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Penalized estimating equations.

Wenjiang J Fu1

  • 1Department of Epidemiology, Michigan State University, 4660 S. Hagadorn Road, Suite 600, East Lansing, Michigan 48823, USA. fuw@msu.edu

Biometrics
|May 24, 2003
PubMed
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This study introduces a penalized bridge estimator for generalized estimating equations (GEE) in longitudinal studies. Penalized GEE improves estimator performance without requiring a joint likelihood, enhancing regression analysis.

Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Collinearity in regression analysis is a common challenge, often addressed by penalty models like Ridge, Stein, Bridge, and Lasso estimators.
  • The Lasso penalty has been successfully applied across various models, including linear, logistic, Cox proportional hazards, and neural networks.
  • Generalized Estimating Equations (GEE) are widely used for longitudinal data analysis but typically require a joint likelihood, which can be problematic.

Purpose of the Study:

  • To introduce and analyze the bridge penalty model, specifically with the penalty sigma(j)/beta(j)/gamma, for general estimating equations.
  • To apply this penalized bridge model to Generalized Estimating Equations (GEE) in the context of longitudinal studies.
  • To overcome the limitation of GEE requiring a joint likelihood by utilizing penalized estimating equations.

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Main Methods:

  • The study employs the bridge penalty model with the functional form sigma(j)/beta(j)/gamma.
  • This penalty is applied to the estimating equations framework, specifically targeting Generalized Estimating Equations (GEE).
  • Asymptotic results for the resulting penalty estimator are derived and provided.

Main Results:

  • The penalized estimating equations approach effectively bypasses the need for a joint likelihood in GEE.
  • Asymptotic properties of the penalty estimator are established.
  • Simulations and a real-world application demonstrate that penalized GEE can enhance the performance of standard GEE estimators.

Conclusions:

  • The penalized bridge estimator offers a viable solution for collinearity issues within GEE for longitudinal data.
  • This method improves GEE estimator performance and retains desirable properties similar to linear penalty models.
  • Penalized GEE provides a robust alternative when joint likelihoods are difficult or impossible to formulate.