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Simultaneous selection and inference for varying coefficients with zero regions: a soft-thresholding approach.

Yuan Yang1, Ziyang Pan2, Jian Kang2

  • 1Parexel, Waltham, Massachusetts, USA.

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|July 17, 2023
PubMed
Summary

This study introduces a new soft-thresholded varying coefficient model to identify zero-effect regions in dynamic analyses. The model enhances variable selection and provides sparse confidence intervals for accurate statistical inference.

Keywords:
non-parametric regressionopioid usesparse confidence intervalsvarying coefficient with zero regions

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Area of Science:

  • Statistics
  • Epidemiology
  • Biostatistics

Background:

  • Varying coefficient models are crucial for analyzing dynamic effects across various scientific fields.
  • Existing models often overlook the presence and impact of zero-effect regions.

Purpose of the Study:

  • To propose a novel soft-thresholded varying coefficient model capable of handling piecewise smooth coefficient functions with zero regions.
  • To enable variable selection, identification of zero regions, and estimation of coefficients within these regions.

Main Methods:

  • Development of a soft-thresholded varying coefficient model.
  • Incorporation of piecewise smoothness and zero regions into coefficient functions.
  • Construction of sparse confidence intervals accommodating zero regions.

Main Results:

  • The proposed model facilitates variable selection and detection of zero regions.
  • Point estimates for varying coefficients, including those in zero regions, are obtained.
  • New sparse confidence intervals demonstrate desired coverage probability in simulations.

Conclusions:

  • The novel modeling approach effectively addresses limitations of existing methods by incorporating zero regions.
  • The method provides a robust framework for statistical inference in dynamic analyses with sparse effects.
  • The approach is validated through simulations and applied to a real-world preoperative opioid study.