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Statistical Methods for Generalized Linear Models with Covariates Subject to Detection Limits

Statistics in Biosciences volume 7, pages 68–89 (2015)Cite this article

Abstract

Censored observations are a common occurrence in biomedical data sets. Although a large amount of research has been devoted to estimation and inference for data with censored responses, very little research has focused on proper statistical procedures when predictors are censored. In this paper, we consider statistical methods for dealing with multiple predictors subject to detection limits within the context of generalized linear models. We investigate and adapt several conventional methods and develop a new multiple imputation approach for analyzing data sets with predictors censored due to detection limits. We establish the consistency and asymptotic normality of the proposed multiple imputation estimator and suggest a computationally simple and consistent variance estimator. We also demonstrate that the conditional mean imputation method often leads to inconsistent estimates in generalized linear models, while several other methods are either computationally intensive or lead to parameter estimates that are biased or more variable compared to the proposed multiple imputation estimator. In an extensive simulation study, we assess the bias and variability of different approaches within the context of a logistic regression model and compare variance estimation methods for the proposed multiple imputation estimator. Lastly, we apply several methods to analyze the data set from a recently-conducted GenIMS study.

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Acknowledgements

Wang’s research was supported in part by NSF award DMS-1007420 and NSF CAREER award DMS-1149355 and Zhang’s research was supported in part by the HIH grant R01 CA85848-12 and the NIH/NIAID grant R37 AI031789-20.

The authors are grateful to the editor, an associate editor, and two anonymous referees for their valuable comments. The authors also would like to thank Dr. Lan Kong of Penn State College of Medicine and the CRISMA (Clinical Research, Investigation, and Systems Modeling of Acute Illness) Center at the University of Pittsburgh for providing the GenIMS data set.

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Affiliations

  1. Department of Mathematics and Statistics, Villanova University, Villanova, USA

    Paul W. Bernhardt

  2. Department of Statistics, North Carolina State University, Raleigh, USA

    Huixia J. Wang & Daowen Zhang

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  1. Paul W. Bernhardt
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  2. Huixia J. Wang
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  3. Daowen Zhang
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Correspondence to Huixia J. Wang.

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Bernhardt, P.W., Wang, H.J. & Zhang, D. Statistical Methods for Generalized Linear Models with Covariates Subject to Detection Limits. Stat Biosci 7, 68–89 (2015). https://doi.org/10.1007/s12561-013-9099-4

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  • DOI: https://doi.org/10.1007/s12561-013-9099-4

Keywords

  • Censored predictor
  • Complete case
  • Conditional mean imputation
  • Detection limit
  • Improper multiple imputation