Interpretable inference on the mixed effect model with the Box-Cox transformation.

Area of Science:

• Biostatistics
• Clinical Trial Methodology
• Statistical Modeling

Background:

• Mixed-effects models are crucial for analyzing repeated measures data in clinical trials.
• Existing methods may face challenges with model misspecification and interpretability of treatment effects.
• Accurate statistical inference is vital for drawing reliable conclusions from clinical trial data.

Purpose of the Study:

• To develop a robust inference procedure for comparing model medians between treatment groups in repeated measures analysis.
• To provide interpretable estimates of treatment effects within the framework of mixed-effects models.
• To address challenges related to model misspecification and asymptotic theory in parameter inference.

Main Methods:

• Utilized the Box-Cox transformation within a marginal model for mixed-effects models.
• Derived inference results based on asymptotic theory.
• Developed a robust variance estimator for maximum likelihood estimators, accounting for model misspecification.
• Proposed an inference procedure for the difference in model medians between treatment groups at specific time points.

Main Results:

• The proposed method provides interpretable estimates of treatment effects.
• Simulation studies indicate the method effectively controls Type I error across various scenarios.
• The method exhibits moderate to high statistical power compared to existing approaches.
• Demonstrated practical application using cluster of differentiation 4 (CD4) data from an AIDS clinical trial.

Conclusions:

• The developed inference procedure offers a robust and interpretable approach for analyzing repeated measures in randomized clinical trials.
• The method's performance in simulations suggests its reliability for statistical testing and power.
• The application to CD4 data highlights the practical utility and interpretability of the proposed statistical framework.