Multivariate non-parametric methods for Mann-Whitney statistics to analyse cross-over studies with two treatment...

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Analysis

Background:

• Cross-over studies are common in clinical research.
• Analyzing ordinal data in these designs presents statistical challenges.
• Existing methods may not fully address complex period and treatment interactions.

Purpose of the Study:

• To develop a robust non-parametric strategy for analyzing ordinal data in two-treatment sequence cross-over studies.
• To provide methods for estimating treatment effects and their associated uncertainty.
• To evaluate the impact of periods and treatments on study outcomes.

Main Methods:

• Utilizes Mann-Whitney rank measures of association for period-specific comparisons.
• Employs U-statistics to estimate the covariance matrix of Mann-Whitney estimates.
• Applies modified weighted least squares with linear or log-linear models to assess period and treatment effects.
• Incorporates methods for controlling strata and adjusting for concomitant variables.

Main Results:

• The proposed strategy effectively analyzes ordinal data in cross-over designs.
• Consistent estimation of the covariance matrix is achieved.
• Linear (or log-linear) models successfully evaluate period and treatment effects.
• The modified weighted least squares method handles potential covariance matrix singularities.

Conclusions:

• The non-parametric approach is suitable for interval or ordered categorical response variables.
• The methods offer flexibility for controlling design factors like strata and covariates.
• The strategy is demonstrated through practical applications in three distinct cross-over studies.