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Biometrika Advance Access originally published online on June 26, 2009
Biometrika 2009 96(3):545-558; doi:10.1093/biomet/asp024
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© 2009 Biometrika Trust

Article

Empirical Bayes estimation for additive hazards regression models

Debajyoti Sinha

Department of Statistics, Florida State University, Tallahassee, Florida 32306, U.S.A. sinhad{at}stat.fsu.edu

M. Brent McHenry

Bristol-Myers Squibb, 5 Research Parkway, Wallingford, Connecticut 06492, U.S.A. brent.mchenry{at}bms.com

Stuart R. Lipsitz

Harvard Medical School, Boston, Massachussets 02115, U.S.A. slipsitz{at}partners.org

Malay Ghosh

Department of Statistics, University of Florida, Gainesville, Florida 32611, U.S.A. ghoshm{at}stat.ufl.edu

Received for publication 1 January 2006. Revision received 1 November 2008.
  Abstract

We develop a novel empirical Bayesian framework for the semiparametric additive hazards regression model. The integrated likelihood, obtained by integration over the unknown prior of the nonparametric baseline cumulative hazard, can be maximized using standard statistical software. Unlike the corresponding full Bayes method, our empirical Bayes estimators of regression parameters, survival curves and their corresponding standard errors have easily computed closed-form expressions and require no elicitation of hyperparameters of the prior. The method guarantees a monotone estimator of the survival function and accommodates time-varying regression coefficients and covariates. To facilitate frequentist-type inference based on large-sample approximation, we present the asymptotic properties of the semiparametric empirical Bayes estimates. We illustrate the implementation and advantages of our methodology with a reanalysis of a survival dataset and a simulation study.

Key Words: Gamma process • Integrated likelihood • Posterior process


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