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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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A simple and effective method for simulating nested exchangeable correlated binary data for longitudinal cluster

Rhys A Bowden1, Jessica Kasza2, Andrew B Forbes2

  • 1School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia. rhys.bowden@monash.edu.

BMC Medical Research Methodology
|August 8, 2024
PubMed
Summary
This summary is machine-generated.

A new simulation method efficiently generates correlated binary data for complex longitudinal cluster randomized trials. This tool enables better testing of statistical methods for trial designs like cluster crossover and stepped wedge.

Keywords:
Block exchangeable correlation structureCorrelated binary random variablesHierarchical modelsLongitudinal cluster randomised trialsMulti-level modelsNested exchangeable correlation structureSimulation

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Area of Science:

  • Biostatistics
  • Clinical Trials Methodology
  • Statistical Simulation

Background:

  • Simulation is crucial for evaluating statistical methods and study designs.
  • Existing methods for simulating correlated binary variables have limitations for longitudinal cluster randomized trial designs.
  • Challenges include computational infeasibility and restricted correlation structures with increasing observations per cluster.

Purpose of the Study:

  • To present a novel, simple method for simulating binary random variables.
  • To accommodate specified prevalences, correlation matrices, and changing outcomes over time or due to treatment.
  • To support 'nested exchangeable' correlation structures relevant to hierarchical data and longitudinal cluster randomized trials.

Main Methods:

  • Developed a simulation method for binary variables with user-defined prevalences and correlation matrices.
  • Incorporated ability to model changing outcome prevalence and nested exchangeable correlation structures.
  • Demonstrated method via simulation of 1000 datasets for a cluster randomized crossover trial.

Main Results:

  • The proposed method is significantly faster (orders of magnitude) than existing general simulation techniques.
  • It supports a broader range of correlations compared to alternative approaches.
  • An R package, NestBin, is available for implementing the method.

Conclusions:

  • This is the first simulation method enabling practical and efficient generation of large binary datasets with nested exchangeable correlation structures.
  • It is particularly suited for longitudinal cluster randomized trials.
  • Facilitates more robust testing of designs and inference methods for such trials.