Biometrika

Biometrika Advance Access originally published online on June 4, 2008
Biometrika 2008 95(3):679-694; 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 , where 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 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 Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by Lu, X. Articles by Tsiatis, A. A. Search for Related Content Social Bookmarking          What's this?