Parametric variable selection in generalized partially linear models with an application to assess condom use by HIV-infected patients

Authors

  • Chenlei Leng,

    Corresponding author
    1. Department of Statistics and Applied Probability, National University of Singapore, Singapore
    • Department of Statistics and Applied Probability, National University of Singapore, Singapore
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  • Hua Liang,

    1. Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, NY 14642, U.S.A.
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  • Neil Martinson

    1. Perinatal HIV Research Unit, University of the Witwatersrand, Johannesburg, South Africa
    2. Johns Hopkins University, School of Medicine, Baltimore, MD 21231, U.S.A.
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Abstract

To study significant predictors of condom use in HIV-infected adults, we propose the use of generalized partially linear models and develop a variable selection procedure incorporating a least squares approximation. Local polynomial regression and spline smoothing techniques are used to estimate the baseline nonparametric function. The asymptotic normality of the resulting estimate is established. We further demonstrate that, with the proper choice of the penalty functions and the regularization parameter, the resulting estimate performs as well as an oracle procedure. Finite sample performance of the proposed inference procedure is assessed by Monte Carlo simulation studies. An application to assess condom use by HIV-infected patients gains some interesting results, which cannot be obtained when an ordinary logistic model is used. Copyright © 2011 John Wiley & Sons, Ltd.

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