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Conservative confidence intervals for the intraclass correlation coefficient for clustered binary data.

Guogen Shan1

  • 1Department of Epidemiology and Biostatistics, School of Public Health, University of Nevada Las Vegas, Las Vegas, NV, USA.

Journal of Applied Statistics
|June 27, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces importance sampling to create accurate confidence intervals for intraclass correlation coefficients in clustered binary data. The new method improves coverage and interval width, especially in challenging small sample or boundary scenarios.

Keywords:
Clustered binary dataconfidence intervalimportance samplingintraclass correlation coefficientprofile confidence limit

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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Clinical Research Methods

Background:

  • Traditional asymptotic methods for intraclass correlation coefficient (ICC) confidence intervals in clustered binary studies show limitations.
  • Poor performance in coverage is observed with small to medium sample sizes, or when correlation/response rates approach boundary values.

Purpose of the Study:

  • To propose and evaluate an improved method for constructing confidence intervals for the ICC in clustered binary data.
  • To enhance the accuracy and reliability of ICC estimation, particularly under conditions where asymptotic methods falter.

Main Methods:

  • Utilized importance sampling, a variance-reducing simulation technique, to develop profile confidence limits for the ICC.
  • Incorporated four existing asymptotic limits for sample space ordering within the importance sampling framework.
  • Conducted simulation studies to assess the performance (coverage and interval width) of the proposed intervals.

Main Results:

  • The proposed accurate intervals demonstrated improved performance in coverage and width compared to traditional asymptotic intervals.
  • Intervals based on Fleiss and Cuzick asymptotic limits generally offered narrower widths.
  • Intervals derived from Zou and Donner asymptotic limits showed superior performance when correlation and response rates were near their boundaries.

Conclusions:

  • The importance sampling method provides a robust approach for constructing accurate confidence intervals for ICC in clustered binary studies.
  • The proposed method offers a valuable alternative to asymptotic approaches, especially in scenarios with limited sample size or extreme parameter values.
  • Specific choices of asymptotic limits within the importance sampling framework can be tailored for optimal performance based on study characteristics.