A power approximation for the Kenward and Roger Wald test in the linear mixed model

Area of Science:

• Statistics
• Biostatistics
• Clinical Trial Design

Background:

• The Kenward and Roger test is widely used for analyzing data from complex study designs.
• Accurate power calculations are crucial for designing efficient clinical trials.
• Existing methods may lack precision, especially in scenarios with small sample sizes or missing data.

Purpose of the Study:

• To derive a novel noncentral chi-squared power approximation for the Kenward and Roger test.
• To evaluate the accuracy of this new approximation using Monte Carlo simulations.
• To demonstrate the method's utility in practical applications like group-randomized trials.

Main Methods:

• A method of moments approach was employed to approximate the distribution of the Kenward and Roger scaled Wald statistic under the alternative hypothesis.
• The approximation relies on the moments of the unscaled Wald statistic.
• Monte Carlo simulations were conducted to assess the performance of the proposed power approximation.

Main Results:

• The derived noncentral chi-squared power approximation demonstrated high accuracy for cluster randomized trials and longitudinal study designs.
• The method maintained its accuracy even with small sample sizes and the presence of missing data.
• The approach was successfully illustrated with a power calculation for an unbalanced group-randomized trial in oral cancer prevention.

Conclusions:

• The new power approximation offers a reliable tool for sample size and power calculations in complex longitudinal and clustered studies.
• This method enhances the precision of power calculations, particularly in challenging data scenarios.
• The validated approach supports robust study design in biostatistical applications.