Test of Association Between Two Ordinal Variables While Adjusting for Covariates

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Analyzing associations between ordinal variables requires accounting for covariates.
• Existing methods may not adequately handle complex relationships or treat variables symmetrically.

Purpose of the Study:

• To develop and evaluate new test statistics for examining conditional independence between two ordinal categorical variables (X and Y) while adjusting for covariates (Z).
• To provide methods that treat X and Y symmetrically, without pre-specifying one as an outcome or predictor.

Main Methods:

• Fitting separate multinomial models (e.g., proportional odds) for X and Y on Z.
• Computing conditional distributions of X and Y given Z for each subject.
• Developing two test statistics: one comparing observed and expected joint distributions, and another based on residuals from the multinomial models.
• Proposing methods for calculating p-values using empirical or asymptotic distributions.

Main Results:

• Simulations show the new test statistics perform well in terms of statistical power and Type I error rates.
• The proposed methods outperform traditional proportional odds models when X is treated as continuous or categorical.
• The methods were successfully applied to real-world data from studies on visual impairment and cervical abnormalities in HIV-infected women.

Conclusions:

• The developed test statistics provide a robust and flexible approach for analyzing associations between ordinal variables adjusted for covariates.
• These methods offer advantages over existing techniques, particularly in their symmetric treatment of variables and improved performance.
• The findings have implications for statistical analysis in various fields, including public health and medicine.