Partial covariate adjusted regression

Damla Şentürk, Danh V. Nguyen

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Covariate adjusted regression (CAR) is a recently proposed adjustment method for regression analysis where both the response and predictors are not directly observed [Şentürk, D., Müller, H.G., 2005. Covariate adjusted regression. Biometrika 92, 75-89]. The available data have been distorted by unknown functions of an observable confounding covariate. CAR provides consistent estimators for the coefficients of the regression between the variables of interest, adjusted for the confounder. We develop a broader class of partial covariate adjusted regression (PCAR) models to accommodate both distorted and undistorted (adjusted/unadjusted) predictors. The PCAR model allows for unadjusted predictors, such as age, gender and demographic variables, which are common in the analysis of biomedical and epidemiological data. The available estimation and inference procedures for CAR are shown to be invalid for the proposed PCAR model. We propose new estimators and develop new inference tools for the more general PCAR setting. In particular, we establish the asymptotic normality of the proposed estimators and propose consistent estimators of their asymptotic variances. Finite sample properties of the proposed estimators are investigated using simulation studies and the method is also illustrated with a Pima Indians diabetes data set.

Original languageEnglish (US)
Pages (from-to)454-468
Number of pages15
JournalJournal of Statistical Planning and Inference
Issue number2
StatePublished - Feb 1 2009


  • Asymptotic normality
  • Binning
  • Confidence intervals
  • Multiple regression
  • Varying-coefficient models

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability


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