Homogeneity test for correlated binary data.

Area of Science:

• Ophthalmology
• Biostatistics
• Statistical Inference

Background:

• Ophthalmologic studies often involve paired eye measurements, which exhibit high correlation.
• Ignoring this correlation can lead to inaccurate statistical inferences.
• Existing methods, like Tang et al.'s (2008) asymptotic method, primarily focus on two-group comparisons.

Purpose of the Study:

• To investigate and compare three statistical testing procedures for the equality of proportions across general g (≥ 2) groups in the presence of correlated data.
• To evaluate the performance of these procedures, particularly the score testing procedure, in terms of type I error control and statistical power.

Main Methods:

• The study extends existing work on testing equality of proportions to handle multiple groups (g ≥ 2).
• It involves simulation studies to assess the performance of the proposed testing procedures.
• The methods are illustrated using real-world examples from ophthalmologic studies.

Main Results:

• Simulation results indicate that the score testing procedure offers satisfactory control of type I errors.
• The score testing procedure demonstrates reasonable statistical power.
• The performance of the three investigated test procedures converges as the sample size increases.

Conclusions:

• The score testing procedure is a reliable method for comparing proportions across multiple groups in ophthalmologic studies with correlated data.
• The proposed methods provide a robust framework for analyzing such data, improving the accuracy of statistical inferences.
• Larger sample sizes enhance the consistency of the tested procedures.