Ranking subjects based on paired compositional data with application to age-related hearing loss subtyping

Analysis approaches for single compositional data are well established; however, effective analysis strategies for paired compositional data remain to be investigated. The current project was motivated by studies of age-related hearing loss (presbyacusis), where subjects are classified into four audiometric phenotypes that need to be ranked within these phenotypes based on their paired compositional data. We address this challenge by formulating this problem as a classification problem and integrating a penalized multinomial logistic regression model with compositional data analysis approaches. We utilize Elastic Net for a penalty function, while considering average, absolute difference, and perturbation operators for compositional data. We applied the proposed approach to the presbyacusis study of 532 subjects with probabilities that each ear of a subject belongs to each of four presbyacusis subtypes. We further investigated the ranking of presbyacusis subjects using the proposed approach based on previous literature. The data analysis results indicate that the proposed approach is effective for ranking subjects based on paired compositional data.