Efficiency comparisons of rank and permutation tests based on summary statistics computed from repeated measures data

Area of Science:

• Biostatistics
• Clinical Trials
• Statistical Methods

Background:

• Repeated measures data analysis in clinical trials often uses scalar summary statistics.
• Rank and permutation tests are common for comparing treatment groups based on these statistics.
• Existing efficiency analyses primarily focus on linear, continuous summary statistics under simple group differences.

Purpose of the Study:

• To investigate the non-null behavior and asymptotic relative efficiencies of various discrete and continuous summary statistics.
• To address limitations in understanding summary statistic performance with complex data distributions and non-linear group differences.
• To examine the impact of left censoring on summary statistic comparison, particularly relevant for markers with detection limits.

Main Methods:

• Utilized recent theoretical advancements in the non-null behavior of rank and permutation tests.
• Employed a flexible linear growth curve model to represent repeated measures responses.
• Assessed asymptotic relative efficiencies of popular discrete and continuous summary statistics across diverse settings.

Main Results:

• Demonstrated complex distributional differences for common summary statistics under various scenarios.
• Quantified the asymptotic relative efficiencies of different summary statistics, revealing performance variations.
• Highlighted the challenges posed by left censoring in comparing summary statistics.

Conclusions:

• The choice of summary statistic significantly impacts the power and reliability of treatment group comparisons in clinical trials.
• Findings provide guidance for selecting appropriate summary statistics, especially in complex settings and with censored data.
• The study offers valuable insights for analyzing data in diseases like HIV/AIDS where repeated measures and detection limits are common.