COVID-19 has a spectrum of disease severity, ranging from asymptomatic to requiring hospitalization. Understanding the mechanisms driving disease severity is crucial for developing effective treatments and reducing mortality rates. One way to gain such understanding is using a multi-class classification framework, in which patients' biological features are used to predict patients' severity classes. In this severity classification problem, it is beneficial to prioritize the identification of more severe classes and control the "under-classification" errors, in which patients are misclassified into less severe categories. The Neyman-Pearson (NP) classification paradigm has been developed to prioritize the designated type of error. However, current NP procedures are either for binary classification or do not provide high probability controls on the prioritized errors in multi-class classification. Here, we propose a hierarchical NP (H-NP) framework and an umbrella algorithm that generally adapts to popular classification methods and controls the under-classification errors with high probability. On an integrated collection of single-cell RNA-seq (scRNA-seq) datasets for 864 patients, we explore ways of featurization and demonstrate the efficacy of the H-NP algorithm in controlling the under-classification errors regardless of featurization. Beyond COVID-19 severity classification, the H-NP algorithm generally applies to multi-class classification problems, where classes have a priority order.

A common issue for classification in scientific research and industry is the existence of imbalanced classes. When sample sizes of different classes are imbalanced in training data, naively implementing a classification method often leads to unsatisfactory prediction results on test data. Multiple resampling techniques have been proposed to address the class imbalance issues. Yet, there is no general guidance on when to use each technique. In this article, we provide an objective-oriented review of the common resampling techniques for binary classification under imbalanced class sizes. The learning objectives we consider include the classical paradigm that minimizes the overall classification error, the cost-sensitive learning paradigm that minimizes a cost-adjusted weighted type I and type II errors, and the Neyman-Pearson paradigm that minimizes the type II error subject to a type I error constraint. Under each paradigm, we investigate the combination of the resampling techniques and a few state-of-the-art classification methods. For each pair of resampling techniques and classification methods, we use simulation studies to study the performance under different evaluation metrics. From these extensive simulation experiments, we demonstrate under each classification paradigm, the complex dynamics among resampling techniques, base classification methods, evaluation metrics, and imbalance ratios. For practitioners, the take-away message is that with imbalanced data, one usually should consider all the combinations of resampling techniques and the base classification methods.