## 1 Introduction  
Obstructive Sleep Apnea (OSA) is a syndrome characterized by the partial or complete obstruction of the upper airways during sleep. This blockage leads to frequent awakenings to reopen the airway, disrupting sleep, causing excessive daytime sleepiness, and triggering a stress response in the body. The obstruction can also result in lowered blood oxygen levels during sleep [1], increased carbon dioxide levels, and potential damage to the cardiovascular system. OSA is also linked to a variety of health issues including stroke, high blood pressure, and even death [2; 3; 4; 5; 6]. These health problems are especially pronounced in individuals who are overweight and vary based on gender and age. The occurrence of OSA, estimated to be between 9% and 38% of the Italian population, varies widely, with a higher likelihood in older adults, men, and those who are obese [1; 7; 8]. Among older individuals, its prevalence may rise up to 84% [1]. Despite an increase in research and medical attention towards OSA in recent years, it remains a condition that is frequently not diagnosed. This underdiagnosis can be attributed to the lack of biomarkers capable of identifying the disease [9; 10; 11; 12; 13]. In 2019, CERGAS (Research Center on Health and Social Care Management at the Bocconi University) released data estimating that the annual costs associated with OSA in Italy are approximately 31 billion euros. On average, the cost for each patient with severe OSA was calculated to be around 3850 euros. Despite having an estimated 12 million people with moderate to severe OSA, only about 460,000 individuals in Italy have been formally diagnosed, and merely half of these diagnosed patients have received treatment. This situation places Italy at the bottom among major countries in terms of the number of individuals diagnosed with OSA [14]. Considering that each patient is diagnosed many years after the onset of the disease, the direct and indirect healthcare costs impose a significant burden for the National Health System (NHS), which affects every single citizen. Prevention and early diagnosis are the only ways to achieve an improved quality of life and cost containment [9; 15]. For the diagnosis of OSA, polysomnography (PSG) is considered the gold standard, and the severity of OSA is typically measured using the apnea-hypopnea index (AHI), with thresholds set at \(\geq\)5/h for OSA diagnosis, \(\geq\)15/h for moderate to severe OSA, and \(\geq\)30/h for severe OSA [1]. However, this method is expensive [9] and requires the patient to be monitored continuously by healthcare professionals [16], leading to a scarcity of available testing and, consequently, delays in diagnosis and an increase in the burden of disease [17; 18; 19]. Therefore, Home Sleep Apnea Testing (HSAT) is often used as an alternative. HSAT offers several advantages over traditional PSG. One of the foremost benefits of HSAT is the convenience it provides; patients can undergo testing in the familiar and comfortable setting of their own home. This not only reduces the anxiety and discomfort often associated with spending a night in an unfamiliar sleep lab environment, but also removes the logistical challenges of arranging for an overnight stay away from home. Furthermore, HSAT stands out for its cost-effectiveness. Generally costing less than laboratory-based PSG, it becomes a more accessible option for a broader range of patients, breaking down financial barriers to obtaining a diagnosis. Recent advancements in software technologies and Machine Learning (ML) methods have significantly enhanced the development of effective predictive and diagnostic tools, becoming increasingly prevalent in various fields of medical research and applications, including for OSA [11; 12; 13; 20; 21; 22; 23; 24; 25; 26; 27].