Comparison of statistical methods for analysis of clustered binary observations

Area of Science:

• Biostatistics
• Clinical Trial Methodology
• Statistical Analysis

Background:

• Randomized controlled trials (RCTs) often involve correlated observations within clusters (e.g., clinics, physicians).
• The independence assumption is violated in clustered data, necessitating specialized analytical methods.
• Binary outcomes are common in clinical research, requiring appropriate statistical models for analysis.

Purpose of the Study:

• To compare the performance of four statistical methods for analyzing clustered binary observations.
• To evaluate methods including full likelihood, penalized quasi-likelihood, generalized estimating equations, and fixed-effects logistic regression.
• To assess performance based on Type I error rate, power, bias, and standard error under various simulation conditions.

Main Methods:

• Computer simulations were employed to compare four statistical methods: full likelihood, penalized quasi-likelihood, generalized estimating equations, and fixed-effects logistic regression.
• Simulations varied effect sizes, intraclass correlation coefficients, number of clusters, and observations per cluster (up to 100).
• The first three methods explicitly account for within-cluster correlations, while fixed-effects logistic regression does not.

Main Results:

• Full likelihood and penalized quasi-likelihood methods demonstrated superior performance for analyzing clustered binary observations.
• These methods maintained robust performance, even when within-cluster correlations were negligible or zero.
• Generalized estimating equations and fixed-effects logistic regression showed varied performance depending on simulation parameters.

Conclusions:

• Full likelihood and penalized quasi-likelihood methods are recommended for the statistical analysis of clustered binary data in RCTs.
• These methods provide reliable and accurate results, offering advantages over traditional approaches like fixed-effects logistic regression.
• The superiority of these methods holds even in scenarios with minimal or absent within-cluster correlation, enhancing their general applicability.