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Logistic Mixed-Effects Model Analysis With Pseudo-Observations for Estimating Risk Ratios in Clustered Binary Data

Hisashi Noma1,2, Masahiko Gosho3

  • 1Department of Interdisciplinary Statistical Mathematics, The Institute of Statistical Mathematics, Tokyo, Japan.

Statistics in Medicine
|September 22, 2025
PubMed
Summary

This study introduces a new statistical method for analyzing clustered binary data, enabling direct estimation of risk ratios in multilevel models. This approach enhances the interpretation of effect measures in complex health studies.

Keywords:
case–cohort designclustered datageneralized linear mixed‐effects modelpseudo‐observationrisk ratio

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Statistical Modeling

Background:

  • Logistic mixed-effects models are standard for clustered binary data but yield odds ratios, which are difficult to interpret as direct effect measures.
  • Odds ratios approximate risk ratios only when event frequencies are low, limiting their utility in many health research scenarios.

Purpose of the Study:

  • To propose a novel statistical method for estimating risk ratios within the multilevel statistical model framework.
  • To provide a consistent and interpretable effect measure for clustered binary outcome data.

Main Methods:

  • Augmenting original datasets with pseudo-observations.
  • Analyzing modified datasets using logistic mixed-effects models.
  • Calculating standard errors and confidence intervals via the bootstrap method using the R package 'glmmrr'.

Main Results:

  • The proposed method yields consistent estimators of risk ratios in multilevel models.
  • The method was illustrated using a cluster-randomized trial and a longitudinal respiratory disease study.
  • Simulation studies confirmed the accuracy and precision of the risk ratio estimation.

Conclusions:

  • The novel method provides a valid and interpretable risk ratio estimator for clustered binary data.
  • This approach enhances the analysis of complex health studies, including longitudinal and cluster-randomized trials.
  • The 'glmmrr' R package offers a practical implementation for researchers.