New Quadratic Discriminant Analysis Algorithms for Correlated Audiometric Data

Paired organs like eyes, ears, and lungs in humans exhibit similarities, and data from these organs often display remarkable correlations. Accounting for these correlations could enhance classification models used in predicting disease phenotypes. To our knowledge, there is limited, if any, literature addressing this topic, and existing methods do not exploit such correlations. For example, the conventional approach treats each ear as an independent observation when predicting audiometric phenotypes and is agnostic about the correlation of data from the two ears of the same person. This approach may lead to information loss and reduce the model performance. In response to this gap, particularly in the context of audiometric phenotype prediction, this paper proposes new quadratic discriminant analysis (QDA) algorithms that appropriately deal with the dependence between ears. We propose two-stage analysis strategies: (1) conducting data transformations to reduce data dimensionality before applying QDA; and (2) developing new QDA algorithms to partially utilize the dependence between phenotypes of two ears. We conducted simulation studies to compare different transformation methods and to assess the performance of different QDA algorithms. The empirical results suggested that the transformation may only be beneficial when the sample size is relatively small. Moreover, our proposed new QDA algorithms performed better than the conventional approach in both person-level and ear-level accuracy. As an illustration, we applied them to audiometric data from the Medical University of South Carolina Longitudinal Cohort Study of Age-related Hearing Loss. In addition, we developed an R package, PairQDA, to implement the proposed algorithms.