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Generalized Semiparametric Regression with Covariates Measured with Error

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Statistical Modelling and Regression Structures

Abstract

We develop generalized semiparametric regression models for exponential family and hazard regression where multiple covariates are measured with error and the functional form of their effects remains unspecified. The main building blocks in our approach are Bayesian penalized splines and Markov chain Monte Carlo simulation techniques. These enable a modular and numerically efficient implementation of Bayesian measurement error correction based on the imputation of true, unobserved covariate values. We investigate the performance of the proposed correction in simulations and an epidemiological study where the duration time to detection of heart failure is related to kidney function and systolic blood pressure.

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Acknowledgments

The authors thank Thomas Augustin and Ludwig Fahrmeir for valuable discussions at various stages of preparing this paper. The Atherosclerosis Risk in Communities Study is carried out as a collaborative study supported by National Heart, Lung, and Blood Institute contracts N01-HC-55015, N01-HC-55016, N01-HC-55018, N01-HC-55019, N01-HC-55020, N01-HC-55021, and N01-HC-55022. The authors thank the staff and participants of the ARIC study for their important contributions. The support for Ciprian Crainiceanu was provided by contracts N01-HC-55020 and R01-DK-076770-01.

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Authors and Affiliations

  1. Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111, Oldenburg, Germany

    Thomas Kneib

  2. HypoVereinsbank Munich, München, Germany

    Andreas Brezger

  3. Department of Biostatistics, Johns-Hopkins-University Baltimore, Baltimore, USA

    Ciprian M. Crainiceanu

Authors
  1. Thomas Kneib
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  2. Andreas Brezger
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  3. Ciprian M. Crainiceanu
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Correspondence to Thomas Kneib .

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Editors and Affiliations

  1. Fak. V - Mathematik und, Universität Oldenburg, Ammerländer Heerstr. 114-118, Oldenburg, 26129, Germany

    Thomas Kneib

  2. Institut für Statistik, Universität München, Akademiestr. 1, München, 80799, Germany

    Gerhard Tutz

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Kneib, T., Brezger, A., Crainiceanu, C.M. (2010). Generalized Semiparametric Regression with Covariates Measured with Error. In: Kneib, T., Tutz, G. (eds) Statistical Modelling and Regression Structures. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2413-1_8

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