Performance of a mixed effects logistic regression model for binary outcomes with unequal cluster size

Area of Science:

• Biostatistics
• Clinical Trial Design
• Epidemiology

Background:

• Clustered randomized controlled trials (cRCTs) are frequently used in research.
• Unequal cluster sizes can pose challenges in statistical analysis.
• The assumption of independent observations within clusters is violated in cRCTs.

Purpose of the Study:

• To compare the performance of maximum likelihood estimation in mixed-effects logistic regression models with equal versus unequal cluster sizes.
• To evaluate the impact of cluster size inequality on statistical performance metrics.

Main Methods:

• Utilized computer simulations to assess model performance.
• Varied key parameters including treatment effect, number of clusters, and intracluster correlation coefficients.
• Evaluated performance based on type I error rate, power, bias, and standard error.

Main Results:

• Mixed-effects logistic regression models demonstrated similar performance irrespective of cluster size equality.
• Type I error rate, power, bias, and standard error remained consistent across simulated scenarios with varying cluster sizes.
• The findings were illustrated using data from the Prevention Of Suicide in Primary care Elderly: Collaborative Trial (PROSPECT) study.

Conclusions:

• Mixed-effects logistic regression models are robust to unequal cluster sizes in clustered randomized trials with binary outcomes.
• Statistical analysis using these models can accommodate variations in sample size per cluster without significant performance degradation.
• This provides valuable guidance for the design and analysis of future cRCTs.