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Biometrika 2005 92(1):75-89; doi:10.1093/biomet/92.1.75
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© 2004 Biometrika Trust

Covariate-adjusted regression

Damla Sentürk1 and Hans-Georg Müller2

1 Department of Statistics, Pennslyvania State University, University Park, Pennsylvania 16802, U.S.A. dsenturk{at}stat.psu.edu, 2 Department of Statistics, University of California, Davis, California 95616, U.S.A. mueller{at}wald.ucdavis.edu

We introduce covariate-adjusted regression for situations where both predictors and response in a regression model are not directly observable, but are contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate. We demonstrate how the regression coefficients can be estimated by establishing a connection to varying-coefficient regression. The proposed covariate-adjustment method is illustrated with an analysis of the regression of plasma fibrinogen concentration as response on serum transferrin level as predictor for 69 haemodialysis patients. In this example, both response and predictor are thought to be influenced in a multiplicative fashion by body mass index. A bootstrap hypothesis test enables us to test the significance of the regression parameters. We establish consistency and convergence rates of the parameter estimators for this new covariate-adjusted regression model. Simulation studies demonstrate the efficacy of the proposed method.

Key Words: Bootstrap; Diagnostic; Linear regression; Multiplicative effects; Smoothing; Varying-coefficient model

Received May 2003. Revised April 2004.


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D. Senturk and H.-G. Muller
Covariate-adjusted generalized linear models
Biometrika, June 1, 2009; 96(2): 357 - 370.
[Abstract] [PDF]


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