On analyzing ordinal data when responses and covariates are both missing at random

Area of Science:

• Biostatistics
• Statistical Modeling
• Biomedical Data Analysis

Background:

• Missing data in biomedical studies, whether responses or covariates, can lead to biased inference.
• Existing methods often address missing responses or covariates separately, neglecting their interdependence.
• Handling simultaneously missing ordinal responses and covariates presents significant modeling and computational challenges.

Purpose of the Study:

• To develop and evaluate a joint statistical model for analyzing data with simultaneously missing ordinal responses and covariates.
• To investigate the impact of the association between missing data processes on inference.
• To provide robust analytical methods for complex biomedical datasets with substantial missingness.

Main Methods:

• Development of a joint model incorporating associations between ordinal response variables, covariates, and missing data indicators.
• Application of Markov chain Monte Carlo (MCMC) and Monte Carlo relative likelihood approaches for model analysis.
• Evaluation of parameter estimation performance in finite samples using simulation studies.

Main Results:

• The proposed joint model effectively handles simultaneously missing ordinal responses and covariates.
• Both MCMC and Monte Carlo relative likelihood methods demonstrate reliable parameter estimation.
• The analysis of an orthodontic study dataset yields significant insights into human habits.

Conclusions:

• Joint modeling provides a powerful framework for addressing complex missing data scenarios in biomedical research.
• The developed methods offer improved analytical solutions for studies with missing ordinal outcomes and covariates.
• This approach enhances the accuracy of statistical inference in the presence of substantial missing data.