:163–70.[Medline]

    Newey W. K. Semiparametric efficiency bounds. J. Appl. Economet. (1990) 5:99–135.[CrossRef]

    Peto R., Peto J. Asymptotically efficient rank invariant procedures. J. R. Statist. Soc. (1972) A 135:185–207.

    Tsiatis A. A. Semiparametric Theory and Missing Data (2006) New York: Springer.


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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
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Right arrow Email this article to a friend
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Right arrow Articles by Lu, X.
Right arrow Articles by Tsiatis, A. A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?