Confidence intervals for intraclass correlation coefficients in a nonlinear dose-response meta-analysis

Area of Science:

• Pharmacology
• Biostatistics
• Psychiatry

Background:

• Meta-analyses of antipsychotic medications often involve complex dose-response relationships.
• Quantifying study heterogeneity using intraclass correlation coefficients (ICCs) is essential for accurate interpretation.
• Nonlinear mixed effects models are frequently used to analyze such data.

Purpose of the Study:

• To adapt and evaluate a generic beta-approach for constructing confidence intervals (CIs) for ICCs in nonlinear mixed effects models.
• To compare the performance of the beta-approach with traditional methods like the delta method and bootstrapping.
• To provide a reliable method for estimating ICC CIs in small-study settings.

Main Methods:

• Application of a beta-approach for ICC CI construction to nonlinear mixed effects models.
• Utilized four estimation methods: maximum likelihood, second-order generalized estimating equations, and two two-step procedures.
• Compared beta-approach CIs against delta method and nonparametric percentile bootstrap methods.

Main Results:

• The delta method and percentile bootstrap CI methods demonstrated poor performance and failed in the analyzed settings.
• The beta-approach yielded good coverage properties when combined with the two-step estimation procedures.
• The beta-approach proved effective for computing ICC CIs in nonlinear mixed effects models, particularly for smaller studies.

Conclusions:

• The beta-approach is recommended for calculating confidence intervals for intraclass correlation coefficients in nonlinear mixed effects models.
• This method shows superior performance compared to the delta method and bootstrapping, especially in small sample sizes.
• Accurate ICC confidence intervals are vital for interpreting heterogeneity in meta-analyses, such as those involving antipsychotic drug efficacy.