Obstructive sleep apnea (OSA), a form of sleep-disordered breathing characterized by recurrent episodes of partial or complete airway obstruction during sleep, is a serious health problem, affecting an estimated 1-5% of elementary school-aged children [9, 2]. Even mild forms of untreated pediatric OSA may cause high blood pressure, behavioral challenges, or impeded growth. Compared to adults, the symptoms of childhood-onset OSA are more varied and change continuously with development, making diagnosis a difficult challenge. The complexity of the data from surveys, biomedical measurements, 3D facial photos, and time-series data calls for state of the art techniques from mathematics and data science. Clinical data, including that considered in confirming or ruling out a diagnosis of pediatric OSA, consist of high-dimensional multi-mode data with mixtures of variables of disparate types (e.g., nominal and categorical data of different scales, interval data, time-to-event and longitudinal outcomes) also called mixed or noncommensurate data.